better sources

This commit is contained in:
WanderingPenwing 2024-09-25 14:50:53 +02:00
parent fe9035fd18
commit 4870c89787
61 changed files with 22319 additions and 1494 deletions

9
.obsidian/app.json vendored
View file

@ -1,4 +1,11 @@
{
"alwaysUpdateLinks": true,
"useMarkdownLinks": false
"useMarkdownLinks": false,
"pdfExportSettings": {
"includeName": true,
"pageSize": "Letter",
"landscape": false,
"margin": "0",
"downscalePercent": 100
}
}

View file

@ -1,6 +1,6 @@
[
"no-dupe-leaves",
"obsidian-excalidraw-plugin",
"open-in-new-tab",
"obsidian-hider"
"obsidian-hider",
"better-export-pdf"
]

59
.obsidian/graph.json vendored
View file

@ -1,22 +1,51 @@
{
"collapse-filter": true,
"collapse-filter": false,
"search": "",
"showTags": false,
"showAttachments": false,
"showAttachments": true,
"hideUnresolved": false,
"showOrphans": true,
"collapse-color-groups": true,
"colorGroups": [],
"collapse-display": true,
"showArrow": false,
"textFadeMultiplier": 0,
"nodeSizeMultiplier": 1,
"lineSizeMultiplier": 1,
"collapse-forces": true,
"centerStrength": 0.518713248970312,
"repelStrength": 10,
"collapse-color-groups": false,
"colorGroups": [
{
"query": "tag:#organisation",
"color": {
"a": 1,
"rgb": 14048348
}
},
{
"query": "tag:#description",
"color": {
"a": 1,
"rgb": 4962028
}
},
{
"query": "tag:#reunion",
"color": {
"a": 1,
"rgb": 9264342
}
},
{
"query": "tag:#archive",
"color": {
"a": 1,
"rgb": 14935011
}
}
],
"collapse-display": false,
"showArrow": true,
"textFadeMultiplier": -0.3,
"nodeSizeMultiplier": 1.29947916666667,
"lineSizeMultiplier": 1.14635416666667,
"collapse-forces": false,
"centerStrength": 0.536458333333333,
"repelStrength": 13.125,
"linkStrength": 1,
"linkDistance": 250,
"scale": 1,
"close": false
"linkDistance": 45,
"scale": 0.4444444444444444,
"close": true
}

View file

@ -0,0 +1,29 @@
{
"showTitle": true,
"maxLevel": "6",
"displayHeader": true,
"displayFooter": true,
"headerTemplate": "<div style=\"width: 100vw;font-size:10px;text-align:center;\"><span class=\"title\"></span></div>",
"footerTemplate": "<div style=\"width: 100vw;font-size:10px;text-align:center;\"><span class=\"pageNumber\"></span> / <span class=\"totalPages\"></span></div>",
"printBackground": false,
"generateTaggedPDF": false,
"displayMetadata": false,
"debug": false,
"isTimestamp": false,
"enabledCss": false,
"prevConfig": {
"pageSize": "A4",
"marginType": "1",
"showTitle": true,
"open": true,
"scale": 100,
"landscape": false,
"marginTop": "10",
"marginBottom": "10",
"marginLeft": "10",
"marginRight": "10",
"displayHeader": true,
"displayFooter": true,
"cssSnippet": "0"
}
}

21221
.obsidian/plugins/better-export-pdf/main.js vendored Normal file

File diff suppressed because one or more lines are too long

View file

@ -0,0 +1,11 @@
{
"id": "better-export-pdf",
"name": "Better Export PDF",
"version": "1.9.2",
"minAppVersion": "0.15.0",
"description": "Export your notes to PDF, support export preview, add bookmarks outline and header/footer.",
"author": "l1xnan",
"authorUrl": "https://github.com/l1xnan",
"fundingUrl": "https://www.buymeacoffee.com/l1xnan",
"isDesktopOnly": true
}

View file

@ -0,0 +1,52 @@
#better-export-pdf {
display: flex;
flex-direction: row;
height: 75vh;
}
#better-export-pdf .pdf-preview {
flex: auto;
position: relative;
display: flex;
flex-direction: column;
overflow-x: hidden;
overflow-y: scroll;
align-content: flex-start;
}
#better-export-pdf .pdf-preview .webview-wrapper {
position: relative;
height: 100%;
width: 100%;
}
#better-export-pdf .pdf-preview .print-size {
position: absolute;
right: 8px;
top: 8px;
z-index: 99;
font-size: 0.6rem;
white-space: pre-wrap;
text-align: right;
visibility: hidden;
}
#better-export-pdf .pdf-preview > div {
flex: 1;
height: 100%;
width: 100%;
}
#better-export-pdf .pdf-preview .filename {
font-size: 0.75rem;
color: var(--color-base-60);
}
#better-export-pdf .pdf-preview .filename:not(:first-child) {
padding-top: calc(var(--p-spacing));
}
#better-export-pdf webview {
flex: 1;
height: 100%;
width: 100%;
}

View file

@ -8,17 +8,7 @@
"type": "tabs",
"children": [
{
"id": "c14c79a0c144d87c",
"type": "leaf",
"state": {
"type": "excalidraw",
"state": {
"file": "organigrames/old.excalidraw"
}
}
},
{
"id": "bc371c138dcce692",
"id": "cb97d956b938e863",
"type": "leaf",
"state": {
"type": "markdown",
@ -30,14 +20,24 @@
}
},
{
"id": "11c1d64e97546e40",
"id": "411c7c01b5860cc2",
"type": "leaf",
"state": {
"type": "excalidraw",
"type": "markdown",
"state": {
"file": "organigrames/knowledge.md"
"file": "to read.md",
"mode": "source",
"source": false
}
}
},
{
"id": "180ec8c9c67d0fde",
"type": "leaf",
"state": {
"type": "graph",
"state": {}
}
}
],
"currentTab": 1
@ -69,7 +69,7 @@
"state": {
"type": "search",
"state": {
"query": "",
"query": "tag:#archived",
"matchingCase": false,
"explainSearch": false,
"collapseAll": false,
@ -90,7 +90,7 @@
}
],
"direction": "horizontal",
"width": 225.5
"width": 219.5
},
"right": {
"id": "2cadbcb31417d474",
@ -106,7 +106,7 @@
"state": {
"type": "backlink",
"state": {
"file": "to do.md",
"file": "articles/secondary/Historical_review_of_Zig-Zag_Theories.pdf",
"collapseAll": false,
"extraContext": false,
"sortOrder": "alphabetical",
@ -123,7 +123,7 @@
"state": {
"type": "outgoing-link",
"state": {
"file": "to do.md",
"file": "articles/secondary/Historical_review_of_Zig-Zag_Theories.pdf",
"linksCollapsed": false,
"unlinkedCollapsed": true
}
@ -146,7 +146,7 @@
"state": {
"type": "outline",
"state": {
"file": "to do.md"
"file": "articles/secondary/Historical_review_of_Zig-Zag_Theories.pdf"
}
}
}
@ -155,8 +155,7 @@
}
],
"direction": "horizontal",
"width": 300,
"collapsed": true
"width": 300
},
"left-ribbon": {
"hiddenItems": {
@ -169,42 +168,99 @@
"obsidian-excalidraw-plugin:Create new drawing": false
}
},
"active": "bc371c138dcce692",
"floating": {
"id": "8c412905917fe5d1",
"type": "floating",
"children": [
{
"id": "d76208ec6ab347a3",
"type": "window",
"children": [
{
"id": "d3ee03a031e2d8e1",
"type": "tabs",
"children": [
{
"id": "f67e822800ec6d63",
"type": "leaf",
"state": {
"type": "pdf",
"state": {
"file": "articles/secondary/Historical_review_of_Zig-Zag_Theories.pdf"
}
}
},
{
"id": "ec3323157a19bcb9",
"type": "leaf",
"state": {
"type": "pdf",
"state": {
"file": "articles/to read/Analysis_of_the_compressible_neo-Hookean_model.pdf"
}
}
},
{
"id": "300a718329f91c08",
"type": "leaf",
"state": {
"type": "pdf",
"state": {
"file": "articles/to read/Viscoelastic_damping_design.pdf"
}
}
}
]
}
],
"direction": "vertical",
"x": 1932,
"y": 39,
"width": 1896,
"height": 1029,
"maximize": false,
"zoom": 0
}
]
},
"active": "f67e822800ec6d63",
"lastOpenFiles": [
"organigrames/knowledge.md",
"to do.md",
"organigrames/old.excalidraw",
"ressources/Neo Hookean Behavior Law.md",
"ressources/Composite laminate models.md",
"ressources/Impact-Shock-Collision.md",
"ressources/Zig-Zag Theories.md",
"articles/Article_Taylor_and_Francis_vfinal.pdf",
"ressources/Equivalent Single Layer Theories.md",
"ressources/Hertz Law.md",
"ressources/Layerwise Theories.md",
"to read.md",
"articles/to read/Optimization_of_composite_laminate_with_viscoelastic_layer.pdf",
"ressources/Hysteresis.md",
"ressources/Viscoelasticity.md",
"ressources/PCLD.md",
"main articles descriptions.md",
"ressources/Accelerance.md",
"ressources/Finite element method.md",
"ressources/Hertz Law.md",
"ressources/Continuum Mechanics.md",
"Failure Theories.md",
"articles/Videos descriptions.md",
"ressources/Composite laminate models.md",
"ressources/Layerwise Theories.md",
"ressources/Finite element method.md",
"ressources/Equivalent Single Layer Theories.md",
"ressources/Kirchhoff's hypothesis.md",
"ressources/Inelastic Collisions.md",
"ressources/Impact-Shock-Collision.md",
"ressources/Impact Models.md",
"ressources/Accelerance.md",
"articles/secondary/Historical_review_of_Zig-Zag_Theories.pdf",
"ressources/Zig-Zag Theories.md",
"plan.md",
"unknown.md",
"secondary articles descriptions.md",
"videos.md",
"articles/to read/passive constrained layer damping.pdf",
"articles/Passive Constrained Layer Damping.pdf.md",
"linux.md",
"ressources/Newmark Time Integration.md",
"to do.md",
"reunions/17-09.md",
"articles/to read/Passive Constrained Layer Damping.pdf",
"articles/to read/viscoelastic damping design.pdf",
"articles/passive constrained layer damping.pdf",
"articles/passive constrained layer daping.pdf",
"articles/viscoelastic damping design.pdf",
"articles/Passive Constrained Layer Damping.pdf",
"articles/to read/neo-hookean model analysis.pdf",
"articles/old_description.md"
"organigrames/First theme links draft.md",
"archive.md",
"ressources/Newmark Time Integration.md",
"articles/Secondary articles descriptions.md",
"articles/Main articles descriptions.md",
"Untitled 1.canvas",
"Untitled.canvas",
"articles/secondary/PCLD_SotA.pdf",
"articles/secondary/Impact_and_vibration_of_hybrid_fiber_metal_laminates.pdf",
"articles/to read/Analysis_of_Laminated_Composites_Subjected_to_Impact.pdf",
"articles/to read/integrated-computer-technologies-in-mechanical-engineering - 2020-2021-243-255.pdf",
"articles/secondary/FEM_of_low-velocity_impact_on_composite_materials.pdf",
"articles/secondary/FEM_of_low-velocity_impact_on_composite_materials.pdf.crdownload",
"articles/secondary/Inelastic_impacts_for_composite_materials.pdf",
"articles/secondary/Inelastic_impacts_for_composite_materials.pdf.crdownload"
]
}

0
.trash/2024-09-25.md Normal file
View file

View file

@ -0,0 +1,33 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
%%
## Drawing
```compressed-json
N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebQBWbQAGGjoghH0EDihmbgBtcDBQMBKIEm4IACUACQA1ADMASX04AFlifQB1ABEARSMAdjYB4kaBzVSSyFhECtxSUjYqflLM
bmcAZgAWOIH4lcgYdYBGJOPtAZ3jgA49g4gKEnVuHgA2AE57yQRCZWkX/aFSDWZTBbhJe7MKCLADWCAAwmx8GxSBUAMTHBCYzGTUqaXDYGHKRZCDjERHI1ESaHWZhweZZKC4yD1Qj4fAAZVgYIkgg8zIgUNhCE6T0kL0h0LYcK5MB56D55XuJL+HHCuTQx3ubHp2DUR01SQhQIgxOEcEaxA1qDyAF17vVyJlLdwOEJ2fdCGSsHMUsrhGS1cxrcUp
tB4OJeECAL6QhAIYjcLaXd4Dd7xDafE2MFjsLiarXZpisTgAOU4Ym4x2r8XiA2rGw2nuY3XSUAT3HqBDC900AeIAFFgplsta3R6TUI4MRcO3E5qBjx6+9Xscl8c7iaiBwYa73fh7sjCR20F38D2TXA2F6cvkgWAClMSsan2Akvf7ffH0+3lnX84eHiD8gU/MN8FCKBEX0fQ1DnAAFa9sj3CcwyheYoAAIS9RwOGUZCDxNLJiCwskvTwtBxwI1Col
IKAAEEFiWb5cHnVBKPuIiGMWChmNYiB5m4gUgj7CgT1QM8wkKWNClDSBygkAANABNeIYGOepNAAMQAVUIDYziEegAH0AHF6jgoR3gFGZIwwdlCDkJB7jWNBnGOLYLkBMMDVQNz3g8y4eBuTcw0eYhnjQDZ4j4E1vl+f40CXAZ7hBeUX1KIVpQRJEUXRbEsSck18UJM1SXJHKqXQGkODpBkkIdNlOW5WzFUTSVhVFcLxUS9qstleVBSRJUTRVSQg2
tQswx1Al9SrI17lKi0rXyUDSkdXBnVY9iTWwn0JFwY4BRJQN1W4WTpgjF4YzjMT3OuHYNgGJI/1KHMS3zVAbnuN683LDhK01DZ3IGV5theuSWzbMSJIQXt+yHDJGTHfd7inGc5yrRdl1XHhbnmrcvV3CiUa3Nhj1YmGpJWWSyj494oBMzSjOUTB3mweo2DYBSAC19GuOCACskkqZYTRsipHA2zg2pNFzUHeOJAPuHy3NeRJAuCrzSjCiLPtOL4fj
+JlNQ+FLcLS3q4QpXKJAxAqcV7AkiWO8rKQqarasCeqTVZdl+paoaZeojqxQlE1MplZqKlao7hFVU7NW1XVZsNdLIEWy1rTtB0nQQF1iZQ0pdrl/ieFjsrxrO+9w1mRLrvD+NWOOd5gq2KKN2+4s8yrJsi1zMsK0jaskke/yBkzZtW2CDHT27WGivh4ckfw1Hp1nW6seb1d9OTLXIG3Im2JJsCybhCm56k8BQP4uA4C5deq9KdREYqIgjdxBhCAQ
CgMKd0qyWtpVCAaJ6igLAR/bAIgvZQEaO2fQXJhSALyvbQqpRIELEZLAjIv8SouyQdScgNV6TQIgVAzBcDNKNX9tHQOpCMHZCwfAqUcJOq6ximgshDC4EIL6lHXktCVgQHQdAxhlQ45jQTp9QRwjyEZAAPLJ1gHNdKQjOEwIoZwKAmkNpsh8lrVR9D1EZE0pojkhAjCRh4ComRXCMgABUsD0Tfh9CAwR6hMmkWoxh99aJcSYiELax9IA2KMfoAcZ
I/E8QCXMRiosOGGMYZEuxl0JAuw/swbAix2QKW4NcY4iQlaFEFJkpE+AlJJj2NoQCAw8mFNKEYTm+hH6vQIEIIeVMikhNEf2SuqT+wf2JCQMxFiXgqMGcQLkCA4DcH0eM1obBiAIHCbgTQwRz7nnnqUcZ+DUA0wwkiPipBlD4gABRBWSrwDulyLlJASAASgFJUBAyh3TzAqEc05PB9LUF4N835EJUC3PiA8jp8ToE8LhAoqAeZkaFwgOtTITzvSk
DIs0yAWQVlrO4NCNp9xsBEGmWgHFmzSgcA2pGYl2ohBQG3BS0gbTQWQDsALBA2AcgcjJW0BZSyyWrOhnPQRBJoWMDsZzfAaKa4tXSGy7ueKhBQgMMk2uR9C771PvyjZh4IJ0RlSKsV+FL5gGkiyNk4QzrRhANGIAA===
```
%%

0
.trash/Untitled 1.canvas Normal file
View file

1
.trash/Untitled.canvas Normal file
View file

@ -0,0 +1 @@
{}

10
archive.md Normal file
View file

@ -0,0 +1,10 @@
#archive
Here lies the work that I do not think will be useful, but could be nice to keep *just in case*
[[First theme links draft]]
First draft of the themes links of the concepts (when I knew nothing about the subject).
[[Newmark Time Integration]]
I came across it in a paper, it is a method used for differential equations.

View file

@ -1,6 +1,9 @@
# optimization of carbon-epoxy plates with a viscoelastic layer
#description
[[Article_Taylor_and_Francis_vfinal.pdf|ref]]
# optimization of carbon-epoxy plates with a viscoelastic layer
*2020*
[online ref](https://www.tandfonline.com/doi/abs/10.1080/15376494.2021.1882626)
[[Article_Taylor_and_Francis_vfinal.pdf|local ref]]
**basis of the work**
@ -10,7 +13,7 @@ This papers explore the use of [[PCLD]], its goal is to optimise the damping (of
The bridges are made by puncturing the viscoelastic layer with holes so that some of the epoxy matrix fills them.
The simulations where made using the finite element model, with 2D elements for the carbon-epoxy layers and 3D elements with a [[Neo Hookean Behavior Law|neo-hookean visco-hyper-elastic behavior law]] for the inserted layer. The simulations are accurate with the experiments.
The simulations where made using the [[Finite element method]], with 2D elements for the carbon-epoxy layers and 3D elements with a [[Neo Hookean Behavior Law|neo-hookean visco-hyper-elastic behavior law]] for the inserted layer. The simulations are accurate with the experiments.
The paper also points out an issue with the manufacturing of the bridges : the epoxy does not fill the holes fully, so there are bubbles or gaps, diminishing the properties of the material.

View file

@ -0,0 +1,187 @@
#description
# Collisions
## Hard and Soft Collisions
*webpage*
[ref](https://www.compadre.org/Physlets/mechanics/illustration8_3.cfm)
A soft [[Impact-Shock-Collision|collision]] is an inelastic collision, which means that kinetic energy
is not conserved (because internal friction). However, the momentum is still
conserved.
A perfectly inelastic collision occurs when the two bodies stays together,
and the energy is lost by bonding the two bodies.
## Inelastic impacts for composite materials
*1990*
[online ref](https://doi.org/10.1016/0263-8223(90)90025-A)
[[Inelastic_impacts_for_composite_materials.pdf|local ref]]
Use the [[Finite element method|finite element model]] to get the dynamic response.
The structure is considered elastic but the loading is considered
inelastic.
The isoparametric linear shell element is modified
to take into account the shear deformation and rotatory inertia.
[[Inelastic Collisions]] : masses added together and
momentum conserved, used for slamming or other wave-like loading
This model is reasonable when the impactor is relatively soft and the mass
of impactor is larger than the mass of the node being impacted.
## FEM of low-velocity impact on composite materials
*2011*
[online ref](https://doi.org/10.1016/j.compstruct.2010.10.003)
[[FEM_of_low-velocity_impact_on_composite_materials.pdf|local ref]]
use of ABAQUS
examination of the validity of different models
propose a benchmark method in low-velocity [[Impact Models|impact modeling]] of composite structures
---
# Background
## Machine Vibration
*2021 (info from the metadata of the PDF)*
[online ref](https://www.machinedyn.com/docs/articles/Real_Physics.pdf)
[[Real_Physics_of_Machine_Vibration.pdf|local ref]]
Very practical paper, an introduction to vibrations in engineering. It has useful definitions and explanations of the terms.
Critique of Newtonian physics ($F=ma$) and Hooke's law ($F=kx$).
Because it assumes constant masse and stiffness.
In a dynamic world, $F = mr\omega^2$.
To preserve the linearity of Newton's $2^{nd}$ law a dynamic mass is defined :
$m(\omega)$.
The reciprocal of dynamic mass is accelerance, and is also a function of frequency : Accelerance $= \frac{1}{m(\omega)} = \frac{a(\omega)}{F(\omega)}$
This paper advocate for less design and more tests because the theory is too far from the real world.
**Symmetry is bad practice because it support resonant modes**
Force is a wave that travels at the speed of sound.
(see [[Accelerance]])
---
# VEM
## Passive Constrained Layer Damping, SotA
*2019*
[online ref](https://iopscience.iop.org/article/10.1088/1757-899X/653/1/012036)
[[PCLD_SotA.pdf|local ref]]
This paper discuss the advancement of the PCLD technique used for structural vibration control. In addition to that, there are a lot of sources on the models developed.
[[Viscoelasticity|Viscoelastic materials (VEM)]] dissipate energy under a transient deformation. Used in a form of a layer that is either freely attached (UCLD ie *unconstrained layer damping*) or in a sandwich (CLD/PCLD ie *constrained layer damping/passive constrained layer damping*).
In most of the analyses, extensional/compressional strains of the viscoelastic layer are not taken into account since the damping comes mostly from the shear strain.
The mathematical models are either [[Finite element method|FE]] or analytical.
(see [[PCLD]])
## Layerwise Analyses VEM
*2016*
[online ref](https://doi.org/10.1115/1.4034023)
[[Layerwise_Analysis_VEM.pdf|local ref]]
This paper evaluates the vibrations characteristics of structures with [[Viscoelasticity|viscoelastic materials]]. The equations of motions are derived with the principle of virtual displacement (PVD) and solved with the [[Finite element method]].
This paper uses the layerwise approach to tackle the analysis.
This paper focus its study on beams.
Layerwise approach : Lagrange-like polynomial expansions have been adopted to develop the kinematic assumptions (?)
Issues of [[Viscoelasticity|viscoelastic]] layers dynamic study :
- the modeling of material properties
-> tests to characterize the material
- the solution of nonlinear complex eigenvalue problems
-> methods have been developed like the modal strain energy technique, the direct frequency response method, the iterative complex eigensolution and the asymptotic solution method
- the kinematic modeling of the structure
-> main topic of the paper
-> damping through maximizing shear => need accurate stress distribution
This paper wish to provide an alternative to the 3D modeling, preserving the numerical efficiency of 1D theories.
## Analysis of the compressible neo-Hookean model
*2023*
[online ref](https://link.springer.com/article/10.1007/s11012-022-01633-2)
[[Analysis_of_the_compressible_neo-Hookean_model.pdf|local ref]]
Analysis of the model implemented in the commercial [[Finite element method|finite element]] software ABAQUS, ANSYS and COMSOL.
Its physical limitations are explored, to underline the model's advantages and limitations.
**To further read, but not necessary at first glance for my study**
## Optimization method of composite laminates with a viscoelastic layer
*2009* #perforated_vel
[[Optimization_of_composite_laminate_with_viscoelastic_layer.pdf|local ref]]
This paper develops a method to transform a multi objective (damping and stiffness)
into a single one, to facilitate optimization.
The [[Viscoelasticity|viscoelastic]] layer is **perforated**, and the sandwich is [[Co-curing|co-cured]].
Co-curing means the viscoelastic material within the composite laminate undergo the temperature and pressure cycle needed to cure the composite material.
---
# Composite laminates
## First order Zig-Zag plate Theory
*2000*
[online ref](https://doi.org/10.1016/S0263-8223(99)00063-X)
[[First_order_Zig-Zag_plate_Theory.pdf|local ref]]
This paper develops and assess a laminated plate theory x 3D finite element, based on [[Zig-Zag Theories|first order zig zag sublaminate approximations]].
Zig Zag functions are evaluated by enforcing the continuity of the transverse shear stresses at layer interfaces.
=> accounts for discrete layers without increasing the number of degrees of freedom as the number of layers is increased.
5 degrees of freedom per node (8 nodes brick), 3 translation and 2 rotations.
full name : zig-zag in-plane displacement theories
[[Equivalent Single Layer Theories|ESL]] : the laminate is modeled as an equivalent single anisotropic layer
-> most popular : [[Equivalent Single Layer Theories#First-order Shear Deformation Theory (FSDT)|FSDT]] , but does not account for warpage of the cross section.
High-order Shear Deformation theory (HSDT)
[[Equivalent Single Layer Theories#High-order Shear Deformation theory (HSDT)|HSDT]] : it is assumed that the displacements are of higher order polynomial form and are $C^1$ continuous through the thickness. This allows for non-linear variation of displacements, strain and stresses through the thickness.
[[Equivalent Single Layer Theories|ESL]] issue : unable to account for discontinuities in transverse shear strains at interfaces between layers with different stiffness.
[[Layerwise Theories|Layerwise]] : unique displacement field per layer + interlaminar continuity of displacements (and sometimes of transverse stresses).
-> very computationally expensive, since the number of degrees of freedom increase proportionally with the number of layers.
FZZT (First Order Zig-Zag Theory) :
In-plane displacements are assumed to be layerwise linear and continuous through the thickness.
5 degrees of freedom (does not depend on the number of layers) achieved with the transverse shear stress continuity at each interface.
-> very good with symmetrical laminates
HZZT (Higher Order Zig-Zag Theories) :
FZZT + piecewise linear variation of in-plane displacement on a continuous cubic function of the transverse coordinate.
-> better displacement field for unsymmetrical laminates.
\+ homogeneous shear traction boundary conditions at the top and bottom surfaces to keep 5 degrees of freedom.
issue : the transverse deflection degree of freedom $w_0$ is required to be $C^1$ continuous. Therefor additional rotational degrees of freedom (gradients of $w_0$) are present -> more than 6 degrees of freedom -> tough to implement in commercial finite element software.
Goal : keep it accurate, $C^0$ continuous and 5 degrees of freedom
(see [[Zig-Zag Theories]])
## Historical review of Zig-Zag theories
*2003*
[online ref](https://asmedigitalcollection.asme.org/appliedmechanicsreviews/article-abstract/56/3/287/446373/Historical-review-of-Zig-Zag-theories-for)
[[Historical_review_of_Zig-Zag_Theories.pdf|local ref]]
This papers explore the history of the development of zig-zag theories, their hypothesis and use-cases. It intends as well to properly address who contributed to what.
[[Zig-Zag Theories]] are theories which describe the piecewise form of transverse stress (Zig-Zag, ZZ) and displacement fields (Interlaminar Continuity, IC).
This papers explain thoroughly the different theories developed and how they function (maybe a bit too much for what I need).

View file

@ -1,50 +1,77 @@
#description
# finite element method
# Finite element method
full notes : [[Finite element method]]
[weak formulation](https://www.youtube.com/watch?v=xZpESocdvn4) *(30min)*
### Weak Formulation
[video](https://www.youtube.com/watch?v=xZpESocdvn4) *(30min)*
The weak formulation is the formulation of the differential equation so that it becomes solvable using the finite elements method.
This video shows how the weak formulation is derived from the initial problem, and its use.
[finite element method](https://www.youtube.com/watch?v=1wSE6iQiScg) *(40min)*
### Mathematical Finite element method base
[video](https://www.youtube.com/watch?v=1wSE6iQiScg) *(40min)*
The finite element method is a mathematical method to be able to computationally solve a differential equation.
The core of the method is to discretise the problem, because computer cannot solve the problem analytically.
# continuum mechanics
# Continuum mechanics
full notes : [[Continuum Mechanics]]
[continuum mechanics](https://www.youtube.com/watch?v=rhDkluTuWlQ) *(10min)*
### Continuum mechanics
[video](https://www.youtube.com/watch?v=rhDkluTuWlQ) *(10min)*
This video goes over what is continuum mechanics, and the uses of fields to describe matter. It presents as well the boundary value problem.
[strain tensor formula](https://www.youtube.com/watch?v=X-H3Fwdm-kI) *(10min)*
### Strain tensor formula
[video](https://www.youtube.com/watch?v=X-H3Fwdm-kI) *(10min)*
The strain tensor is the symmetric part of the gradient of the displacement field vector.
This video manages to make this confusing statement a lot clearer.
[visualizing the strain tensor](https://www.youtube.com/watch?v=UQ4GnWACesY) *(10min)*
### Visualizing the strain tensor
[video](https://www.youtube.com/watch?v=UQ4GnWACesY) *(10min)*
This video makes the physical effect of each element of the tensor more apparent.
[stress and traction](https://www.youtube.com/watch?v=NtTVEzZS3Bg) *(10min)*
### Stress and traction
[video](https://www.youtube.com/watch?v=NtTVEzZS3Bg) *(10min)*
In continuum mechanics, the force over an area is not the stress, it is traction. This video helps getting a clearer understanding of the stress tensor.
# laminate analysis
# Laminate analysis
[composite materials](https://www.youtube.com/watch?v=j3rvtgqrGsQ) *(1h30)*
### Composite materials course
[video](https://www.youtube.com/watch?v=j3rvtgqrGsQ) *(1h30)*
This video is a course on the analysis of composite laminate. Mainly the maths to compute the stress/strain relationship with discrete layers.
(see [[Layerwise Theories]])
[modeling layered composite](https://www.comsol.fr/video/modeling-layered-composite-structures-with-comsol-multiphysics-nov-29-2018) *(1h)*
## Modeling layered composite
[video](https://www.comsol.fr/video/modeling-layered-composite-structures-with-comsol-multiphysics-nov-29-2018) *(1h)*
This video exposes multiple models for composite laminates, for example equivalent single layer (eql) and layerwise (lw)
(see [[Composite laminate models]])
# Failure theories
full notes : [[Failure Theories]]
### Failure theories
[video](https://www.youtube.com/watch?v=xkbQnBAOFEg) (15min)
This video presents a few failure theories, and their physical meaning :
Ductile materials :
- Tresca
- von Mises
Brittle materials :
- Coulomb-Mohr

Binary file not shown.

Binary file not shown.

View file

@ -0,0 +1,173 @@
---
excalidraw-plugin: parsed
tags:
- excalidraw
- archive
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
study of shocks
to a carbon-epoxy plate with
an inserted viscoelastic layer ^27UZMz0J
inelastic collisions ^I9y5xW57
inelastic impacts to
composite materials
(naval context) ^a6Zsyp5G
impact models for
composite structures ^JtNEDx2B
passive constrained layer damping ^V8vHzeG4
viscoelasticity ^RfgLXN72
model for impact on
fiber metal laminate
with a viscoelastic layer ^6hgiwXJq
impact analysis of
laminated composite plates ^n1hf1yIu
finite element modeling of impact
on laminated composite plates
(ABAQUS) ^KHykGchi
hard impact on
laminated composite
(recent) ^pQjM5Y0t
study of shocks ^tcohMC3g
## Element Links
27UZMz0J: https://sci-hub.se/10.1080/15376494.2021.1882626
a6Zsyp5G: https://sci-hub.se/https://doi.org/10.1016/0263-8223(90)90025-A
JtNEDx2B: https://sci-hub.se/https://doi.org/10.1016/S0263-8223(00)00138-0
V8vHzeG4: https://iopscience.iop.org/article/10.1088/1757-899X/653/1/012036/pdf
6hgiwXJq: https://sci-hub.se/https://doi.org/10.1016/j.ijmecsci.2021.106298
n1hf1yIu: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=6fc8e48508ef0e5929372f19a8b12ec23a04f607
KHykGchi: https://sci-hub.se/https://doi.org/10.1016/j.compstruct.2010.10.003
pQjM5Y0t: https://sci-hub.se/https://link.springer.com/chapter/10.1007/978-3-030-66717-7_19
%%
## Drawing
```compressed-json
N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebQBWbQAGGjoghH0EDihmbgBtcDBQMBLoeHF0XFJSNip+UsYWdi40HiSANgAWeshG1k4AOU4xbgBGdqSk0YBOCYAOAGYeiEIO
YixuCFwAKVSSyEJmABF0qARibgAzAjDlkk2KAEUABTgAK06eAHV9Z4AtR70P5HZ4IABCCzgAEk9qVLoR8PgAMqwYKbQQeWECKA1ADWCC+JHU3D4hWxeIQKJgaIkGPuyxqfkkHHCuTQo2WbDguGwahgY0my2syhpqCSy0w3AA7O0Fsl4lMkvE2kk2lLpst+Wh4p0pdopTxOotOkaFaMeO1lswcWx8QBhNj4NikTYAYlGCA9HqxEE0PNxykZawdTpd
Ehx1mY3MC2R9FCJkgFiVG5rmowV8XiowWPHiy0kCEIymk3Gmc20n3iUqlC0W7VzCwWUqtCHOJKSnWzsplSzJEEDwmhxDZqDyAF1lpdyJkoRc0BwhIiGcI1izmCPivsyogSWSAL7LTQr4gAUWCmWyI/HyyEcGIuDOc9QowN7Xib4W2bmn2WRA4uO4Bclz7J1sHxJ9rnwW4+2tKooDBVZHA4ZRuE3Up0gvKBZ02KA9EkABZO0FhQnpIEuNhsCEEckm
0do6J4NpjWmLspTmDUyUgZRcDgMY4gNI0FhNOYzVzaZe32MjCEwc5njYVYoEAxd8H3ZYsmIBC1lWFC0DQyAMKyLCnwgKFphgeJMC+KssTIiiqO4Gi5iVdo5gmLoph4dULVI/tuN42jq11OYpU6JskjmNVvPhaTiFk+TFMRFSQNCKAHX0fQ1EfWLY3nJSrSiUgoAAQWqWoC1wJ8gPwVS1mKmoKDKoyqjqn04Dky98g4goJLAcUOJ6jiJ06vrnFGJV
tBTHg0wzLMczzPqywrXNq1rBZ63iRspQGslBq3IIjwoNs0EgsJCgPQo0O3CoMERQg5CQZY+maUtJoeph+g4IYOBGdkkk/TsFjE9it0QjYJFwABpfAfUOE5gkfK4bgQO4jIAcTtMFiE0AAlABNbAABVRlxAAJQgjjogB9YdmAGH14URKlRQgOkLjyilCWIYlWjZ21KVRK6WZ9RlizXEcOT7LkeT5AVeq3YVRVl0pJTQatSS3LVUHonn7UdZ03S9T1
7r7P0wIHIRg11sN0AjDgoyqAy4wTbhOiVfNC2LBT2RdltDufAGFSlUY2PFrczaHK8OIgHgkRPPQAA0EBxin6EuO0pSEAAZZxcRgUYKCOCBtsnacEGwnLgK3INiFF1DI9gHdWkSrcj3N09zwMiOJN0g4jIsZgkWcLHtkE/DiYGSR8EuYnNHwABVTp2msyB66uprakLiSzq7vqViM0RSHoUYYA4I5cQoWfcU6P5tixsE4AANSEI3usuzY16oDit/2b
vd82CmTyOLgFGs8eAU0eMQR4hAKaSBzAAeTjsoe+owl6vzBiVD+m8i59lvPeeG7JXzvnWlmCYzYQKrAAuXKqIEKLgQRlBJGfZKLWgMIAqItcJIQGCFxbAMB8ZYCgF8cgPE0A4ifvuU69QLorxwvwn0j1ODSnVK9JogxhgVHGDqYK2ZphzWBmsUGlQM7Q2OKcX2x0GHAyMh5Wefx8JGCSLsScCJkT83RI6ekMEbT4g5lzXg2s+bUgFu41mfZhbMlZ
GMTk3JeSwBlkKZCCsJTcEWDRdUXRzSzFrO0YKmpuDOVIVua0FIQx6wkO6Q23pDz+jNhbUMOFyC22jA7ZY8ZOaJjQAsMK+o3wuWYi7NabsiwlhVtMCs0xxkTMmeMkOpQwi+xTEHWYnZ0zLDDrOTuW5o6xzYAnJOKc06Z2zrnfOG8Sg7ThCXMuqBKrLlbjXShh5jxngyB3fI5zIA4IfPMghH5iFJAKaUP8FD0DSFkPIJQzBeTOA0DoMIChRrjTCkke
F60ZSdGmJ0bQbQeCjHGnMcK9ZF6/hoWYxGk5OBQCRIQIwFQcXjSmQy6YrFyXZAAGK4HSvgDWujShnEwJ7dA1ohDEBgKgNglxUDMEkDQ5gqAAA62Q2CoFwKgPApAjwuAQK1TAoqfBfNQPGdQ8qODWFQKsMIBVzioDMJCtgQRkrmFQPgXAMAmBC0oHw/l6IoDCtFeKyV0qwKyoVVAJVKq1UatcNq3VzqzgGrUJIY1przVMEfNaw4eh7XWkdc611Lpl
h8qKkQZQLR0BiGyG65RUBzAEEKsW0t0AuQ+j0NkXAqwmBXJuRLUgRZVgEE9QK5mPqRViolVKmVxrQ3KtVVUSNWq2A6tQHquNhrE0KuTbbVNVqbWZuddm7ATqXWVr7LgIQoasbhGpRUURFjAXtuJu7YZz4sXxAkedPs0jwyyOUe9ZJzkf3NE+t9VAn5lTuWyXcfRytKj4WMbDBAeDUDmORpsEyZkLJWScQzVxtJgk+iKbzHx7S/GeIpIzIJmJbkiw
ieyKJUtYk/UVpAeWFQmMQGg7qcSpQNaym6KR3mJSrYQHKQbH0JsAxV0E/UyMTTYwtKdvguIok0yjBdixNWpQCxDIFbmH2T5RrtGmJMF8Ky+xrOHG84uHLS4VVyqE489zrl2ebk89u7U0BdW/jve4EgnivA+N8X4AIgQgnBJCGEpFl7lDfug05JQv4lB/j59AONConnaK1We+MkgIEKsoTQlw3iOFkggCmKDP2VFi5/LBW5PmIZfBaQhPAyxNh5ZA
IF8UqFblArQo6ZLGFUVDfoVhuB2HdYQNw3h/DBG+REaQMR+wEsQHItkKlNL2wsqgOyzl3KC2yIkO2vd1aD16Buu9XIDIPX7fQIdh1J3HREHOz6QtdaiwNuCJcBSVaa34FeyWnCTblgtqiO20gnbnOlGdL2k1+AB2bFu/u1VD3DjNAuyes9bAL2sHW3Np+v572PoFbi3Mb7Esfui1+r1AGFHsnGEDBob1ANqN4kaKU742dzEg+saDWxaZ3BMXDUl9
CUNg3aH8Zg8B4gozps48jbjKP8e8QpkjhSvEBKZoLKj4T1yRIltE6WjH4kilY0kjp6LckdPGf4qTZSDaVONtUyTltpONPtnJvsrTfEzFSQDRygdJpGYGX2LTHtpRteZq2fTqoVMyhmKsxk4dLN9inNZ8HFdShV0c12lzrdnmYQ2WTl+yWMAUD+BQY49BmD42cDjN4s85hvEoO0O0cAcblYp5V5qn9SJJaMql9LmXsu5fy4V4rdqyuRdQZ39e3eOK
982JIbYmB4hGFgfjZ4bwTyEE0MTdoxNcD4TBF8AYs928N2nxgxbNXSh1e+Rab82TmJJCt2Q/8C+ZByEUAoSFhBoVaG0HCqCp/koMQHJNoM6DEAiqNOMAoKqLKM4OFDwAsAABRGYACURmqo8QzghUPoPWQu0EW4TCQ2I2Y2gKE2PIU2/KM2wiqAN6TccIFKa2tKbGK2W2HKCIu2H612KwLIR2jqhA+g0SOQdBbACqegQhbArAca+gXyPaNwCqyBJq
9ABASOFa/KaB7qFAcOB2fBd2ZqQhPIIhoa4hBgrU0hCAqAshZw8hUEihyhqhwO/Cmhe2/Kf2Da5aNhciqaP27hAOPEQOFKbaLIYOtm6ekAUO/g/aPBCOx2BhwhsqJhX0ZhUhaglh1hTAVgdhHAShuAKh+AahhaLh6O56l6OOdB82t67WBO2mYwL6pORQ5O5+0A36fY8ipaKYHQ1OH0zO7IOKzkHYzE4eIMPOuAzwcGpiEE/Wlimw2wUAAwACmAPA
YIMu2GgS8uHiqu7MyuGm5IvMcuuGCulcwg1GOutGeu9GGso0bGLG9kpuz4qoAKkAGsLsbGBGOsdStuFSz8pQ4mNSxANu1sDSdsMYX2HuOxHQFYMwrEnQOo8QbE34fGW4IeT6CoemYwwk9YLkAMTx/YCe6ySeW4KeM4YRXWGeDmNGTm4RvormLy7mo4c+3mRk+Acws8lwzg+gHAjwWMkgxMFAxMhUXwMAuIRw2WPAZ+q8VWm8PeTJmwCApe5eRwle
1ete9ejeFAzereEpMWXe0pjJReRkZ4s8bAAAjieCjM/nAGCGCFCNgJIH8CjCjBTObNqWgrqYtjKQaZsH3APEPCPGPBPFPDPPPESjvBVlsFKVfvsO8hALfvpj8utG0J8EiXem/hIEAeCt/lCjCgAQgAoBmV/qAYQOAaQJATRNAe0AoEiHAQsAgQxCgZMGgcZrWM4CkMSmBAQVURAMQSwg+KNjpJHFwpQQOjQdwPQR6cnkwVehtpOWyhwVytwOHoWv
DoYdgFAFYWwOsFBEhs6KYZIRYZKqImuSIOEFoToTdqueufoJuUELKuRKQHueYWkYefNseYEGjluC9vWt6QZMeluI0MdrWt+eGIDowkEaDmnmSRET2lEbDjEZeRuVuXebuckfuc+UUkIG+aeUKBjljtObjl2X+AgA+rUeyPUfFpIk0ZKc1N0WMGJJzm0Yzqol9OosqFKGFOtDolzgYlsI8BMYLlMcLn2MXv3hlmwFljlnlgVkVoQCVhPsnrLjhoKn
hv4kRiSP4gccpUceSUyI5jMhEfrgxg8TcQkibn2NBmxdoC5CFPWBxaph2BbprLporggICcJnbj8ZAH8U7p8UCTJm7mCVuJ7sRsFGMkgQxOFFMC+GzoMqHl7FxgIJHhiTiimMJM5aHPiRZh5jGcSTZp1rcquJSbpFPjwAwV5bSfnoSTfneF8vGY1h+J8DKGxh1g8tQh2YJYQbMvlPBIhFpGQXpG5oZKhqZOZJZFKNZMtrZCOK2ViiaKtI2Eys5IsJ
mPTqUFxLQatZJNFFlAKpVGVRgGsBpEhNpKgMVfpNkFclsGLhLnAFLhNeREwvZONB5GJDMEgeMi7OtOaN5OtckpFFJDJG1LtUpPtUdqlOlDIIDXFK1arnBLVKVCEKSdVMQPDfVIjTqevMsK1PJAXmAJ5vsExiUEkANKRPjSUM4KFeiuFZNG0CmNWG1uTapgsFtNGapPgPtJ2Q0VIh3hGTRYxSoqWhaK7Pze9EBqxbMOxXNcMVBm/FjPxQhp2SLmWi
YL6cPJ0KPOPJPNPHPAvKsS4usYcZsV1dsW0upS5ZpczCpfZrpZSfpRAJLDElcYKCeqZU9TMPigaEZmWOMgDE2LidBhiu0FZeMFMFmAxC+GmI5cQuNC+L9KxOFOqDqNbs7l8aJlUqbD5aUn5a7qCY7KbWgGxFirKLMKNLMP8v9LFU+l0LREzfiqphMGFJaDBElX0QxClRovHoOASdlVZiSfldbYVWcadXXB3qVROTnmsHnq8j3dgjVfVgmTmB2IaP
jmmVSVBZwiSh1V2bBAVEdX1QORwudUNeGHhIRMRPdVNU9ZmKNJ8LWAxH0i5E3Rwr9WgKMpmOikymxMFJ0jirsVtVDdlGvftWpHvchP1ddHScfegHMQsUcEsSsZFJfWgDRB0GFMJDKIHLqGJLCU8ZxLNs+LiqqCaDimzp0gvIJP9dtUDZ1qDclODRlAA8DdSTvUVOgg1P3btDVGw+jW6ZjX2NjfSWTWTT1JFsTRJO8njX1IXRaADO0KXSQhXcNNXX
IyFHXQvJMC5CzWcmzRzVvVzVRRjXUCLU9OyNkrie0WLWMOxYaHRNmHbSMW/EiPLYhshsJXvNgAfEfCfGfBfFfDfHfI/J5ctopQbVpUbXsUrvnSrsbfsUpZbdpZAGEnpXRo7XEi7cbnceZWMEHHKM1h2ADB2MQ3Hn2BrDWHEFmMFFmOigsJmL9Mnb5e5d8WJo7seG5TbCCc0uCVEzMHKOxTohMDopmKxNmJXQKoXR2D0+tEaNmDmAxYUi3Q8TUw1s
/glXiV3VlaODlZckjQPdXEVSPefmPRRcbBVdPZszeHPXfm+L8iHbiS1Wve2b1khtMV1XBKAydWdYNZdWjBjNjHjITCTGTJTNTHzpHA9XZMg1ZZNOiiFKqIaGJM1gzT5LQUHYi4aOaJ2DqHI2+JQ4wzQ+PehIdb1WAwfbtF80ZFjJcMoBnHHAMAaBfY9ZC++IaP8kgf8gqJNKtD9fg3M0SQDTFNQ5QrQ9aPQ5DQK9DQ854nDdw+VBw4SyjTK41LFl
jUDbjcI4Tf1OI6TX1D0/qM/u+Pq0M2mAleTeM52GJFM8a7M1o2ADGXtLUJzcc4XryjzcubRdqBQ8Y8xcBlmGWBy8LXotzm/PjM44rW45sPfHMPQMTDSijJ0HrRbZri5WpdzObXE0m8cTbUPXbQ7QbsZUboklk+yDmHbS8aNPU1nY02nQ7hna0yndnR0+7kFcrjmEHSFLMEyvVelZpoTiSOHnMk+I2C7GzoM53beN3ec8nts3K4kxSUPdnr8ac4I/
qRwsXvvIfMfKfOfJfNfLfA/E/K6RfnFmAAlo0V6RIH8JgCeHaPfBnJIMoFjFjBTODPQNoRTDonHJ0KNpPuGe/Me6e/PhIF8MQM4HHHAMTLPLPNgJcJcCeDjEiCKiKc8DALBj+zzX+9VqzbPbglc01pxY5CvcClIB/pmewHILyFkGINoGRyWTEHBOYMEPCuWWg/CmzlKAgeMnHAoB+PCrAeaL9JWXeJcHgZvXQp1ZAD2cNn2eA0OTwiOUImOZUftW
wcwTOUSRSttpwYua4YOtyOuIQIwGoUUsEVarmkwKgPeEIX1ZdtoTwXp6wIZy2sZ+2sQIenmhZxynANZ9wW4cBegB9oFQzgVL4X542gEWBa2hBTs1uJEX2nBV6hIPZwZ5YU5xGC525+Z5Z152AzhaUdjtepUSvcRb22RSTk62ey680W6166WmBt0ZY8W1WMXeMriQ42DKfvzvBi4y8z3JsJS9S7S/S1hvrRrlbVsYRjsRpem2NzpacWLCk3m9cQW2
ZVuNBl+OHjxqZuNx8ZWyJobM07W63G08CbJoF5AMFWMLWFZeMgSoMY5LqKM32+idqGzh0PRHbeZleFs6ntFzpYPSOAu+VbnoNbjYB+gMB6B+B5B9B7B/B4hyCCh4e7zTPnqdvOe+gOu141u747uwEwe2h80Rh6j15ujxAJe9e7e/e4+8+6+/jO+/EJ+9+2Geh5GfFtfh8pc3Vdc8qJmIJOHvc4Dxve1WJ12ZJ6QaS+QZNvJ/g+OeVzZKtvhbwKwR
p/OVwZ+TwTunavwakzZ+eQwBmlr3dtLDp34RIAF94cF+4Kb9bKBUQeBSEZBZyDBXF3r5r1msdsbyUZjmUQV3jq/sV6Rc+mVye5RZ+Sz3zf+UxR0f0vV70X7PinIwZqtbwUG2DPfKG1vUrWT1eze3ew+0+y+2+x+1+wm9Nwk0Oibb4rsRX7E6E/E+ExAEk7bQt0ZUt+k4W6t2MAvKMqxGFBtOxc/gxI5SQhW0Jnt/bs3C00d/W9ACdwFXnb4qMjMO
MEaNMEgUHLmN+I96Y0/bMgs/ZTKEM5+GO4njPUSdOzDX93s0PcVRVkcyHyc8D5A19xczh1z3h1M/z+QjO0L08647DbvWJYfNI4R9S6v1xpZ0txSiDRlmKCxSqgskUzT8M5H44mtkWf1MFvyx2r4s5eB1dSEAPAagCjIkbaNrG3jbQCIWsAqKuqFmYdhv6NTM0NyxRa4txWgDPagS3ax0MDAENTKIK0lYADWGdUdhpfz0hcNBBPDI9iqxxodQJI6r
URiTSGjdQl+zELoGxHX7hR4SKZfYCNDog2s7W7NB1no3K7c0qurRSPgLTyQuRY+LFZ2GFCNAaNVmbXSoH8Az4i8s+7Qe9oQAoBxxtgJpUvnXwzYxNImVfKbv4Jm6zss283C4qk0Nzt8VuSsbJuxUcozBk+7xVyjP3H5BNvKdbBpu01O4L9iMSBTFEykWrOQcGv0b6sHhK6oAYqzdX2G0B0SgYtEJ/CdteCnY/cf+meSkoLxbiT0Qe0gknqu2ZKsl
2SnJbkryX5KClhSopVUEjyJ7sCKuMxIDiBzA4QcoOMHODghymHIdUOzPQnqzxPbs9YynPKxvVXWhYkawhHd/GCi/w/4/8sKPMgWRAJgEICTHRFDATeDUc3gmQbAD/jgF0oDMzWOYCJ2F59YhKRBQbL2TYQS92sFBOTtNgU4EVlOU5com0E2yacFy2oHTpsGvJbkdypAeIkYTFQcBjU8ITQOZ0yBRACizqdKCajjQKpV006N3trwy75pQkV2BLugB
xFBA8RBItckSJJHb5yRCGVQtSL7R0iOADIlVEyP0JmdWR6vXzm9h/IVo5RQXQCr9lC6hpwudvSLg71+7QVoc0RDkRAC5EFF7yvI9cpwAFFkj8RFIkURwVpGWF6RCaRkQb3d45oj0Ko5jLhR96Kc/e3WGonFSD6vojBBjXhkYzMG/p2QU0KwcBlUyaIXIzWexjLTBiaAXBoI8Tr/DN7DCOSXJHknyQFJCkRSYpPwaN3L6pCU20TCJurgowN8m+2bF
vk7RMoZNkG9xCaHEGfwl1cwFoEdht24C+1R++sJpunQkzZDK2uQ+fvJm6ZIFaITYQSG3TYghQkC2/B4riQHa8ROk8QMSPWGT6fcqqZEC/nwKv6OZb+o9faj0LbjP89xRwt/icO56rRJoOSV/MCkF74FM+UrQAZpBJbD1D65LWYvMUWLLEGWFAmagxA6ATIugGKZUH9CRYv1qhzArAUK3YG4D3mBA38RIHcGqAvBPgoCdNRQZl1PwHQU0IHD6a4M0
BfReCbwLYE4CwaXAhhiwKYbr0WGqNIQYeJEEKsxBsrMMS1FVb9CSgsgvqGIyw4yCdW047sHOIioYocwJrMACNH+S6CdGBgkXvozD57CI+QXSMc+GWQxj1EbdDsBoIcHJjKg2ANMc8zBGlBi8EPFYdD3WFw8thiPYbomzCE18ghBQkIaWNrEnFtckQmLoZUbHLdMmnfL2JmHGj+xGqs4zsI5Rj4uU3KGQg7iOOn45C5+udScb4mrDJBQMbdOiJmBU
zLjzQiQUCV2LCjNYh2vLRKt8mNA4pNxuJXcWfwuTtDhBjfOdhuAOa0ozxS7HIFeLjK3jCE94oKJoM4Tf8Gpr41we+J6qfjgBP4yBpdWIExsEAcbHCdwBmr/JRoNTFQSv2EiLBGBzsCiRKyokP9OGeA8aahKmlGQMJng7wb4PIG4SKwCoIzBUzYgWscUW/SOLBKDrVgmUWDWOllJNA7TWBINJCTRLSh0SEJrEodNKw4l6jcBzE8Qcj3DGlABGHUjz
AoIkgatBJ2jZGVoLSnlDlQDELKfCRTCRYRouYLFNijAzhQxIgkOYPJL7D2sDohg/aQsKnywyLeGk9MEuJq4NdeATKV8I5AMmp9KgISYGALgVpvjFhIKJfCvjXwb4t8O+PfAfiPwn4SxNYwWYEIJCTc02oQ8vnWO8mQ5fJanUoLcRbFFtUAsJfKe9KDgTBDQfUxyrWFKnOS0hDTWKcOP+LHd/KyUrpl7iDo3dxgsjWsOmHDwokBUGKGOk9M+obTjW
z3AhoQmSFBRmhGzVoef3qmgzOhN/FqbuCQnnip6gjGMl1MUx3jyG3sJ8T/2Gnpjt63VFCdCIgaYRLquAa6pLmlxXS3aa/TMPC1WipgEWu/NavgwJkYCqGu0/6TgJAb4DK5hAzYBwFGCSBLgR8KEEIAWmQtJo1xSYDog5w6Ig4ME/BqRKih4tEJ1EzgUDLFYgzBeTExVj/zUjQzOJEg/hjxKRnCTuoqM+QbfIkjaDtA3s4urKCmgM0ZJwciaEHDDn
wljW1MslroyUkhiVJV0arhGJMaoAqwdtCxnHwGYWtoS3FUYkExhiTERpYsiAOPMnnTzZ5Dksvg33LHqztu1YjYirPCFzddcPky4vrOYyu0jZgU58IZkcqGh+2auGKR5TikuyZ+4492c2yiYWglM6oNnOQxciBxk+gcxcm8X37phGw2SGBXHJf5tC+6DUlOQDwhxA9ehl4m+QMMwWL5l8q+dfJvm3y7598h+Y/B112HUUUeUZdGbVmOF5yepBc5qo
NJBQkcv8MScIK2FICYBqO1obQHICEDaBzgQgBQKAUoiYQAA/IEC87EAAAvDEtGAAAyFeHEqE5JKiycS9oJcGwBzAEApoMKAgEuA5ZNxxUg0FPOmC4A5gmgc0AgGwBIFcAHYS4CQmBF/8eu3ZCEVJyhHfjxsUveETLyU5ISVOivVEbOXYI7ZtOPnQdIIWELKoYcMAVgLKnFQKpRRDo1zhISfJxpl02FNkbZyNEzLCR1gAgAssOCjoVl9o2qkjjQpb
LY0Oy+UUWkVESBPCf5VUSF0eU28tRpQYHCZ1CI/9YuMOPXgcr5FHKuUiys5RwFWWXKNlqRG5V8g/IGzvR+XX0YRQDFPpicwYhmcYPAWmD1JUC+mtpLor9Fvw5M5BW/GE6dd0FpcrPuDGJjCkUYdpQgErLIX4Y1cFY6vqkMclazPJyTKIYt2dpyx6FYoe4oZk7kQANYjEAcanX27OzM6QmXhZ034W+JW240TcXRDSRBQA5VQmofM3mRiRPa9EaqZl
SUWJyVFycpqT/0zl9CdFzrTBfKTLwV4q8NeOvA3ibwt428BPaxZfjZ5CTqqN4xxW+CQIjs7mri4jtcIhTZl/8gBdxU8OLIvCoCUwSsh8I2UYU1ycA+NckF+itKw24I5hF0v7I9LJew5fpbQVl4Mz5elKEZcrznITLMRUyzYPCA4DPkj6iFIIFpFHTmjjUloyFWmmhUHltlzARQoVDBCFRHgs8JEMUUrjsjB0DaptYNRbV/hlA7aoFeuQVRdqLlPa
lIn2tuUDqciQ6kdWOonW8p+E1vbsr+U9EMAfCVvDUbby+X28O0kM/5YaOnWrBZ1kDedW2v9TLrO1xI7tVal7XPl+1g64daOvHU+hT0eXRXjeiK4kVAx6K5SZV09UsyoFMwQuZAu9bqJOwD4lRq10MlbASIwlYWd1zMm9cJAdqxUsqSdVqlXVWpfBZrMIWsriFqszlR5IiFULdZNCmIQKubFCrjZK0viHGPVBBRipRoG2cxFoj1hOwzkORlWEmiir
UhHCocTW3im1IxxSUhVaUAu7ahywAzWwSy0WCrQ7Zkin6HqHoiSaXI6YA0JYNqFPh0kCoT8OzIyrrNjVdU01YLzUXgM7+bUp/pVVqkc8/Vz4BekmWXpFyhponKlaNIrkFqBqJ0v8bA3gZzzUAM1R/BFXYorS0whmVAbBPLAbR4Sn4WsI1WzBIst59E7AWWuQnDyotVcgyJdRpV0qGVCWmap8HGBBRawGKWgazi2nnEOExWw+QPLK2AzuB280GcfI
hmnzRBCNC+czMkHLtH5BNOQVqwxnk14StEZ/Lppdj6b/0w0UaCZok3NbpNlm9oIAvQj6C6ZICzFaGOtg4regUfRcsyg5lx8cUaDWEtttJVgxEwFKgShgvMlGQ4AjwN4PhHiA4wkgZ3YJmsXcnkL7ZbKtycrKFjcrm+vK1vvyoNmCq2M0Gd+TbLRLRT0hnCmVaOLlVqam2Gm5XChpfmCbzQ9YNUHU0qGB9tVe/eZM/mChBRDMO4o1VeNyqO9dmWeD
RTSW81nMyaYPCAEaVNLmlLS1pW0vaUdLOkuAHqwxv+0OG5yAtpwnMDC1Wb3NQ1wBLMr/hzJRqw1CgIFAATgA9pkITAXQAYAUB2luINhV4dcSlAKBP6zgWsr9CSDOA1VL4CmhTBmBZrRZXyzpeL0q2ycqCAiBERUQWw4DhlKIqteMq061r7lC+KoK5y/WWjzlNIqFZurSKKFAgnhQ9YkynVx7SACehCknohXrq/1aes4BnrqUGRs9LRBUf9ieVnqL
eaok9ZqObR3rflDUx9fF0HSSB49Haovb+vWVl6EAFerPWBsRWQbCu/vGDWivIrnawFsu91tUIgz3brBaACYKijylJj+ZWwRlR9pFlfaSN6AIXWaQtLTArSNpO0g6SdIulaN4OllZX1ckay79WuHldQuiH5tYhAU+IT9BxSRTpxfPasNZWCgeRJV6AJ2Upu4WJS3Z6m87sTru3Ikqhn4PFB5GEhe015P06zbxCwJLJYSiitnQeLc3mrK5nmjOe1Oc
1+baq3Uj8LmDymXDQtII0yRmJYaRbPmMWiQDAwAkIMwWSDRLTREXGctiGwirKZlvwadz/6JWneWVqHlHSR5aE9AL9v+2A7gdDWmiKJC6CmhWFswcmZoLwa0EEUqoKYC1venNYlqv0hicKxSi0SD5lE7nSNom2Qyz5J8ridNsRkMlZtRNebT6r4lbb4DT8pAxv1Yibjn86BzoEdoGrALS58GqLCYKpw1cBQ1fOBavqX1dBgo4yaWtvtwAAQ99RGjM
cXlwhsACIREfDXyzB0w7VKjGqscxoh3ay2NBlDjR/q40d9v91Qg0FigH6e1QodNKOuWyx2OycdEB2VS7kbYg7NNz4TcTdL9aYaqp1zZcd2zKlPhEBcjZiIaqc34Gk5hBu5F0O52WrtFbh3Rd9oeAvB3gnwH4P8EBDAhQQEIaELMP2EAdZSTylWoPDVoa1Ay2tEMjcfdJy8FhBxiQP/EATAJQE4CSBNAjgQIIkEHxmxd6rsW+rKD/q9aIJEwJ0HQZ
Jcxg6L193SdK5Ae6XiWsGVh7kRLBNEar0mWx7aQw6P1GOkDS4h4VOevZYOiFQjp/U46INM9mPWhdnl56gCm8rr0fLW9Oo+9X8ud4AqeC9J8kwGhlRj6IN5RKDVPqqFwbQFCGhfXEe1Dh5EjsYx+jWGfyyhXtlQKGNkezU/H0AfxoBCAjAQQIoEMCHgPAkQTIJb9ZR5NhUftlVHYdrGrrexvf1t9GjcQyAAHQBi0RN+19Jet+GT48ZlQtENrUMR6b
fhVm8m7HYpsn6HcVN+O6A4TtgNRMawfp+EgGc+BBn+pRmlcWGZdgRn6KIUSOZ8EWqx5VmNUydiaryqqKiDlWkgzgJ2M+bqzMJ+ekrqrDopRVAvbnSif/6vMPxx1Y6dXNRjoxMYuMAmETFJjkx2gVMdcKC2608G8JJh3UO/IJRf0/6ZEh4toEbA5g2cHkBUL9B1A6Hgmfcv6QlCQnSGhzshtg9bFPpFGEtKDdMD0nVBBxrK74HFi9O7mE1TzQ2vaU
tgG3AybDzDbqufIcPja0ak2v9i4bVYCTPD0J7w91Appyg1owkLMIGZhaEzttBZ4I763y3M1xGhw2mY6wOG2t+AWwOAHABRBfIxs0AAsJkE2DFoSw9QfXvKTBBT9EzboGDtxfJWFAOl1QarWcH0AohiksZ6tj7oEsXUhL7FhMwCR4UE7Au/F0ElCCEusoQmz+vi5REktYQhLIlibgIpYtaXlLultXE6cMsiBjLGQLGHDvrGaWLLgljILAj1mcaJO9
lqSxkFZQq8a10C8y9pZUseX8T+spSw5f0ADoT15vXy5ZeEugWnDh44K+5f0AngILLEqbXZb8tCXUa+MHmlXFhDMwPGD2OOItOzB4TldPYHRCywBR5WagiINvMqZ3MfSpgjYbFF0B5QQAjAbAAwGQQYAEAD2kLYSNUypnld4rOlqy/WcamtxcrgYEgKp1aCKw8S01s4LQVatTXiA+EG8kldwAzx9T81uS75QuhghHQe8fLLgGQIkNqAvAF8OdbOuw
D4g1ei9MoEXBVBNgpZP0Kdc6RXX3rvAT6zRFuunIv4w1vS/iCcvVpOA6i9PMthLgXp9ERuiaYS02vBAnw0pogkQBxN+jSgJqBiwRU5BnoiKyKhovbU0BvA6lOQJECajgBrX1gG1ra97q2Brlku+MDq1DAl5MywgwQOmwoiBydKsr5+F8WFtRO/hkohUOm4wAZuOhsBe4cAFvFB2nkdIEtvcEAA==
```
%%

View file

@ -0,0 +1,145 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
x ^nC08p2Ha
z ^b0bUYAoW
A ^cNzsewAD
A' ^FAPf2i6B
A ^1UqNmzTk
A' ^IkWnryBa
geometric midplane ^4ETCitlj
(a) Undeformed ^YxHRA4dE
(b) Deformed ^UMONNFg8
%%
## Drawing
```compressed-json
N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebQBWbQAGGjoghH0EDihmbgBtcDBQMBLoeHF0XFJSNip+UsYWdi40AEYAZiT6yEbWTgA5TjFudoA2HnjxgE52gHZuiEIOYixu
CFwUhcJmABF0qARibgAzAjCto4kADQBRAEl6QIBlABViZgBFVrgAWQBhP48Cj4foAdVSJUgx0I+HwT1gwTWgg8ENKzCgNQA1ghQSR1Nw+IUBBi2Nj4TBERJkSRUZAan5JBxwrk2gs2HBcNg1DBuK0kl0iesOMpKagBZCIJhuM52jw4rN4gseWgACwq7QTWYADlaEwW6KxCD+bHwbFIawAxK0prNWtgeLSIJpOZjlPTlsbTeaJBjrMwOYFso6KHjJ
NxRgtJAhCMppNwVUl2vqEIcRvF4irZklRorBW7hHA7u98gBdBbHciZIvcDhCWELd3EJnMFmoYoS2CIAlEgC+C00wmWN2CmWyrbyZcFQjgxFwB0uqFasx4WdmoymU1GWvi4tKRA4mJrdfwC1N2GxC9O+HOgvRVSgACElo5hUf64KssQn8slso3yfBXwUIoGNfR9DUecAAU2CWKB/31KJSCgABBapaijXAF1rd8JU/VCagoDCF3WNC6kFOAYLHfIiT
AApIRKXdISSGjJ3ouj6OcCMaLAZwE3aFiiVY0oggHChUzQK8wkKPtCnbSBOwqEiCMdXpmm4KZCQlVSBiGCp0yXWYVRtLZllWCRcFaR1tj2YJ5xOM4EAuNYXk0GBIJeZR2gAaVmZwACs2CeYgAHF+kwGBMR+J5HWhWFyVFCBqSOBDDVxYh8TQTS0RJMkEUUpLHXpWNm1bVo2Q5LlYF5fkFmsEUKkYyVpXaG1tAVJVpVaUZWjalUeFaLV2tvHKjRNM
1LWtW17UdZ1z3zIQPTG710F9Dh/SqLI4IWEN0rDNB4hayNo1jOC0HmW8UwXcY5VaHd2jKvN6ULYs0AnctKwQas0GwgCJUbEruDk+Tym7SEZIlAcFuIYcMk28chMgadZzstpl1XLN+QGriJX3Q9vuPU82HPcTUEkxzhvvb8Xz/fGcOE5Yqd/QGaIwEdNq+9AOD+JItTgHgAAlcFpKEiaEUrtBVToJm3doxhXHg5e6SBlFwOBqqViBoUwQ5oNg/9e1
PYDQPAmQdco07UB+hD73w9CQiwgmP2WW3CPttYqmUhYKNg8caPYpilbAZj6IR2juIOqZA+cWYBMhBHWdEkmyek+o5LKLsJH3JAFm0lpUFGFUc6YPoOEGDhhjadoVVurMFaTQVnzMyoHS2XZ9iThynIkBBkMkUZkKSSCAE1Zj+BBuvoTBINaTA/JuIXyxhOE8qRE0aRS0kcVDAkN9yil8rX5LBSKxlmV5crOW5arGrq0VGqlNBnGltrcwlZVUBlbN
ev6wbX+yw1PTjQkFaBArRQHZ0FLNV0jZAHLWgOQNaAZNrBm3pldMR0YxxjQPXCUYQSaTSmDuLcswcGlHms9eG71cBVgdnTOkg4mxnzQEDdOFQeAG0gQwmGo4cilgWEjOc+C0ZJDXCqQass/6QFxvBQCRMLz2WvOTXBiFHzPiZrTX69MvxqNfBow26JjYQTNnrPRFMkIuyIjI3CztSKWNMRKb2VFXp+24oxBiLElb+xKBMSRJQZSxxKCWFOslBQKT
WFnFSxc1JoC1IXQUucy4V0XCqUYa4eBbgehKRuD9KjtCsm3WyHdFFd3QLMB8EwbjKFmPzBAAB9doRgfg/D2GaKYAAZG4MUl7xQPiiXeW9do72GoaHpq8+nH2EMVJhi4L6VXfnyG+wo74LByU/HcL8OqP3aIkQyP8hrKIAUtCa4CwEzRdPNRaXo1irXWoGLagodoZV4Ps0oUZMEWzibgy6IweBTH5KMHMCxyFFkoYKCs1DPq0M0fQqGANmEszCZlD
hEMuFsycagN6U4ZyCIXEuFcIiC42hSVqU8Sw8aW0djjORRSbzKMpjommFK6EYAZgyqxe4jYGBNlBc27LiQ21sW7exWiLFCqZdCiAjjeHOLYq4wOwc46eO4iuXxPEVQBLAEEko4MiihJBpnJYECtJRM4ASLUkd4kmtLrpXkRl4j9UIZLEyKwcnrFGPkmyCAUak07g3Yi+AYA3DgO0AAqscegtT9BPFqR8fmAAtD4VxsQvAAPJdLiivKkh9HQGk3ml
J5WViQjMzegAqDZJmnxbOfQU7JL5VTaDVQUt8GorOahswU79P5TG/gNF5RbN6wOOWA05/ZzkwKOT6BBtzkHbVQbwElgo3knQJIZZMJMq72vXOuIFT0QV8LBR9DmVsJmwumSwxFvBkWlEhkONF0qMXxwEd6vFq4cxV2zAunGZK+UQDPPIiSvq6VIUZro8VCxPwgcZcenGnKwJGOILrIMwr+XmMFZhH9eE0NQq9ubX2sr6JB3lR4lxBG3FgBasR/D9
ELUEYzJRyEXiwDnQIwqejJRGM8DI4QtjYcWOB1aB0HjjHbr8clkJ7iT9+PdXEwRga/HtQyfosx+i/V1UhyVQRngnyVM8C1IpyE6TA4rjU3HQSwSShpwvb+w1kSmimuwaMRqCSbXYL5HMRz5rnVN3WLMD17dLyAdKDSCQUxnCYlqaMO4+A/gACUKDMAAGqtBi0IHYHxQEPksovDN+8xnr2GXmudhbEojVGVm8Zf0K1wpmTWiqV8G2LPqtwe+0p0lJ
G0JuRzYj1y6niFMT9pRO2dFGNodoWokjpO6rLFJvzJElcOVc4Bw7wFnLmuOxbK0p1IKDLOwZmUBuQCXVg55pCBDfMrpMJIbmpiZLIbul6D6qE0J/f9M9CL9WXrBv2VFsN0WYolE+oR+K1wZgkcV6RyHf3UoC8Usxqifygeg1oyDP6gIGK5fBxDFskcoZQlhjDNiCJ2LA+RXD1EqMB1cfpvxNH6Jjep4R8O/F1MkY4oWkohkGcCcDlMEzgSNNs/47
qBn2N6KtD6gz5w3PuJdQVfz1nkJaeQgMpL9nYB+rM8VQrkoInlUri58pgzJCNVarADqyzH3oBYHucauzec+pFzt4kio4u+vxF1FqPUDdTKutwFqPzhSYe0qC8RLmPM+aC3TcvXL5X8sHMK3t3g/SyuluzeWhk1XbuQFrXM6+tUlktsFDk3UPUvdv06vELUPbf79MHUtm0doW6QLHQwuvm2/TbZt6UR5e1eCl7XPyJINoczjDm0dj5c28G4o0gmSW
GlDcQGBQ9/7pRwXPch69qtkOb3QzvXhyEQNIDBfQC5NyHlvK+QCkFUK4VIrRUDqw92pEIA0R7IJfh2Ln3CNmBjK7WpRdSLfqQ5/o0pKKr6cBQBPCEBGAVBjDlgQEABi1CMI78c2BwmAFsTUDYlALw1uawUoCw6BKERAygecv6CAxwXePQTAUA5gBAyEJBZBUA7Ijoeg2QuAhqpAR6lKpQZoMYSwBAuBGB+BjouAQgzBMW4Q0BFQGIQgYBgBTINS7
yvIGo8Q5muqHYluRBtmJcvI2yjuJczu4YsS4u/U263uLq7sUwAeXqoBJSToSQmgIaQ8yEbA4I2W0eCUZaBW2I+avexWuae8XhaeJ6UyW+NWEoOe9Wi4jaEozazWraWynuo2Wo42/IYinuOoZeg2zU4wGofUvak+I0beEAVoDe00o6a2reE67eiCG0O2DyRWWeUgx0x2Kok+52yS8ssoaozRS+oKEoa+kKL2DC1WOOToP2PCAxpQgOuK3+64m424j
UEOJOVKxMQe8hmsEBUBMBIwABWx2QSB4EAa3AaBeBEgRghUOB5x6AlxhB1uDBMYZBwQlBtmtB7gjxpB1yLBCwbBUQnB3BzKfB/gghNxEAdxTa4hbAkhrAuxaAshmxWcShy6bQqh6hFuGc6AESBh0SqATqlqTuLmvAV2OYG4aoC+2S7syENh3qZM9hhAlSMAtSyEIakgD42Q+AfkXkzAmIWoMA/MAAjoeB4SnolCEfHr4UVsniWmKRVqUCfJnrMtE
Qsvnk1mgC1o/FpiNn2hAJ2uNtXjqYEaNBtqUctiOs3lUVDCUTcp3igonpNhgiiagB0STJxhuL8gJt1DugWHuq9PHEMYCRKpvq2Oeh9uwl9pwlDNwnDPugDp/kDq+n1j/rLKSgeKjtDgosHrjijpDhBmysAbBtysYkhqsdlAKkTmKuMZhhWehpDlKvvuxnKlTizhTt4gClHGoSHGZtqqnHqpidZkyDobidXDiTpOXBUFqLKOmCQhST7u7A+DSXYX6
msG4cFB8JiDFkPGwHcAAFICkxZwCaA7l3AqjKB7lZZgrdIyneESkDIFrSkx6p5ykwphGlRKn1oxGNbLJF6taObtrl6andQGlFELZALoAgLLarbQLVEmk2n1FUEQA94EjoKLqtEWz7FT68gzApIzBJCZjenTi+mPYHoQqBnp7LDVahmYnhk9mRm3q/b3or6IzxlzHA4AqJhJDu6pnkrjEgEbHWzAb5mlmQB5kI5QY8FSKFmY68qQ53ioY1nYZOzEC
iq1nCWSpk4yoMZNmkYM4+JRyjAm7ol9mKTYkEm6FnRzbObjnxg/5qixIkJea+5/CLn8XLkSCOYpoqhPCzA3DITECzAxa1L4C1I8AvBCBDyQRiRR6ik3n/wJ73k+EIAxXinylVbTLNFREfkqlNoF4JE/mPwdDyhzZDaV7AW141GlEICJgdAXkQwt5WkVVwV3J2lPJK4tHKGqj9RrqsW2gtRZinaL73bTFQiHqKWVanrhFUVsJXqQA77Rl/aPosW8j
zFbiDTbjcXpnrGZmbFyXw7UwE7aJiWo5SWmwIYyVqW7UqVjUir451kaUYra6M46UtlaUEZK4lAFGGW0UWbGVrCBDYBRC5Wjl5wKzA1GFtDWj8j9YiIDWUnmQ7AuXbX2FtIIGBqjBCBtJGBGDBQppsACk7CYAPj9BJB3D9B5IinXkpX9qSn2kPnBHPkQAKnpXvnzKxGlDxHqmJEfyFX/k5GamzDdq7KFHlUmkWhVX3T3RQUXLEDWlbbwUtW95LiOn
Hbi7dXcC2ipK3TWgDX9Gxmr6jUjETUhnvaYma5m7fZRl7563MXIwJkEpbo8z7ErG8UZkAaKJGWaH9n/WA1NbA0rpg1EkCYCYaQKwzCOXuydKtyeq0mBZH7ERxo3Apo8AxZ3AxYJakBCBXAwAxZzCyDEBPAPhXDRWU0M1Gl+FDK3nJUM1M3hEZV1ZZVs2QAc1ihc1S6yy82QBDYKxlWJUlFi3VWS2VHQUNWwVy3NW7ZPLWjK0WxdRq37SyiGQtRh2
PQ+nL7+kG0b6jFvb0SP7YIzUTGW0MXDUQCzHLVsU9bukbXAGu0+ru3fUaGlBWbe3xF+1oCjADVWVJK6aELWh6UWHea4DBSI1u1ZmLDEQ7mjD9Aqi1IpqQRPB4VVXECgg3BaiYj8zITIT8zF2Pmylx5xU00JWV0l14MvmVpvm1Z1qs1fmF4SirK6gjbZGd3SitRC01690VX90S21XXr1WXJgXwId7y0T2K0L7j62pz3Om/J2XbgL661+lPbDGb1G3
Mw70Xpm06qzWTExnyNYq209X239Z9RO1AFqV8XbUe2P2W7P1A1mW4m6jFaf1sIpJ9SGRGTh3mRYNR3+ZI1uUrTbI7DKBS47lCAxauj8xXAcAhoxYcAJZeTWEU04OxXU13n+F029IkOM1pW10s1545Vqkt35Xc3pKqGbIfzrKsOGnFEcPi01VS3rb8NNUzqNGJ5K2oUdXJISP3QJgKwC1tVyPEWDEb1qXBkqOe2wH71zVW06Nxl6Nn2voYxJlX2mM
33Jz30YmKTaGv3EkB3WWZQiLxDagAr4X/2+53DAO32gPH4QDYD9AmAIAUDIQI0JP00ZNl1SmJVV0ZM13kORH11UOqnfm0OdTWgd26nNSxI923l91mlGo8OWl8NwKNMNEShIVtBV4aTjYywrji6xJjbT1pgSP2U8xaaeYr2EVr0KNkUnoUXTLjGTNH3W0n1LWozn06jbLLEmMu1bUgObHHDbHSFmrwGHHIEnH7T3HCESDUnYEUBCGYFSuhIPGMHhI
UEIWNDvH0FKs+g/GCh/EcFMhcHXXZ6kD8EcCgkSvoDytxFQkwkCvwkZ2ImGrIkq1olrO/U+h4FbOg22Njlf2FWSw8wjknPuw7nnN0m+MQAIHISQTHA8CECjALnPPpNHy3nl2ZRpN5bJupUZ7M0UO54NYAs0OlB0MdCguoGzCqHai9Yi38MQUrZD3S2y2CPj3NMFqJCJj9R4VGR7Jj5oUEsXQkwaRXZdR3QEUUKMsBmGuZPKPb5aMLUf6zMsuvqpI
ebaYKE8USVQ7csXO8v8twnzpCtQBHEoGnHitysADkVxMrYJyEF7p7nxzxKrbxdB+A973xasvxEBerTAVLkRxrIJ+AsrawN7oh1rUhe7CJqZCATrM9Lr5tISYz4SNmWzB0B2DAVq4Ni4HQAt6YGkbVcNlQPwobsdYDawQgfwQ8xAPAMACWCWCAwUOwdwVwD4tSQQUALgIa2DLzmbyTqbSeHzxD3HU7r51avzlDuTcRuV6po2U5N27FeFS4W47ZhTV
c6oBzfInuPR1cq6Ha3AqRo2fWV2/IBnBzXp7DotMLdTMFDTY9TTKLRWqHYjmU2nXyJMkw4w64K4OtQ147Qz4xIz8KqjYZEzs7jFi1C7i48xGkAmg0SzXL/627Ale16ialol+1BZ6OcGp1WOP6l1t1KXhOdsql4x9Z5Or19EZGcumqAuTE2g3Ug0nFjm8nhCE2B2JQcwbUumw2qR7R/IumfOVXj1S4GoruGn2oCouyhuJQB0Go2odlOYOHOoMcL1j
ZfG3ErGy3vGKmXGnZWurZTGQuZtA3e3uusmYmG3jGkmMu0m53MurXYAS4emN3q3mm4uulq73iumulAB3inOXZpmrrCHBqg5yHfyOzSSA0nQG4WYc2+H6w/QRHsOWS8dcamIlgO5mID4wUbAkg9AO50EdwQ8xwHA8Qkdl5OWXHOaI0vHARpWAnhUWTPzvBfz4n7NknYo0nEwsnjXWnin+xxePM2g4uhK5qmYCoCsqH787W9X2tcoRCqRS4q782A6H
DFn9b9TiLNnyL3e9n+LTnA1mFaLy4HQmYHQo7RFTFmsvnG7/nbYJt01EZKKh9UxjLp9i7BKUXvasXG7ZjPLiXOZ+Xh1aXpjJ1PKJiF1KiV1B1kfd1PspXK35XRGT3HE715Gj3u3ZXBmw3W4M+JC7RvOWeU37QGoId0XfUg0Mwaf8ue3l3LG/XocwmBfYAvOquQuNFVfGfJQ3393EuSfkIUujfsuDOKfKuvffiauGuXOqqcoS36f8fyuk36uxuf3g
SFjwM/Zpltu5lvAKSYPekjmGSRks5lh5kHwCPlzxE8DOwApEVFAxA2AswLwUwtSON7QfkCWKofkKonHSblPqU7zRDiTKmkJzIYicmeYnfNnkzvgc8+sXUbngp3/x88CQxTOUIsX6iHMjIivTtFpjaiJhemmYVIm52aJGk+6NTQehaWHoItrkmvBCqi1QBtVHOeJLqv2wXDtE+oDXA5mbwpYkV18wzLepNTt6gx76mjJ3towGYzFmWEXNih7xi6AR
OW3vFZsR12r+8qyrKI6ulxAgY4su51cYrlwUpR88uxXe6l4kYwVch+gcT6sv01Sr9d66Aaxr7W9Z5xrQlldDoHV0y9d36pnLJHOXMgxYz+mxK5immODTh8AmASQJoGCiBBJA+gUgB8ASxwBIqO5fQN/wza/94qqTfjoAOroM9QB2eZnhAIk75N2sssTnrAPSLwClOQLTKACglgKw+sJhLdCuH2Lvw8iGYRrrqBagdBNaivYgdUwHrcNZqvDGWo1W
oEK1lquvDpswPjCzZNwPMPpt52mb61SKk7G3lNRGDBcRBc7XRjijmbu9+onvWQWmWvpbtVmcHH6oD1sEIAAaL9BwVhTaqONlq9jAaDDXcaVB78DcApLYVcpI81gTwK4O0E0AClakCWdoBEOcBQBqkCBJICGn0BsApg7hMnp4R/79Jqe6bWPIJ2+Y5CIAmVf5pAIajQCueZQtcAgK5orhu0M2T3BuBuwDQ2WpTTjB1gmxl9YkxCTjJMGrZwJOGtTN
XlZw15NtbO2vFpvQN7ZtAMKnRcbAJh/xaY+i8wsQSNSWGG0aW/AwLqbXWH0VneCwm2tsLd5rhpBC+Z2vIOOEORrBT9S4T7URCesq4u/dWu7nF6yg8O3gyoC8D8H2EYImALUDcA4BJB+gxAF4NgFUCSBIIEWYKH5B8rJC0RqQghukIAEU908wnVkLm2VKN0hQhQ/EaUPk5EiKhRbAkCW1dwHRcBHQBvM0XfgKwRs64NUBX2i7VUF8PQ0WqQP6FOhB
hjbOos2zs4tNRGQoiYS51xQrhBoKAuYJwOPoTt5RjCRUecPUYW1VRogi3q70kGvodRXvZlD723ZGirGJo64Zv1xK/IP6Lg3ZouCrhjZbo2YGHvaPWAccvGgeHxt8IkApofgQ8AUvEDYAJZrASQSgG0igKYAYs+gONEYFPEIjPmgnN5rTQyHRjQiIAuMaJzzafkC2zWFMXJx57EjCmk0bQGkVlDuYswfIfrLSJ1CC9qRHg7ZH8hHxsjLQtYyziPWs
68itekAWga0wlAMDVakwtAGSUlGj5+xPnOUUowVHG0lR4zB3tehC7H1pxL6XYdF11FyCFxCgu+qcIfpr8NmHrG4W0A0iWiG0+/fFICiDbmQEsTo8Nq0BDQCl+g+gIwC8GFK/i6eyI//vgySomSQJipeMQ3WobQTihMA2CeUMQHYIh8CQXUBNkHx8hxgmA5qPKC6jDtZQk5RTpU1ArsjVe5AhtsMPIk0C50A0DrG4Kxa2gxEksBzu2P0L0TFwhCTF
rpgcpksx26oy3mxN4HTs1K9LNUTKKZbhdBJ2ovYTIK/SHDlmBoxHuAWyA7E2EqHPlsK2OKoFT2QHS9oB0laOgiCr7TOI+0dzqsX2mrFaNqwlC6sASk7YEgIQA7XsQOEhMDjIXtaQdoOKhCYMuP7KbM5JWU5wYSR3Ee8nBP+F4esHhFZIPhMdFqXHTWB3BMQoIDgKQBgAPgF4xkzIa8yp5mTkmf4+ntm2yY2ScRBQqAQ5IJFpjeeXNJcO1mh7LgUJ
4ufAcVRGB6crsM5fSF1HGy85CJS2E5LCwGHwshho9GKaMLQTJBZQfIMsd23GEZTOx6tRMKkTGxXYWJhUwcexOHGtg6WfEl3hIJqkedhJ84iVIuLDaDFd2HUg9ke1FbOk+pkrW9sfGuLmsIAwHO9tNPIKvEJpz7UaTNPfY6tP2C0n9EtNNYrTlZqsyEutNhKbS5C209saXh27m43WFwq4TY3XH2Z84C+e4ZlB6Ke50kR44/pUCHiaTLx6AO4K0HwC
YgbgKofoBQB+BxpZgBNZQDcCeAUAbgjhIuomxSGmTAJUYpEVZJzbgSExdkzmoUyly/ISmOnAqgLUhbmSSBfQkiZQMnRkzhGYwtpk6TokMyIay4AFHKHuhszKpHMkqRxNGaWNlRPE4QROM2EzNNRM4glGkh5gDU9RYk5qVJAB6jyTKSHI6QrAcbbiv6fWZdmgKum4Avpt06OkuRDkQAngcARISsFmCxNkIswUgiqE0AvAPgowYgGwCDmZywx2cwhu
ZMBkxjQJERMARBOyrgzC2kAYvPagrkAVUA5bTUFkRArK9zOBMhuSTLIlNi+RlEorH2LbnHZ1qmUrGKYX5CyNpRFvQeX5z4GcTzhbfDRgfUnmhd52M8gWXOIOHrtl58XMWWWUEpqCA+yg73iH2LLY4N2ugwrpO2rJiKf0JXTSnPwYiJ9Z+m3ZXIw28SV8juHfdXLgoIzbgvqkk9Zoh2B5byMJDgjDr1laHLhSWXggOesE0DByQ8QHBLEIFSLMA408
QP3BQE0BX9WSApQgMFAQBfzvpwElNv9KV5BE8541WMcAtyHgDIJuIvKpUN3FxAq46nEHHyF+RetYFfUCWJxQGj9Yf8NoTjEQKqYoLIKXI0iTyMwUUTEKRWHfngotj1S0QnRGuCQj9lcV8p5vdesVMoWlTVhSKcefQt3wMtCpAkyLnVJEmNS4u587hUl0RwbtUuyXXioIrOph8dBEfAwbMoK6uwiuG7aRQ9T26mDR+93PucqimBvcu+g0HRY7POED
lCZaHO3CMFtCKTFwOYATCzMDaWKAG2AWxY9IkB+QU07QHcjuVwAfA40LwYKGEEIAIEEAApHgB8DgD8xakoYp8r9L/45z/5lk8JUArrrRKwFrPQobDIEzJAC4nnDtlplDqlN7GGoc1OMAU5ygPMeM8CpNEbxoLGx06SpbQK1LjD6lZ2IRNXF1C4U5s/TchVb2ZQrCBBvSoQf0vmqMKthX+KQaMuFmEwV5O1FRPwuZRzKZlC4xZdl1kqrK9BuZDZcT
kMGx8ZFiiuRc2QUXCYjlmmE5Qco5XcRzllg03JcvXn6KbluceMFuEeXi5Og4ubMCmTUmVBBO1kbxr73DYUBMQzgTAMwB3J+QEAPwfACGg4D4A7xUazEMcC1A3LYoiIrOYlRRFASwlWbCJVitAWJjm6GpVANuFq5GQlwt0SWO/W2S+TMoILCWuuCuwHRZs1E2uSr1QWlLG5tRVlbFPtI1KaJ7YrlYlE6LNc/kHk0havQHHCqgyVCkedJMEGSSJ5Ay
iqVOP5kjKhZbCzapwsUEqqhKKgwPvMoEUZciySyksisvLKSL9VylNZcyh2XGDtK5XLnFapUw2qLVyqYdfRAdX/cV+a85dUDzdVWpTi6ShoLvJdw2gxussTRUFmPG4Ablwa88aGovkcA40zAZCA+B8hwAdgfkB8FAGHgPiOAKafmBwATYBKC1PHYJUaQAX5yQZhc2yVBJLnxLq5cof/JMBmCdATCtI9cG1E6xSM8KnFd9ck2hY9rIp6vKgc3Jbb+E
f1h2UdVWM6KcZHM05ToAKrIUdKeBXS4eQFxoUqj11k4sLswu3X7CGp7CkWeJNAZKCj16yk9RqpFlartBIi3VbeoD7R81KT6x6vsq/WyYRN3iT9e31kXq45NJQP9QBvC3OqgNzs00SBruXeyd5p0r+hNlui84/ZR844F8pI4SAdgwgO4CmmIB+RcNKaTADcEghXBcA8QD4FqAQJ/A0038pFf+L+moqAZ6KwtZipyb5DcVEMmTqmLgkZjIFBINUKW1
tT2zK2jDEJcaRrbETe16C8pQOvJkRdxhHchpfgmzAiI8K90KUbOtYlabrei63TS6r3p9LyphmphbKtnHyrd1Rw/dRJMi02ClItQIcu7MIReres90AuEPiPl/gzxnwi8XYokBtI2AnowgHcFqRkbZgPwZQFMB2DBQ4AygZCPQHaC+D6tuDRrSir/ktafp6I7IWBJAVFzmNBTeJTWpgV80P4enCpkguxB90eAxwKYAgDVDMropFSwdQWjlDjC1wEjX
tL7MITL0JQgqzTYoyHlcyl1Ng2heOIM1TzxB1UyLhmErYKrZESqv3jZrVWqCg+Cy89dJWWXOab1my8RQarFQPayIDiIwV5vkWBbTVPEOUGrmjgGVHV4GfAInA2L7TFIHsR7VsyF5eqxE6SOYDqH9kAMwwP2+6efxXIPhlwBGoQDuRVACkKAQ8HgNgD+DtAOAkgCgFjURWo7wxKTCumiqx1Ayi1HWmJeAriWZjUYDDVGY/AhYU76VpRGnXToZ0zaW
VtpFuQ5nGEa5OdCoEkj/k4r9yhVnSvbd0rFWfYJVJ2yXRqPO3u9Jg24ZokvIs2K64cqqiVOqvEqaqNdWgrXcylEW679BeqyoM/hwzGrdl6i7zebou5wFlUgmO3R+Ad21BQCzu65LJLdl5xcZxi1we9r6y9yj5hATLVcxVA3AXgfwNQJyTT1JMJtea3OTmoxXWTGNYMrrRAqahotS9pTfvjsgKJsMoWHDGvfTq/716md82pvRF27RXZ+sYwPqAc0Q
Ut6XSV0d+nik43d6BdP7LNjprKm8yhlW6qQQqA6CLzRJM+m7aAy6mQFbW2zMFIgRFa9SFWys5QAgAMBepjW2AVAOBGIA+BrANy8gFe3EOSHMgGIcwHIZICKGDFHYRVk8WVaayCSk0nWdAFmmlB5p+reg0axNZmtMCEhqQ5odkPyHdDNysQpbIEMQcDhUHO2bBzu1WZDpD+04ory9n5xuoaoWlbDQQ1+Qv9xEIeJgH5gxZkIKoaGEAaAEASMdE2uj
RAYLl46mNsSljcXrKaZKdSXdGuaJu7UlKJN3IqTczoW0Hjau1ocRHhWIQ9t2m42g3ouE54kIclM68lnOt70ir9tTBjYdKunlj7O9CsCHvLrWI8Gd2bUgQ5xilkiGT2YhzAgAApcAAASlQCJqVgfLUgJkHRFKzNjOxvY6ZEOPHHhpBhr4mNOMO25TD6s5gnrLmkGzrDi0v9stMGnoAtjux/YxQTNDXHaooHK2dwG8MNTfD7Te2bfvdbCEtmG4L1ak
jwqcY9xR8oyafJDUJdw2IaH4Cmn6D9AECygf3CjuAOZHIx2ewJW1sgP5HoDTdNnuWucAHQRsnFDcGMHtR7iyjBIKuC/DG2U7Jt4U8TXVWJkN6hGMm3kLpgSAC1zUO4JwfdHG0MDOjnRIyO/U4rl9aDlLZYSMZ5ljH+JrB9GImBHxjLzNiq+Ywe3akEhGofB6WaIf0PKyNjmgXY3sCuOphpWPxiAA6adOAmjjrp9Y2YZeKqsaC2s54xYcgBWHv2nx
uw6bM2OOnUAzpoE76ataeHwOW0nwztNRJ7TANWW9AAgXDlE8/IVwHYEPB2BCB2gKaZwCmigA3A4huIYaZbg37FHOIWYBILL0mB7DMYxWLAUX2zC4dDI3UN3KwLwOOYi+7RQyPL3STDs2x7TBMGSPNRQ1em5qHUPsTLVV7a25pYUxQNm11HcDlG8A+ZNAOUmqNwAmk1EpLWNR+dmpn9LDwIBAzGDPSwfauvHUkwdQDeAuKknNFOZINpxd7QCndww8
7pJMCE7xN1M/phl2LTcFrViRtVp9ppyZZAE817KzdaioLVuHyJLmKRG4CkWrnfovxfdy4RoTXDfU9R1OKErhhMDVzrJdMWRBMHyHdz05bVnQNqBxp6zWhUkvOO7r6uSDMzWBpBuoTP2P0SZ7oEsToCInb05hbQHQDi6kgSkFxxc3kg6LaFUX18JMQ2v5EOxETFiSEeFcwTsn6wCZNxOoFJPaiIuC8F5dcGquRcDhF839/IAgdqAr4TZdKGkXqD2O
tAQ8vdPOFk//mLHsX2KvyJy/ArGzNKNwIiWtVPzpGGcMwEwPPjaAC3IWLd+KYvggPm7PLh2VlsYC/AXkomFQ+AuvtVw+qSwmjkPFqEZFSI2hTsH1NyWIjUuxX+sel23T5vojpgq8qm2ygyI0hd8ODSEibLaMIQ5hRzO3ASwRjwkahbLMjc1GNjVD8YBeOYT3GxetGpFfujV+ft2m55l9ecHnQzMqgmzJAdwpViYDmF0ypITc+iDQZl1D4lkvES4V
a+kXWs4VaVSsTjHEE4p4V+sB1+1P/n4vxxrNvC49fPsS7ubj1gN48NJHACsR1gcAOAPCEESjNoAUYTIIh2XT1AGAhAe5p9JFMcNjgWN7G6iGuYiA7kdwA4FGiKU1sIplh/G+zCJvo3Nzop5sWGYpvZBCbGQBAleRz3I3sADNqAEzeJvo6KTeN6oJTYyDwhi0bNwoPzYJtE2YsOO4BeLcFv6AU0eQgvfTYFuM2ibCBYQz1LWPk2VbXNtWxLMtPs3O
b3N2Vv6fGli2ObOt7m9Dfkquakcst1WxkHdH3rt9hu3GxbYlsZAXYLwKxgwlxvMBsANQWEEXTfokJauKVlqN1FmtZREoAdk0PgCDmqgv4PMXUM0rcuNDtM4JNgAYBHkMACAchFQi8srya4dU9t3WxkClulSp2ywXG26BIAWm9myN2u/nQOBqwxWYtpuz8DYArB3RuATQMEC+HKxjWW5g7RAAfAmhiIpAZQM6A2OHy+88wOe9QHZ7xBtjjoSQsoDr
BVA/qU93ADPc6CL2FYXQXgHvaXsr31Cpd4W5vAVu0FOA3MngkVMyCSFTIxrUDGnCyC93+74J1M3NKICt3UAQFyAKawRt2sbZNacQhEmAcIAz7dgWNQDWYBPBTWvwLuwgB7t93Jl6wAGoQEYAvAs7+AHO1ZjCDBAMHpqX4mLGYL6BvbmJCZQPckrohkIGDrBzg/1japwA4MTWDCHCCAw38PYIAA==
```
%%

File diff suppressed because it is too large Load diff

17
plan.md Normal file
View file

@ -0,0 +1,17 @@
#organisation
Part 1: Dynamic response of bridged carbon-epoxy laminates with viscoelastic film (since 2017)
1. Literature review on carbon-epoxy laminates
2. Study of viscoelastic properties and dynamic mechanical analysis (DMA)
3. Research on bridging techniques in composite laminates
4. Analysis of recent developments in viscoelastic film integration
5. Review of dynamic response studies on similar composite structures
Part 2: Impact studies on bridged carbon-epoxy laminates with viscoelastic film
1. Literature review on impact testing methods for composites
2. Analysis of low-velocity impact studies on carbon-epoxy laminates
3. Research on high strain rate behavior of advanced composites
4. Study of impact effects on viscoelastic properties
5. Investigation of potential impact testing methodologies for your specific material

View file

@ -1,2 +1,32 @@
Accelerance is a measure used in mechanical systems that relates acceleration to applied force.
# Introduction
([[Secondary articles descriptions#Machine Vibration|source]])
In a dynamic world, $F = mr\omega^2$. The mass and stiffness are not constant anymore and we cannot continue to use Newtonian physics ($F=ma$) and Hooke's law ($F=kx$).
To preserve the linearity of Newton's $2^{nd}$ law a dynamic mass is defined :
$m(\omega)$.
The reciprocal of dynamic mass is accelerance, and is also a function of frequency : Accelerance $= \frac{1}{m(\omega)} = \frac{a(\omega)}{F(\omega)}$
**Symmetry is bad practice because it support resonant modes**
Force is a wave that travels at the speed of sound.
# Formalisation
([web source](https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Introduction_to_Linear_Time-Invariant_Dynamic_Systems_for_Students_of_Engineering_(Hallauer)/10%3A_Second_Order_Systems/10.05%3A_Common_Frequency-Response_Functions))
We define the dimensionless excitation frequency ratio, the excitation frequency relative to the system undamped natural frequency :
$$\beta \equiv \frac{\omega}{\omega_{n}}\tag{1}$$
And we define :
$$\omega_{n}=\sqrt{\frac{k}{m}}, \quad \zeta \equiv \frac{c}{2 m \omega_{n}}=\frac{c}{2 \sqrt{m k}} \equiv \frac{c}{c_{c}}, \quad u(t) \equiv \frac{1}{k} f_{x}(t)$$
For an $m-c-k$ system, from Laplace transformation of the ODE (*ordinary differential equation*) $m\ddot{x}+c\dot{x}+kx = f_x(t)$, and with use of notation defined in Equations $(1)$ and $(2)$, the equation for complex mechanical admittance is :
$$\left\{\frac{L[x(t)]}{L\left[f_{x}(t)\right]}\right\}_{s=j \omega}=\frac{1}{\left(k-\omega^{2} m\right)+j \omega c}=\frac{1}{k}\left[\frac{1}{\left(1-\beta^{2}\right)+j 2 \zeta \beta}\right]\tag{3}$$
(The inverse being *dynamic stiffness*)
For _accelerance_ (also known as _inertance_), the subject variable is an acceleration, and the reference variable is an action. Since $L[\ddot{x}(t)]=s^{2} \times L[x(t)]$, the accelerance of an $m-c-k$ system, from Equation $(3)$, is
$$\left\{\frac{L[\ddot{x}(t)]}{L\left[f_{x}(t)\right]}\right\}_{s=j\omega}=\frac{(j\omega)^{2}}{\left(k-\omega^{2}m\right)+j\omega c}=\frac{1}{m}\left[\frac{-\beta^{2}}{\left(1-\beta^{2}\right)+j2\zeta\beta}\right]\tag{4}$$
(The inverse of accelerance is called _apparent mass_)

3
ressources/Co-curing.md Normal file
View file

@ -0,0 +1,3 @@
([[Secondary articles descriptions#Optimization method of composite laminates with a viscoelastic layer|source]])
Co-curing means the viscoelastic material within the composite laminate undergo the temperature and pressure cycle needed to cure the composite material.

View file

@ -16,4 +16,8 @@ Those theories describe kinetically each layer. They can be used for very thick
---
## Zig-Zag
[[Layerwise Theories]] with shear continuities between layers to keep the same number of degrees of freedom as the number of layers is increased. (so less computationally expensive)
It captures the "zig-zag" pattern of displacements through the thickness that occurs due to different layer stiffness.
(see [[Zig-Zag Theories]])

View file

@ -1,4 +1,4 @@
see [[videos]] for references
([[Videos descriptions#continuum mechanics|video source]])
The strain tensor is the symmetric part of the gradient of the displacement field vector.
$$\varepsilon = \frac{\nabla{U} +\nabla{U}^T}{2}$$

View file

@ -1,16 +1,27 @@
To [[Composite laminate models|model a composite laminate]] there are a few options, the most important are the equivalent single layer and the [[Layerwise Theories|layerwise]].
Those theories works by computing the homogenized material properties, and solving only at the mid plane. They are useful for global response for thin laminates and are computationnally inexpensive.
Those theories works by computing the homogenized material properties, and solving only at the mid plane.
The laminate is therefore modeled as an equivalent single anisotropic layer. They are useful for global response for thin laminates and are computationnally inexpensive.
-> most popular : FSDT
*They have issue with layers of different properties.*
#### Classical Laminate Theory (CLT), hypothesis :
The normal line to the median plane of the plate before deformation stays normal to the plane after deformation.
#### Classical Laminate Theory (CLT) :
Hypothesis : The normal line to the median plane of the plate before deformation stays normal to the plane after deformation.
-> lack of transverse shear
(see [[Kirchhoff's hypothesis]])
#### First-order Shear Deformation Theory (FSDT), hypothesis :
The normal line to the median plane of the plate stays straight after deformation but it is not normal to the middle plane, the shear constraint stays constant along the thickness of the plate.
(extension of the **Kirchhoff-Love** plate theory)
#### First-order Shear Deformation Theory (FSDT) :
Hypothesis : The normal line to the median plane of the plate stays straight after deformation but it is not normal to the middle plane, the shear constraint stays constant along the thickness of the plate.
Only two assumptions remains :
- *straight lines normal to the mid-surface remain straight after deformation*
- *the thickness of the plate does not change during a deformation.*
#### High-order Shear Deformation theory (HSDT) :
More complex variation of the shear constraint along the thickness of the plate, but more computationally expensive.
It is assumed that the displacements are of higher order polynomial form and are $C^1$ continuous through the thickness. This allows for non-linear variation of displacements, strain and stresses through the thickness.
([[Secondary articles descriptions#First order Zig-Zag plate Theory|source]])

View file

@ -0,0 +1,20 @@
[[Videos descriptions#Failure theories|video source]]
The hydrostatic stress is the average stress on all axis, it relates to the stress that want to change the volume like under water pressure (hence hydrostatic), by contrast to the deviatoric stress that act on the shape of the element.
### For ductile materials :
The hydrostatic stress has no effect on failure.
Tresca : easier to apply, more conservative
*hexagonal prism in stress space*
von Mises : better agreement with experimental data
*cylinder in stress space*
### For brittle materials :
Compressive strength >>> Tensile strength
The hydrostatic stress affects failure.
Coulomb-Mohr : general case of Tresca

View file

@ -2,13 +2,15 @@ The finite element method is a mathematical method to be able to computationally
The core of the method is to discretise the problem, because computer cannot solve the problem analytically.
[weak formulation](https://www.youtube.com/watch?v=xZpESocdvn4) *(30min)*
## Weak formulation
([[Videos descriptions#Weak Formulation|video source]])
The weak formulation is the formulation of the differential equation so that it becomes solvable using the finite elements method.
This video shows how the weak formulation is derived from the initial problem, and its use.
[finite element method](https://www.youtube.com/watch?v=1wSE6iQiScg) *(40min)*
## Mathematical Finite element method base
([[Videos descriptions#Mathematical Finite element method base|video source]])
The finite element method is a mathematical method to be able to computationally solve a differential equation.

View file

@ -1,4 +1,4 @@
[ref](https://www.sciencedirect.com/topics/engineering/hertz-theory)
([web source](https://www.sciencedirect.com/topics/engineering/hertz-theory))
describes the contact between two elastic solids

View file

@ -1,3 +1,3 @@
[ref](https://en.wikipedia.org/wiki/Hysteresis)
[web source](https://en.wikipedia.org/wiki/Hysteresis)
the dependence of the state of a system on its history.

View file

@ -1,11 +1,16 @@
# collision
# Collision
A collision is a broad term that describes any event where two or more bodies exert forces on each other for a relatively short time.
# impact
The [[Hertz Law]] describe the contact between two elastic solids.
There is also [[Inelastic Collisions]].
# Impact
An impact is a type of collision with a high force over a short duration.
# shock
(see [[Impact Models]])
# Shock
A shock is a transient high force event with clearly defined parameters for testing purposes. Can be an impact, an other type of collision, an explosion, etc...

View file

@ -0,0 +1,5 @@
During **inelastic collisions**, masses are added together and
momentum are conserved. This can be used for slamming or other wave-like loading.
This model is reasonable when the impactor is relatively soft and the mass
of impactor is larger than the mass of the node being impacted.

View file

@ -0,0 +1,7 @@
([web source](https://www.sciencedirect.com/topics/engineering/kirchhoff-hypothesis))
- *straight lines normal to the mid-surface remain straight after deformation*
- *straight lines normal to the mid-surface remain normal to the mid-surface after deformation*
- *the thickness of the plate does not change during a deformation.*
![[Kirchoff's Hypothesis Diagram]]

View file

@ -2,9 +2,12 @@ To [[Composite laminate models|model a composite laminate]] there are a few opti
Those theories describe kinetically each layer. They can be used for very thick laminate, and useful to compute delamination. They predicts correct inter-laminar stresses and there is no need of shear correction factor.
## Stiffness
There is a unique displacement field per layer + interlaminar continuity of displacements (and sometimes of transverse stresses).
-> very computationally expensive, since the number of degrees of freedom increase proportionally with the number of layers.
([[Secondary articles descriptions#First order Zig-Zag plate Theory|source]])
[course](https://www.youtube.com/watch?v=j3rvtgqrGsQ) *(1h30)*
## Stiffness
([[Videos descriptions#Composite materials course|video source]])
When pulling on the material, strain is the same for every ply, but stress is not.

View file

@ -1,10 +1,12 @@
hook law for large deformations
[ref](https://en.wikiversity.org/wiki/Advanced_elasticity/Neo-Hookean_material)
([web source](https://en.wikiversity.org/wiki/Advanced_elasticity/Neo-Hookean_material))
neo-Hookean material ~ hyperelastic material
Hook law for large deformations
no linear relationship between stress and strain
Neo-Hookean material ~ hyperelastic material
No linear relationship between stress and strain
even better : [mooney-rivin solid](https://en.wikipedia.org/wiki/Mooney%E2%80%93Rivlin_solid)
---
Even better : [mooney-rivin solid](https://en.wikipedia.org/wiki/Mooney%E2%80%93Rivlin_solid)

View file

@ -1,3 +1,3 @@
[ref](https://www.sciencedirect.com/topics/engineering/newmark-method)
([web source](https://www.sciencedirect.com/topics/engineering/newmark-method)) #archive
A method of numerical integration used to solve certain differential equations.

View file

@ -1,10 +1,9 @@
([[Secondary articles descriptions#Passive Constrained Layer Damping, SotA|source]])
*Passive Constrained Layer Damping*
[[passive constrained layer damping.pdf|ref]]
[[Viscoelasticity|Viscoelastic materials (VEM)]] dissipate energy under a transient deformation. Used in a form of a layer that is either freely attached (UCLD ie *unconstrained layer damping*) or in a sandwich (CLD/PCLD ie *constrained layer damping/passive constrained layer damping*).
UCLD : unconstrained, the dampening occurs through compression/traction.
In most of the analyses, extensional/compressional strains of the viscoelastic layer are not taken into account since the damping comes mostly from the shear strain. However, with a thick layer, compressional damping cannot be neglected.
CLD : constrained, the dampening occurs through shear, but compressional
damping cannot be neglected (especially if thick layer)
Usually done using a [[Viscoelasticity|viscoelastic material]]
The mathematical models are either [[Finite element method|FE]] or analytical.

View file

@ -11,5 +11,7 @@ its stiffness depends on the strain rate
A viscoelastic substance dissipates energy when a load is applied, then removed.
### nota bene
The properties of a viscoelastic layer change with the frequency of excitation
In most of the analyses, extensional/compressional strains of the viscoelastic layer are not taken into account since the damping comes mostly from the shear strain.
### Nota Bene
The properties of a viscoelastic layer change with the frequency of excitation .

View file

@ -1,12 +1,38 @@
first-order zig-zag theory (FZZT),
[ref](https://www.sciencedirect.com/science/article/abs/pii/S026382239900063X)
*zig-zag in-plane displacement theories*
allowing for discontinuities in displacement between layers.
 captures the "zig-zag" pattern of displacements through the thickness that occurs due to different layer stiffness.
 
The first-order zig-zag theory introduces additional terms to the displacement field assumptions used in classical laminate theory:
To [[Composite laminate models|model a composite laminate]] there are a few options, the most important are the [[Equivalent Single Layer Theories|equivalent single layer]] and the [[Layerwise Theories|layerwise]]. However there was a need to get theories that were less computationally expensive than the layerwise, and more accurate than the equivalent single layer.
1. It adds a zig-zag function that allows for slope discontinuities at layer interfaces.
2. It maintains continuity of transverse stresses between layers.
3. It satisfies the traction-free boundary conditions on the top and bottom surfaces.
They are theories which describe the piecewise form of transverse stress (Zig-Zag, ZZ) and displacement fields (Interlaminar Continuity, IC).
# General Zig-Zag Theories
([[Secondary articles descriptions#First order Zig-Zag plate Theory|source]])
[[Layerwise Theories]] with shear continuities between layers to keep the same number of degrees of freedom as the number of layers is increased.
It captures the "zig-zag" pattern of displacements through the thickness that occurs due to different layer stiffness.
Improvements of the model consist in keeping it accurate, only needing $C^0$ continuous and 5 degrees of freedom.
# First Order Zig-Zag Theory (FZZT)
In-plane displacements are assumed to be layerwise linear and continuous through the thickness. This allows for slope discontinuities at layer interfaces.
5 degrees of freedom (does not depend on the number of layers) are achieved by using the transverse shear stress continuity at each interface.
This theory is the most accurate for symmetrical laminates.
# Higher Order Zig-Zag Theories (HZZT)
To improve the [[#First Order Zig-Zag Theory (FZZT)|FZZT]], a piecewise linear variation of in-plane displacement is superimposed on a continuous cubic function of the transverse coordinate.
This allows for better displacement field of unsymmetrical laminates.
The homogeneous shear traction boundary conditions at the top and bottom surfaces allows us to keep 5 degrees of freedom.
However the main issue is that the transverse deflection degree of freedom $w_0$ is required to be $C^1$ continuous.
Therefore additional rotational degrees of freedom (gradients of $w_0$) are present -> more than 6 degrees of freedom -> tough to implement in commercial finite element software.
# Refined Zig-Zag Theory (RZT) ?
https://rzt.larc.nasa.gov/

View file

@ -1,3 +1,4 @@
#reunion
# Objectif principal du mémoire
état de l'art post 2020 sur les composite avec couche visco-élastique pontés

View file

@ -1,78 +0,0 @@
# optimization method of composite laminates with a viscoelastic layer
[ref](https://d1wqtxts1xzle7.cloudfront.net/33874260/2011-2-libre.pdf?1401929433=&response-content-disposition=inline%3B+filename%3DMulti_objective_Optimization_of_Co_cured.pdf&Expires=1726671246&Signature=X30Tmzd9RIn7nsIGU2Q4ZgeCchtgP~md5owXYAwnVnZj9pZCx1Ck~6owvGcTyWQwCJcm~i3zbXCXioNqPemkodqkkJ3m3mQZJ5yY7FYpc2i86ZUsACau8A-Gr3YNQ0XNFIGO4drqLGq21zz67T-CnsYfUV3LRpvY4wiZ2TWs4Q~ImvfTtlxcDTCCr4JW5abxR75Fi0yiSe6og7qjwdLh8E50qFdcXTvijO6qm9dnpW854ozStXkGkhsq16PzBfIbFLE7yrXc6zzAtUUHF5YpUfZRYl7V2xfu8s51Cvp9-YIJ8gt2v-qm2uQM92DPbZ9J62unLsIog2pr-HUWUxjqDw__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA)
This paper develops a method to transform a multi objective (damping and stiffness)
into a single one, to facilitate optimization.
# experimental investigation of the dissipation of a viscoelastic inserted layer
[ref](https://sci-hub.se/https://journals.sagepub.com/doi/abs/10.1177/1077546319844545)
This paper try to assess the damping qualities of a visco elastic insert. It found that it is very efficient in medium and high frequency ranges.
---
---
# model for impact on fiber metal laminate with a viscoelastic layer
[ref](https://doi.org/10.1016/j.ijmecsci.2021.106298)
_can teach about impact on viscoelastic sandwich impact_
Use a specific criterion to quantitatively estimate whether the composite
structure is damaged subjected to impact excitation.
Reddys high-order shear deformation theory for the viscoelastic layer
---
# Hard and Soft Collisions
[ref](https://www.compadre.org/Physlets/mechanics/illustration8_3.cfm)
A soft collision is an inelastic collision, which means that kinetic energy
is not conserved (because internal friction). However, the momentum is still
conserved.
A perfectly inelastic collision occurs when the two bodies stays together,
and the energy is lost by bonding the two bodies.
# inelastic collison for composite materials
[ref](https://doi.org/10.1016/0263-8223(90)90025-A)
Use the finite element model to get the dynamic response.
The structure is considered elastic but the loading is considered
inelastic.
The isoparametric linear shell element is modified
to take into account the shear deformation and rotatory inertia.
-
inelastic collision : masses added together and
momentum conserved, used for slamming or other wave-like loading
This model is reasonable when the impactor is relatively soft and the mass
of impactor is larger than the mass of the node being impacted.
# finite element modeling of low-velocity impact on laminated composite plates and cylindrical shells
[ref](https://doi.org/10.1016/j.compstruct.2010.10.003)
use of abaqus
examination of the validity of different models
propose a benchmark method in low-velocity impact modeling of composite structures
# Analysis of Laminated Composites Subjected to Impact (p 243)
[ref](https://link.springer.com/chapter/10.1007/978-3-030-66717-7_19)
very recent paper, propose both theoretical and experimental approaches to
the analysis of laminated composite response to impact loading

View file

@ -1,31 +1,37 @@
#organisation
- [x] get used to the college library (download pdf ?)
- [x] read thesis
- [x] read articles 58->61
- [x] find article who reference article 57->61
- [x] format latex
- [ ] mail Herve for project launching
- [x] mail Herve for project launching
- [x] analyse de risques
- [ ] [get article](https://www.tandfonline.com/doi/abs/10.1080/15376494.2022.2097355)
- [ ] plan
- [ ] work on [[plan]]
- [ ] check [[unknown]]
- [ ] doc revue lancement de projet
- [ ] gantt
- [ ] stage (5 candidatures)
# to read (take notes)
- [ ] [[accelerance.pdf]]
- [ ] [[neo-hookean model analysis.pdf]]
- [ ] [[passive constrained layer damping.pdf]]
- [ ] [[viscoelastic damping design.pdf]]
- [ ] [[zig-zag.pdf]]
- [ ] [[Impact_and_vibration_of_hybrid_fiber_metal_laminates.pdf]]
- [ ] [laminate theory of composite materials](https://link.springer.com/book/10.1007/978-3-031-32975-3)
[[to read]]
- [x] Machine Vibration
- [x] Analysis of the compressible neo-Hookean model
- [x] Historical review of Zig-Zag Theories
- [x] Layerwise Analysis VEM
- [x] First order Zig-Zag plate Theory
- [ ] Viscoelastic damping design
- [ ] Experiments on dissipation of VEM layer
- [ ] Optimization method of composite + VEM
- [ ] Analysis of composites subjected to impact
- [ ] Model for impact metal fiber laminate + VEM
# to watch
- [x] [composite material modeling](https://www.comsol.fr/video/modeling-layered-composite-structures-with-comsol-multiphysics-nov-29-2018)
- [x] obsidian tutorial
# to fill (check things to read)
- [ ] [[Accelerance]]
- [ ] [[Zig-Zag Theories]]
# to fill
- [x] Accelerance
- [x] Zig-Zag Theories
- [x] PCLD
- [x] Viscoelasticity
- [ ] [[Neo Hookean Behavior Law]]
- [ ] [[PCLD]]
- [ ] [[Viscoelasticity]]
## bonus
[naval impact study (without viscoelastic layer)](https://sci-hub.se/https://doi.org/10.1016/0263-8223(90)90025-A)

37
to read.md Normal file
View file

@ -0,0 +1,37 @@
#organisation
## Viscoelastic damping design
*2023*
[online ref](https://www.sciencedirect.com/science/article/abs/pii/S0022460X23001529)
[[Viscoelastic_damping_design.pdf|local ref]]
## Experimental investigation of the dissipation of a viscoelastic inserted layer with perforations
*2019*
[online ref](https://journals.sagepub.com/doi/abs/10.1177/1077546319844545)
[[Experimental_investigation_of_the_dissipation_of_a_viscoelastic_inserted_layer_with_perforations.pdf|local ref]]
This paper try to assess the damping qualities of a visco elastic insert. It found that it is very efficient in medium and high frequency ranges.
**perforations ~ bridges ??**
## Analysis of Laminated Composites Subjected to Impact (p 243)
*2021*
[online ref](https://link.springer.com/chapter/10.1007/978-3-030-66717-7_19)
[[Analysis_of_Laminated_Composites_Subjected_to_Impact.pdf|local ref]]
Propose both theoretical and experimental approaches to the analysis of laminated composite response to impact loading.
## Model for impact on fiber metal laminate with a viscoelastic layer
*2021*
[online ref](https://doi.org/10.1016/j.ijmecsci.2021.106298)
[[Impact_and_vibration_of_hybrid_fiber_metal_laminates.pdf|local ref]]
_Can teach about impact on [[Viscoelasticity|viscoelastic]] sandwich impact._
Use a specific criterion to quantitatively estimate whether the composite
structure is damaged subjected to impact excitation.
Reddys [[Equivalent Single Layer Theories|high-order shear deformation theory]] for the [[Viscoelasticity|viscoelastic]] layer
# bonus
[naval impact study (without viscoelastic layer)](https://sci-hub.se/https://doi.org/10.1016/0263-8223(90)90025-A)

View file

@ -1,9 +1,16 @@
#organisation
### to learn
classical plate theory/classical shell theory (Kirchhoff hypothesis)
finite elements and alternative : the immersion method, the method of R-functions
accélérance
Zig-Zag model theory
finite elements and alternative :
- the immersion method,
- [the method of R-functions](https://asmedigitalcollection.asme.org/appliedmechanicsreviews/article-abstract/48/4/151/401230/R-Functions-in-Boundary-Value-Problems-in)
Zig-Zag Theories
[[Secondary articles descriptions#Layerwise Analyses VEM]]
the principle of virtual displacement (PVD)
complex eigenvalue problems
modal strain energy technique
### questions