All Questions
156 questions
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42
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How to connect two surfaces to create a solid on MATLAB?
So I have this code where I am creating two surfaces using zernike coefficients and polynomials. Now I want to connect them and make it as a solid object. How can I do that in Matlab? The ...
- 73
2
votes
1
answer
86
views
Why would finite deformation theory be necessary in an updated Lagrangian formulation?
I am recently informed about the large deformation theory, and its concepts like curvilinear coordinates. But so far I understand in an updated Lagrangian formulation, the reference configuration is ...
- 151
0
votes
0
answers
128
views
Heat Equation for fast source with FiPy
I'm trying to solve the following differential equation with FiPy, basically laser irradiation on a surface
$$
\rho_{s}C_{p,s}\frac{\partial T}{\partial t} = k_{s}\frac{\partial^{2}T}{\partial x^{2}} +...
- 11
2
votes
2
answers
150
views
How to calculate the deformation gradient between two configurations of material points?
Let's say, I have a triangular element which its initial and deformed coordinates are taken from measurements, so I have the point coordinates. Please also consider a certain rigid body translation ...
- 151
3
votes
0
answers
53
views
Datasets for inverse heat transfer problems
I was wondering if there is an available, real-life known inverse heat transfer problem dataset to benchmark oneselfs algorithm, as in MNIST for deep learning. Talking about... (well in this case I ...
- 191
1
vote
1
answer
256
views
Coupled Partial Differential Equations
I'm trying to solve the following system of coupled differential equations, the two-temperature model for $e$ = electrons and $l$ = lattice.
$$
\rho_{e}C_{p,e}\frac{\partial T_{e}}{\partial t} = k_{e}\...
- 11
1
vote
0
answers
50
views
How can I apply a mixed boundary condition to a multi-material heat transfer problem using Crank-Nicolson?
I am working on a mixed material model for a melting material and need to enforce both a Dirichlet and Neumann type condition at the interface. Subject to an external surface heat flux at the top of ...
- 11
3
votes
1
answer
191
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how to compute the rate of deformation gradient in finite-element context?
I am implementing hyper visco-elastic material models similar to those from Pioletti et al. see here
There, a viscous potential, e.g
$W_v = \eta [I_1-3]J_2 \quad \text{with} \quad J_2 = \mathrm{tr}(\...
0
votes
0
answers
38
views
Thermo Hydraulic Mechanical modeling of energy wall slab in Comsol multiphysics
I am currently working on a complex simulation project involving an energy wall slab, and I need assistance in accurately modeling and validating it using COMSOL Multiphysics. Here are the details of ...
0
votes
0
answers
74
views
Lumped (diagonal) vs. consistent (non-diagonal, symmetric) mass matrix in Nastran
I've been tinkering with DMAP to explore the procedure followed by Nastran when solving a complex modes analysis.
I've reached a passage I cannot understand: at some point Nastran formulated what it ...
0
votes
1
answer
124
views
What do diagonal (DOF-to-self) terms of stiffness matrix physically mean?
I am used to interpreting each entry of a solid mechanic system's stiffness matrix as a 1D (linear or angular) spring joining one DOF (column index) to another (row index).
But this interpretation ...
2
votes
0
answers
106
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Iterative solvers for problems in solid and structural mechanics
I am looking for comprehensive literature (papers, books, reports etc..) on iterative solvers for solid and structural mechanics problems to understand the best iterative solvers and preconditioners ...
- 964
1
vote
2
answers
121
views
How to handle non bilinear weak form?
I solved the 2D heat equation using the finite element method. It all went well first with the adiabatic case, however problems occured when I introduced cooling with the enviroment.
I modeled the ...
- 63
0
votes
1
answer
53
views
How to implement the interface extension of fluid "displacement" in ALE?
In ALE, we first set a referenced space for fluid, then we extend the boundary fluid displacement to the whole fluid region, take harmonic extension as an example, we need $$\Delta \left ( \hat{u} \...
- 193
2
votes
1
answer
411
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Where am I making a mistake in solving the heat equation using the spectral method (Chebyshev's differentiation matrix)?
I would like to numerically solve the following heat equation problem:
$$ u_t = \Bigg(2{a \over l}\Bigg)^2 u_{xx} \tag 1$$
$$ x \in [ -1, 1 ] \tag 2$$
$$ u(x, 0) = 0 \tag 3$$
$$ u(1, t) = A \sin \Bigg(...
1
vote
0
answers
41
views
Recommendations for some new books about computational contact mechanics in solid mechanics
I want to simulate some frictional contact problems, but I'm not familiar with this field, could you please recommend some new books as introductions?thank you
- 193
2
votes
1
answer
163
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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 ...
- 123
1
vote
1
answer
339
views
Why does scipy Conjugate Gradient solver fail to converge for non-steady heat equation using Crank-Nicolson method
Could someone please explain why my implementation of the Crank-Nicolson method applied to the non-steady heat equation won't converge? There shouldn't be any nonlinear aspects to my implementation ...
- 13
2
votes
0
answers
114
views
Efficient heat diffusion implementation with varying coefficients
I have the following heat diffusion equation:
\begin{alignat}{3}
\partial_t u(t, \vec{x}) &= g(\vec{x})\Delta u(t,\vec{x}), &\quad& \vec{x} \in\Omega, \, t\in(0,\infty],\\
\partial_n u(t,\...
- 2,892
2
votes
1
answer
207
views
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}...
- 23
0
votes
2
answers
169
views
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,...
- 23
5
votes
1
answer
107
views
Prediction of sphere (i.e. roast) core temperature heated in an oven
The real-life problem
Assume I put a spherical roast with initially constant temperature of start_temp=25 (°C) into an oven with ...
- 161
1
vote
1
answer
308
views
2D Heat equation solved with finite element method converges in skewed way
I tried to solve the 2D heat equation with the finite element method, using triangles as elements. Currently generated by a Delaunay triangulation. The base function I'm currently using is basically ...
- 63
0
votes
1
answer
143
views
How to get a normalized gradient with FreeFem++?
I am trying to use FreeFem++ to solve the heat geodesics algorithm.
The algorithm is:
solve $\dot u = \Delta u$ at a specific time $t$.
compute $X = \frac{\nabla u_t}{|\nabla u_t|}$
solve $\Delta\phi ...
- 379
4
votes
1
answer
237
views
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 ...
- 45
0
votes
0
answers
84
views
How to solve evolution equation numerically?
How do I solve the following evolution equation numerically:
$$
\dot{\boldsymbol{\mathcal A}} = -\lambda A_1|\boldsymbol{s}-\boldsymbol{\alpha}|^2\left[(\boldsymbol{n}_r:\boldsymbol{\alpha})\...
1
vote
0
answers
115
views
Accuracy of the Crank-Nicolson method for non-linear, inhomogeneous heat equation
I am currently coding a solution to the following PDE:
$\frac{\partial T }{\partial t} =\frac{\partial}{\partial \theta}(A(\theta ,\phi )\frac{\partial T }{\partial \theta}) +\frac{\partial }{\partial ...
- 11
2
votes
0
answers
113
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Conceptual doubt regarding 2D conjugate heat transfer modelling (COMSOL and Mathemtica)
I have been dealing with some conceptual flaws in my understanding of modelling, which I will elaborate herein. I am modelling conjugate heat transfer of a reciprocating fluid, which flows with ...
- 41
3
votes
1
answer
316
views
Is it really necessary to solve a system of linear equations in the Finite Element Method?
When we solve some boundary value problem by Finite Element Method, the appropriate system of linear equations is built, $$Ax=b.$$
Usually we use the solution x just for plugging it into some ...
2
votes
1
answer
516
views
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 ...
0
votes
1
answer
148
views
Problem with my Octave code (unsteady heat equation with FEM)
I want help with my Octave code regarding the unsteady heat equation.
My geometry and mesh are generated with FreeFEM++, so there is no problem with that (I tried it with the steady problem with no ...
- 3
0
votes
1
answer
127
views
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 ...
- 1
1
vote
4
answers
929
views
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 ...
- 31
6
votes
1
answer
411
views
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 ...
- 201
1
vote
2
answers
388
views
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 ...
- 133
1
vote
1
answer
161
views
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....
- 73
1
vote
0
answers
146
views
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} \...
- 31
1
vote
1
answer
153
views
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 ...
- 23
1
vote
0
answers
79
views
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 $\Delta$ ...
- 325
2
votes
0
answers
92
views
How to accelerate the computing of implicit finite difference method for heat conduction between two solids
Edit on May 3rd: I have found the problem. Because the difference of between $k_1$ and $k_2$ is huge, a very small time step need to be chosen so that the right green part can "feel" the ...
- 21
0
votes
1
answer
78
views
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 ...
- 133
3
votes
1
answer
367
views
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 ...
- 325
3
votes
2
answers
1k
views
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 $F = I \implies C = F^TF = I \implies I_1 = 3$
...
- 325
2
votes
0
answers
294
views
Rosenthal equation for multi track
Rosenthal's equation lets one calculate the temperature profile of a moving point heat source analytically for thin and thick plates. For simplicity I use the equation for thick plates defined as:
$$T-...
- 840
3
votes
2
answers
422
views
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 $\...
- 435
1
vote
1
answer
2k
views
How to solve heat equation in spherical coordinates with finite differences?
I have a problem dealing with heat transfer which is spherically symmetrical. I was thinking it should be possible to solve this as a 1d problem in spherical coordinates using the radius only.
...
- 111
3
votes
2
answers
303
views
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 ...
2
votes
2
answers
64
views
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 ...
- 133
1
vote
0
answers
252
views
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 ...
2
votes
0
answers
76
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.
...
