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#description
Collisions
Hard and Soft Collisions
webpage ref
A soft Impact-Shock-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 Impact of Composite Laminated Plate
1990 online ref Inelastic_Impact_of_Composite_Laminated_Plate.pdf
Use the Finite element method 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 FEM_of_low-velocity_impact_on_composite_materials.pdf
use of ABAQUS
examination of the validity of different models
propose a benchmark method in low-velocity Impact Models of composite structures
Background
Machine Vibration
2021 (info from the metadata of the PDF) online ref Real_Physics_of_Machine_Vibration.pdf
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 PCLD_SotA.pdf
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 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 or analytical.
(see PCLD)
Layerwise Analyses VEM
2016 online ref Layerwise_Analysis_VEM.pdf
This paper evaluates the vibrations characteristics of structures with Viscoelasticity. The equations of motions are derived with the Principle of Virtual Displacements and solved with the Finite element method. This paper uses the Layerwise Theories 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 layers dynamic study :
- the modeling of material properties -> tests to characterize the material
- the solution of nonlinear complex Eigenvalues and eigenvectors 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 Analysis_of_the_compressible_neo-Hookean_model.pdf
Analysis of the model implemented in the commercial Finite element method 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
Model analysis theories
First order Zig-Zag plate Theory
2000 online ref First_order_Zig-Zag_plate_Theory.pdf
This paper develops and assess a laminated plate theory x 3D finite element, based on Zig-Zag Theories.
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 : the laminate is modeled as an equivalent single anisotropic layer
-> most popular : Equivalent Single Layer Theories#First-order Shear Deformation Theory (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) : 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 issue : unable to account for discontinuities in transverse shear strains at interfaces between layers with different stiffness.
Layerwise Theories : 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 Historical_review_of_Zig-Zag_Theories.pdf
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).