Questions tagged [solid-mechanics]
Studies the behavior of solid materials, and deformation under the action of forces
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How to Make the 'Weak Inequality Constraint' Converge as Well as 'Contact' Constraint In Solid Mechainc Module of Comsol Multi-Physics?
I try to understand the modeling of indentation in Comsol Multi-Physics.
For spherical indenter, assuming frictionless and hard contact, the 'Contact' constraint in Solid Mechaincs module converge ...
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Is there any papers about simulating material damage under supersonic combustion?
I'm quite interested in this field, Is there any papers about simulating the damage of material(such as alloy) under supersonic combustion, after searching for a while, I didn't find anything
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FENICSx or deal.ii for modeling fluid structure interaction of cylindrical energy harvesters in various arrangements
I'm trying to model fluid-structure interaction of cylindrical energy harvesters in various arrangements. I have chosen OpenFOAM for the fluid part but I have no clue which framework to use for the ...
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Neumann BC in the current configuration in a finite-strain problem
For a hyperelastic problem, I understand the variational formulation can be written as the minimisation of $\Pi$ with
$\Pi = \int_{\Omega} \psi( \pmb{u} )dx - \int_{\partial\Omega} \pmb{T}\cdot \pmb{u}...
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Determination of the domain of nonlinearity in a Neo-Hook solid model (Finite elements)
For a FEM simulation of a Neo-Hook solid model, how do we know we are in the "regime" of nonlinearity of the solid? In other words, how do I know the hyperelastic material law is really used,...
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RFEM: Equilibrium over plate section
I'm calculating a simple plate arrangement in RFEM:
The plate has dimensions of 1m X 1m, thickness of 50mm. Elastic modulus of the material is 205000.0 N/mm2, Poisson's ratio is 0.3.
The plate is ...
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Estimating forces on a model from the displacements of nodes
In any FEM problem involving mechanics, we try to solve the differential equation for the displacement field, $u$ given the force vector in the nodes, $F$. In industry, we often see our automobiles ...
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How to solve evolution equation numerically?
How do I solve the following evolution equation numerically:
$$
\dot{\boldsymbol{\mathcal A}} = -\lambda A_1|\boldsymbol{s}-\boldsymbol{\alpha}|^2\left[(\boldsymbol{n}_r:\boldsymbol{\alpha})\...
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Is it really necessary to solve a system of linear equations in the Finite Element Method?
When we solve some boundary value problem by Finite Element Method, the appropriate system of linear equations is built, $$Ax=b.$$
Usually we use the solution x just for plugging it into some ...
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Finite Element Modelling of Hyperelastic Material under 2D Plane Strain Conditions
I am currently working on writing a MATLAB code for running a finite element simulation of a hyperelastic material in 2D. Since I am building this simulation as a part of a fluid-structure interaction ...
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Calculate strains based on X,Y Deformation gradient with time
Recently I have obtained a csv value form and experiment I have computed. However, I was trying to understand how each individual component being calculated. The image attached shows sample point ...
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If FEM is exact at the nodes, why do first and second-order elements give very different results?
I'm looking at the solution to a structural mechanics problem that is modeled with first-order elements and then as a comparison with second-order elements. It is clear that the first-order elements ...
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Why FEM for incompressible materials is ill-posed?
I am an engineer who is trying to get a deeper understanding of FEM. I have been using the Zienkiewicz texts as my bible. It touches on the issue of incompressibility but I need a more intuitive way ...
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What is the difference between non-linear elastic simulation and linear elastic simulation with plasticity?
I'm learning how to do Finite Element calculations using Comsol Multiphysics.
In Comsol, Linear Elastic Material and Nonlinear Elastic Material are available as material models:
Using Linear Elastic ...
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What are the prerequisites and resources to self-learn the Boundary Element Method for Contact Mechanics problems?
What are the prerequisites to learning BEM?
In which order is it advisable to learn BEM and FEM - either one before the other, or does it not matter?
What are some good resources to self-learn BEM?
P....
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Derivation of the second Piola-Kirchhoff tensor
I tried many formulas to find the components of the second Piola Kirchhoff. I need help to derive equations 27-29 on reference 1.
[![enter image description here][1]][1]
we have
$$
\mathbf{C}=C_{11} \...
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Applying Stress Boundary Conditions in Commercial Finite Element Analysis Codes
I am trying to replicate a finite element analysis given in a research paper titled On the Detection of Stress Singularities in Finite Element Analysis 1 by G.B.Sinclair et. al.
The geometry of the ...
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Stretched Elastic Sheet with Horizontal Cut in Interior
Given a rectangular finite elastic sheet $ABCD$ containing an arbitrary horizontal cut (or discontinuity) $EF$ in its interior. The edge $AB$ of the sheet is tethered but $CD$ is stretched by $\Delta$ ...
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Beam theory: does finer meshing make any difference if the shape functions used are 3rd degree polynomials?
I'm studying the Finite element method for structural mechanics, and I'm reading this source.
3rd degree polynomials are used as shape functions for beam theory, since they are required to be ...
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Total stored potential energy of finite element mesh from nodal point displacements and strain energy density function only
I am interested in calculating the total potential energy stored in a finite element mesh given its nodal point displacements alone. The forces that created the displacements are irrelevant because ...
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Second Piola-Kirchoff Stress Tensor of Neo-Hookean solid at "zero deformation"
The strain energy of an incompressible Neo-Hookean solid is given as:
$$
W = C_{10}(I_1 - 3)
$$
Implying that at zero deformation $W = 0$, because $F = I \implies C = F^TF = I \implies I_1 = 3$
...
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Modelling question: example of a physical phenomenon with this jump condition at an interface?
in our finite element class we were talking about interface problems our teacher came up with the following, where $K_i$ are two given functions and $u_i$ is the restriction of the solution $u$ to $\...
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How to enforce fluid and solid dynamic coupling in fluid-structure interactions using the finite element method?
I apologize in advance if the question has been posted before or if it sounds a bit naive.
I am writing my own code in MATLAB for a staggered finite element solver for fluid-structure interaction ...
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How does RFEM give non-linear results with a two-node mesh?
I did this simple analysis on RFEM, of a rigid-supported beam loaded with a point moment. Before analysis, I didn't assign any kind of mesh manually. When I turn on the FE Mesh visible on Project ...
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Varying Young modulus in FEM simulation
I'm working on a project for which I have inherited some FEM code. This implemented FEM calculates, given some force field, displacements on a discretised square using square elements and assumes a ...
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Extracting a mid-plane for thick shell analysis
I have a complex part that contains features of the form shown in the figure below.
Because of the cost of 3D finite element simulation of the part, I want to try an analysis with 2D thick shells.
...
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2
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Dyadic operations, fourth order tensors and Tensor algebra
I am trying to understand the dyadic operation for a while since I am interested in Elasticity problems. I believe an intuitive understanding (rather than assuming) will give me good problem solving ...
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How to interpolate stress at unknown points from the stress values available based on geometrical position for constant load?
I am working on a combined contact, bending, and torsion problem. I have data on geometrical points and their instantaneous stress components. However, based on the available data, I have to ...
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Approximation in the derivation of the Arc Length method
I am studying the proof of the Arc Length method in section 2.2 of this thesis. In equation (2.2) the author introduces the supplementary conditions
$$
(\Delta {\bf u} + \delta {\bf u})^T \cdot (\...
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relation between different tangent stiffness
I need to find a relation between the tangent stiffness $L_1$ of the first Piola-Kirchhoff stress tensor with the tangents stiffness $L_2$ of the second Piola-kirchoff stress tensor. They are defined ...
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Transition from 2D to 3D finite element code, what are the inevitable modifications to be implemented?
Imagine we have a simple 2D FEM solver (we are dealing with solid mechanics) and we would like to develop it to a 3D FEM solver (let's say for the same solid mechanics problem) in this case what are ...
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How to solve a linear problem A x = b in PETSC when matrix A has zero diagonal enteries?
I am solving a structural mechanics problem that involves setting constraints, and I use Lagrange multipliers to set it. Consequently, some diagonal entries of the tangent stiffness matrix vanish, and ...
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How are the classical set of equilibrium equations for linear elasticity derived?
In linear elasticity, the governing PDE is the equilibrium equations (absent of vibration considerations):
$$
-\nabla \cdot \sigma = F
$$
Is this equation simply derived from the sum of forces and ...
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Hi I am trying to model a 2D Lug angle using Gmsh 4.6. How can I combine transfinite quad and regular full quad meshes in the following geo file?
I need transfinite mesh a small section of the bolt hole to insert a crack. However, The transfinite mesh and regular full quad mesh seem being incompatible and throwing errors. How can I combine ...
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Global stiffness matrix from element stiffness matrices for a thin rectangular plate (Kirchhoff plate)
I have the element stiffness matrix for a thin "kirchhoff" plate. The plate is 3 [m] x 5 [m] and is simply supported on all edges. It's thickness is 0,2 [m]. On the plate there acts a ...
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implementation of shell elements in a topology optimization algorithm
I am working on developing a topology optimization solver based on the finite element method and I want to add a triangular shell element in it. I used the classic finite element method but I didn’t ...
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How to determine global stiffness matrix is constrained or not
Background
In solid fem, we often solve $$\mathbf{Ku}=\mathbf{p}$$
where $\mathbf{K}$ is global stiffness matrix, $\mathbf{u}$ is displacement, $\mathbf{p}$ is global load vector.
If displacement not ...
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4th order tensor rotation - sources to refer
I am trying to model a linear elastic material in Abaqus using a UMAT. For my application, I need to rotate the 6x6 compliance matrix for a given set of eigenvectors (or a rotation matrix). I came ...
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Uniaxial stretching solution not uniform in FEM code
I am trapped here for a long time. I wrote a toy Matlab FEM code. I want to run the follow simulation.
Mesh
Suppose we have a cube, and we divide it into subcube along $x,y,z$ axis, then each subcube ...
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FEM with elastic inhomogeneous properties leads to mesh-induced anisotropy
I'm solving an elastic homogenization problem and I'm having problems with mesh artifacts.
I would like to first give a brief summary of what I do: I have a system with inhomogeneous (but isotropic) ...
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I wrote a 2D Finite Element program for Axial Loaded Plates, but the results are unexpected
TLDR: I used Python to write a 2D Finite Element program using 'Constant Strain Triangles' and my beam keeps pointing slightly upwards instead of straight sideways (like the force). I'm new to FEA and ...
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At what l/d ratio will a frame element start to behave as a shell element?
I'm working in ETABS. There are few columns of dimension 300mmx1400mm. The height of building is 36.6 meter above ground level and the dimension of building is 26mx68m. I'm getting the time period of ...
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Why does smoothed aggregation multigrid method used as preconditioner in conjugate gradient slows down the solution time?
I'm solving a system of linear equations obtained from the FEM discretization of a simple linear elasticity problem on a cube with zero displacements at one plane and a load on the opposite one. The ...
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Well posedness dirichlet BC in elasticity
I always thought that a Dirichlet BC need to be prescribed on at least one part of the domain in order for linear elasticity to be well-posed. Is this correct?
But I was recently told by a colleague ...
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Determining Displacement Field on a Sphere
I need to find the displacement field for this sphere shape in terms of $\delta$. So far, by applying boundary conditions, I know $u_r = u_\theta = u_\phi = 0$ at $r = a$ and $u_r = \delta, u_\theta = ...
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When does reduced integration lead to artificial zero energy modes in stiffness matrix?
This question relates to the topic of locking free finite element development.
In the case of application of reduced integration to global stiffness matrix for the Timoshenko beam element with ...
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Why the solid FEM problem can not be solved after constraining 3 degrees of freedom?
I write a simple MATLAB code for solving solid FEM problem.
The problem looks like that
(1) (2)
x-------x
| / |
| / |
| / |
x-------x
(3) (4)
...
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Dynamic linear elasticity problem is stiff (numerically)
I am considering a dynamic linear elasticity problem applied to a simple structure such as a beam. In system form, the PDE can be written as $M \ddot{X} + D \dot{X} + XK = F$ where $X$ represents the ...
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Extracting FEM matrices in matlab pde toolbox
I am trying to follow the dynamic linear elasticity in Matlab, link here. My goal is to extract the FE Matrices using the function assembleFEMatrices in matlab and solve the resulting system of second-...
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Evaluation of slope at iteration ith - Newton-Raphson method
I'd like to know how Ansys computes the slope (=stiffness matrix) at point x1 in figure. I'm studying the way in which Ansys uses the Newton-Raphson method when there are nonlinearities.
In the slide ...
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