Questions tagged [finite-element]
A means of solving ordinary and partial differential equations. The domain of the problem is broken up into elements, and the solution in each element is expanded in a basis of functions. The Finite Element Method lends itself well to adaptive refinement, irregular geometry, and good error ...
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17 views
Simple FEA truss example help
I'm trying to find the global stiffness matrix for the truss example in the picture given, but I'm a bit confused.
I know the matrix should be 8x8, but I don't understand how. My understanding is ...
3
votes
0answers
59 views
$L^2$ norm error estimates of conforming FEM about Poisson’s equation with mixed boundary conditions
Consider Poisson’s equation
$$- \Delta u = f{\rm\qquad{ in }}\;\Omega $$
with following mixed boundary cconditions
$$u = g{\rm\qquad{ on }}\;\Gamma \subset \partial \Omega $$
$$\frac{{\...
0
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0answers
28 views
What is the difference between Abaqus and Calculix contact input?
I would like to say first that am new at using Calculix.
I'm using Abaqus/CAE to create a cup deep drawing simulation and everything worked perfectly but my objective is to run the same exact ...
0
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1answer
63 views
Penalization parameter for DG with jump penalization
I adapted this FEniCS code for my problem and I'm wondering if there is any good resource about how to choose the penalty parameter $\alpha$? Best case would be, if I can define it through some ...
0
votes
2answers
69 views
Taylor-Hood finite hexahedral elements, pressure diverging
I am developing a FEM fluid solver using the Taylor-Hood algorithm, i.e. quadratic interpolation for velocity, and linear for pressure.
I have developed the code for 2-D quadrilaterals and triangles, ...
2
votes
1answer
92 views
Prevent single node spikes in a FEM-simulation (using continuous Galerkin)
I am trying to solve a non-linear time-dependent heat equation
$$\partial_tT=\nabla \left(k_T(T)\nabla T\right) + f$$ (similar to question Solving a non-linear heat equation with the galerkin method ...
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0answers
55 views
Coupling multiple structural components without introducing numerical problems
Is there a recommended way of coupling together multiple sets of nonlinear equations representing structural components that does not cause problems for the solver? I believe this may have something ...
-2
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0answers
61 views
Stiffness Matrix Computation for 6-nodes Iso-parametric Triangle
Hi Guys so basically i'm dealing with a neutron diffusion equation. I am concerned with the fission term:
I am concern with the integral of following term:
and i am using 6-nodes iso-parametric ...
0
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0answers
19 views
Globalization strategy for semismooth Newton methods
Currently, I'm trying to implement a semismooth Newton method for a nonlinear problem of the form
\begin{align*}
a(y,v) + \langle F(y), v\rangle = \langle f,v\rangle \quad \forall v\in V
\end{align*}
...
0
votes
1answer
79 views
seminorm of solutions of Laplace equation
If $u_1$ and $u_2$ are solutions of (weak-form) Laplace equation on a connected domain $\Omega$, with Dirichlet boundary values $u_{\partial\Omega, 1}$ and $u_{\partial\Omega, 2}$, respectively. If $$...
0
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1answer
63 views
Compute outward normal and surface area for 8 noded brick element in FEA
I have a cube which is divided into 8 small cubes by bisecting each edge, I am trying to find out the surface area of each of the faces and the corresponding outward normals for them. This operation ...
2
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0answers
60 views
Which SciPy nonlinear solver when Jacobian is analytically known and sparse?
I have a nonlinear function fun with n inputs and n outputs. I also have a function jac which calculates the Jacobian, which is ...
4
votes
1answer
59 views
Stabilization parameter for an elliptic equation
I simply want to solve the elliptic equation:
$$
-\kappa \nabla^2 u + u = f
$$
where $f\in [0,1]$. When using continuous Galerkin with Lagrange elements, I have noticed that $\kappa$ has to be greater ...
0
votes
1answer
59 views
Connectivity matrix in Finite Element Method in Triangular elements
Imagine a simple triangular base mesh in finite element method with an unknown number of elements (varying by the user). How can connectivity matrix be coded to be generated automatically?
1
vote
1answer
116 views
Can a second-order ODE be “inconsistent” with its boundary conditions?
I am trying to solve a set of coupled, nonlinear ODEs. The only dependent variable is a 1-dimensional spatial coordinate, let's call it $x$. For now, I've managed to approximate away some of the ...
1
vote
1answer
125 views
Does a generic method for solving a system of PDEs exist?
There are generic methods for solving systems of ODEs numerically. Are there generic methods for PDEs? If so, what are they? If not, why not? To elaborate...
Any set of ODEs can be written in ...
0
votes
1answer
76 views
How is nonlinear flux interface term assembled for Discontinuous Galerkin method for hyperbolic conservation laws?
For example, for 1D Burgers equation
$$
u u_x = 0 \\
$$
equivalently,
$$
\frac{dF(u)}{dx} = 0\\
F(u)= \frac{u^2}{2}
$$
If I want to obtain $A_{ij},i\ne j$ for two DOFs ($U_i$ and $U_j$) of two ...
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0answers
51 views
Confusion about Rayleigh beam formulation
Sorry for disturbing you, my friends. Recently, I am reading books on Rayleigh beam theory where the rotary inertia can be taken into account without introducing rotational degrees of freedom. For ...
1
vote
0answers
35 views
How to analyze the dispersion and dissipation of a certain FEM?
In Finite Difference method or Finite volume textbook. Dispersion/Dissipation can be analyzed by set $u = u_0\exp{\omega t +\mathbf{kx}}$。
However, I cannot find something about this kind of analysis ...
3
votes
1answer
85 views
Why Coercivity is so important in FEM framework?
I know Lax-Milgram theorem is fundamental to FEM. But it did not explain what will happen if coercivity is not met.
My understanding is if it is met, eigen value of the operator (or its corresponding ...
0
votes
3answers
114 views
Why is the test function space in FEM chosen with homogeneous boundary conditions?
It is so confusing, especially when I learns discontinuous galerkin method in broken Sobolev space and weak Dirichlet boundary condition.
If the trial function is chosen with homogeneous boundary ...
3
votes
0answers
43 views
Should I expect computational gains using a second-order splitting method here?
I am trying to solve a three-dimensional baroclinic transport problem. The hydrodynamic (three-dimensional shallow water) equations are:
\begin{align}
\nabla \cdot \vec{v} = 0, \tag{1} \\
\frac{\...
1
vote
1answer
84 views
A reference request for computational plasticity
My background is in applied mathematics and I'm trying to learn plasticity. I have successfully understood the theory and finite element implementation of: linear elasticity, hyperelasticity (Neo-...
1
vote
0answers
78 views
Basic approach for numerical solution of PDE
I'm looking for some guidance on how to write a program to numerically solve a PDE. As an example for comparison in 1D:
$$\frac{d^2u}{dx^2} = f\;\;\;\;u(0) = 0\;\;\;\;u(1) = 0$$
We could try 6 ...
4
votes
2answers
101 views
Analytical testing/quality control for scientific software in professional setting
I am charged with maintaining a buildserver on Teamcity which is meant to test our in house FE software. Currently our test suite consists of a list of benchmarks which run every time a commit is made ...
2
votes
1answer
50 views
Oscillation term in a posteriori error estimator
Assume that in the a (residual type) posteriori error estimator of some PDE is a term of the form $h_T\|g\|_{L^2(\Omega)}$ involved where $h_T$ is the diameter of an element and $g$ is some known data ...
2
votes
1answer
104 views
Influence of node numbering in a FEM problem?
In a FEM mesh, does the order of node numbering in an element has any importance?
I'm currently trying to code my own FEM solver, which seems to work fine with quadrilateral elements, however I'm ...
1
vote
0answers
81 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, ...
5
votes
1answer
119 views
How is rigid bodies implemented in finite element codes
I am writing a finite element code for structural analysis, and I want to implement rigid bodies. How is this usually done? Say that I have a square mesh, with one half of the mesh being defined rigid ...
0
votes
1answer
100 views
Parallelization of FEM calculations
I need to conduct some FEM calculations and I am wondering whether parallelization would be a good idea.
The trouble is that my model is not especially large so it takes few seconds to solve a single ...
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0answers
36 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 $...
2
votes
1answer
95 views
Help debugging finite element solution in nonlinear elasticity
I'm writing some code to solve problems in nonlinear elasticity using finite element methods. I have been following Bathe's book but I am having trouble with some nagging details.
My question is ...
0
votes
0answers
26 views
CGFEM - Adding a solvent flux to a 1D adv-diff system as a source term
I have a system consisting of a narrow pipe with porous walls where the inlet conditions are flow rate and initial concentration, and the goal is to determine the change in concentration along the ...
4
votes
2answers
131 views
Getting started with finite element modelling
I'm a high-schooler building a small vehicle for an independent study. I've had finite element modelling recommended to me as a way to save time during the design process, and I'd like to try it out. ...
0
votes
1answer
67 views
How to simulate thermal expansion in a 2D plane using FEA?
I am trying to model 2D thermal expansion of a square area inside another square using FEATool. I have simulated plane strain by incorporating forces pointing along the $[1 \,\,\, -1]^T$ direction ...
1
vote
0answers
48 views
Getting started with FEM: Ill-conditioned matrix when evaluating flux terms in conservation law?
I have a system of conservation laws of the form
$$ \frac{\partial \mathbf{q}}{\partial t} + \nabla \cdot \mathbf{F}\!\left(\mathbf{q}\right) = 0 $$
I want to use finite elements to solve this ...
0
votes
0answers
21 views
Enforced (prescribed) displacements at more than 1 node of FE model [duplicate]
If I have a structural finite element model (could be continuum or frame elements), I was wondering if there is a way to enforce a prescribed displacement at more than 1 node in the model in a ...
5
votes
2answers
180 views
Unstructured mesh vs hybrid structured/unstructured for numerical simulations
While answering one of the questions on meshing process, I encountered a lack of understanding on my end for the comparison of the mesh quality.
First, consider an unstructured mesh created in GMSH ...
1
vote
1answer
79 views
How to implement Galerkin Method of Lines / FEM with black box integrators in scipy
Suppose I have some time dependent PDE, which can be written in the strong form as
$$
\frac{\partial u}{\partial t} + \mathcal{L}(u) = f
$$
Where $\mathcal{L}$ is some differential operator. If I ...
1
vote
1answer
68 views
Reordering algorithm for minimization of ram usage of a skyline matrix
The stiffness matrix of $Ax=B$ system of linear equations, where $A$ is an $n\times n$ symmetric matrix stored in the form of symmetric skyline matrix, that is associated with a finite element model ...
2
votes
1answer
68 views
FEM-Laplace with Dirichlet in only a few points: Nonsingular operator?
Let's consider the FEM discretization of the Laplace operator without boundary conditions, i.e.,
$$
a(u,v) = \int_\Omega \nabla u \cdot \nabla v - \int_\Gamma (n\cdot \nabla u) v.
$$
For one-...
0
votes
0answers
43 views
Applying base excitation to a MATLAB state-space
I have a state space model that was provided to me by exporting it from an external FEA program. The model can be described as
$\dot x = Ax + Bu$
$y = Cx + Du$
This model assumes forces and ...
1
vote
1answer
57 views
FE discretisation of normal to displacement vector
Having shape functions $N_i(\xi,\eta), i = 1,...,N_n$ and, a normal vector $n = (n_x,n_y,n_z)$, a thickness function $F_\tau (\zeta), \tau = 1,...,N_\tau$ and nodal variables $\mathbf{Q}_u = (Q_u,Q_v,...
4
votes
0answers
64 views
Data transfer in the context of adaptive mesh in finite element method (FEM)
In the context of adaptive mesh in FEM, after a new mesh is created, the data on the old mesh are to be transferred to the new mesh. For the data on the integration points (IPs), it seems the usual ...
5
votes
2answers
123 views
Residual norm of PDE discretization: correspondence in the continuous problem?
Solving a linear PDE like
$$
\Delta u = f \quad\text{on } \Omega,\\
n\cdot \nabla u = 0 \quad\text{on } \Gamma,
$$
with Finite Elements usually goes like this:
Create the discretization $Au=b$ via
$$
...
1
vote
2answers
487 views
How does one calculate reaction force in FEA?
I wrote a UEL (User Element in Abaqus) for one element and compared to a reference UEL which used standard FEM, where the results agreed satisfactorily, except the reaction force. The stress, strain, ...
0
votes
1answer
73 views
Structural mechanics simulation using FLUENT compared to analytical solution
This is a continuation of my previous post, 1D analytical solution vs FEM solution for a bar under compression. For some reason, I cannot comment in it.
The analytical solution to the 1-D static ...
2
votes
1answer
94 views
Non-linear flux interface condition - variational formulation
Context: I am working on implementing this paper and I am struggling to come up with a variational formulation for the Butler-Volmer interface conditions.
To simplify my question I consider the ...
0
votes
1answer
59 views
Lagrange multipliers in minimization problem with bilinear forms
Let $V$ a Hilbert space, $a:V\times V\rightarrow \mathbb{R}$ a bounded, symmetric and positive bilinear form and $f:V\rightarrow\mathbb{R}$ bounded.
Is well known that problem
$$\left\lbrace\begin{...
0
votes
1answer
107 views
Discontinuous Galerkin - Inhomogeneous Dirichlet B.C. for 1D Poisson Equation
I am trying to get some code working for the 1D Poisson equation using the textbook: Nodal Discontinuous Galerkin Methods Algorithms, Analysis, and Applications.
I use the following formulation (for ...
