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