Questions tagged [solid-mechanics]

Studies the behavior of solid materials, and deformation under the action of forces

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38 views

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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2answers
144 views

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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100 views

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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31 views

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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1answer
76 views

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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1answer
78 views

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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1answer
201 views

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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3answers
70 views

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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1answer
328 views

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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47 views

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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3answers
233 views

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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1answer
553 views

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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2answers
68 views

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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1answer
144 views

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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3answers
162 views

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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30 views

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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1answer
105 views

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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35 views

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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1answer
98 views

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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0answers
64 views

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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1answer
93 views

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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1answer
88 views

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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261 views

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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2answers
542 views

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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1answer
181 views

Reference request: Riks method (Nonlinear FEM)

I'm struggling to find a good detailed reference explaining the Arc-length method or, more generally, Riks method and its derivations. I looked for the classical books in nonlinear mechanics (the ones ...
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87 views

Strain propagation from surface to bulk in COMSOL

I am trying to simulate strain propagation from the surface into the bulk. I have a rectangular semiconductor block (~2 μm thick) on top of which metal gates (~25 nm thick) are deposited as seen in ...
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1answer
112 views

Abaqus, ANSYS, and FVM solver for thermal expansion problem converges to different values

Is it reasonable for a FEM and FVM code to converge to slightly different solutions for the same physical problem (identical BCs, geometry, properties, etc...), provided stability constraints are ...
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1answer
107 views

Split solution of FEM problem depending on number of DOF

Assume we have a 3D finite element structural problem discretized with hexahedral elements with 8 nodes and 3 degrees of freedom per node. Instead of solving the global stiffness matrix system for all ...
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29 views

Numerically computing deflection due to thermal expansion

Using linear elasticity formulation, I am attempting to numerically compute the displacement due to thermal expansion. This is done for a 3-D isotropic material. The governing equations are simply: ...
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1answer
130 views

Isotropic thermal expansion

I frequently see the equation $$ \sigma_t = E\alpha \Delta T $$ as the equation for thermal stress. Where $E$ is Young's modulus, $\alpha$ is the CTE, and $\Delta T$ is the change in temperature. ...
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54 views

Strange spectral (finite) element results of a solid plate

I tried to implement the spectral element method1 as proposed in [1]. I simulated an aluminum plate and a vertical concentrated force was applied at the middle of the top left quarter of the plate2. I ...
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1answer
90 views

Linear elasticity modeling load using traction vs. mixed BC

In classical linear elasticity, when modeling a force/load boundary condition, it appears that we could either: Use a pure Neumann boundary condition, where the 3 traction components are specified. ...
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3answers
674 views

Why is the FVM traditionally used in CFD, and FEM in computational structures?

Most CFD codes use FVM. Most computational structures codes use FEM. Why is the FEM not frequently used in CFD, and why is FVM not frequently used in FEM?
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1answer
91 views

Structural boundary conditions - rotational/translational DoFs and displacement/tractions BCs

I am a little bit confused over the concept of translational and rotational degrees of freedom (DoFs) in structures, and their relation to displacement/traction BCs. Do displacement boundary ...
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83 views

Structural Analysis Library

Can anyone recommend a structural analysis library that satisfies the following requirements: C++ API Simulate both beam elements and shell (slab) elements Both static and dynamic analysis Free and/...
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1answer
70 views

Given co-ordinates of 8 vertices, how to calculate the outward normal and surface area for each face of a irregular hexahedron?

I am working on an FEA mesh of hexahedron elements. The elemental level calculations involve finding the surface normals and area for each surface of a hex element. I preferred the vector cross ...
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1answer
128 views

Is steady linear elasticity inherently ill-conditioned?

Compared to the transient PDE for linear elasticity, the steady equations appear to less well-conditioned. Are they inherently ill-conditioned without the transient term? The condition number for ...
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1answer
165 views

Strain from FEM simulations to strain gauge measurements

I am looking for some intuition in making comparisons of FEM simulations to experimental measurements. In particular, I am interested in comparisons to strain gauge readings, and perhaps even LVDTs. ...
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32 views

Is it possible to obtain a 'relaxing lengths' for 8 node hexaedral element

I am using 3D FEM with 8-node brick elements to model a certain type of growth/expansion, which is not a plastic deformation. First, I apply a pressure/load and I get displacement and the new position ...
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0answers
78 views

Thermal stress to displacement through finite volume method

I am attempting to solve for a displacement field where I know the thermal stresses on my discretized domain, which consists of hex cells. My first question is: is easier way to solve for the ...
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1answer
771 views

What is the difference between Abaqus and Calculix contact input?

I would like to say first that am new at using Calculix. I'm using Abaqus/CAE to create a cup deep drawing simulation and everything worked perfectly but my objective is to run the same exact ...
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1answer
472 views

Purpose of compatibility equations in linear elasticity

I have a vague understanding of the compatibility equations for linear elasticity. They appear to be necessary in obtaining a unique displacement field. However, why is it that, in my papers I've come ...
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57 views

Combining fluid flow solver based on lattice Boltzmann method with a mechanical deformation solver based on finite element method

I'm thinking to couple my fluid flow solver based on lattice Boltzmann method with a mechanical deformation solver based on finite element method to take account for solid deformation in my models. In ...
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0answers
366 views

What is the mathematical and physical principle behind of RBE2 element?

I am writing a 3d linear finite element code to solve the standard linear elasticity equation on a tetrahedron mesh of a gearbox. Notice that, the two rectangular plates above the gearbox are fixed, ...
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51 views

Simplest meaningful PDE/FEM calculation for mechanical stress due to heat

W have a complicated structure on which we do some FEM calculations regarding electrical potentials and heat distribution. The equations have the form $\nabla\kappa\nabla u = f + g\rvert_{N}$ where $...
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1answer
106 views

Why are the linear elasticity equations referred to as the "equilibrium" equations?

I asked this question previously on the physics board (LINK: https://physics.stackexchange.com/questions/404539/linear-elasticity-governing-equation), but I thought I'd post it here and see if anyone ...
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1answer
306 views

Modeling orthotropic materials with isotropic assumption

This is really a general question, but my interest is primarily for structural mechanics. Say you are modeling an elastic solid material that is orthotropic. You have the orthotropic properties (...
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1answer
283 views

Boundary conditions in a four point bend test

I am looking into the four-point bend test, such as one in this YouTube video. Sample screenshot from the video illustrating the problem: I am a little confused as to how the loads are prescribed ...
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1answer
603 views

Well-posedness of linear elasticity boundary conditions

I have several questions regarding suitable boundary conditions for linear elasticity. I have read that in order for modeling linear elasticity to be well-posed, the entire boundary cannot be ...