4
votes
Elements on a triangle (FEM)
You can rather easily write Lagrange bases over any dimension simplices. Define a $k$-simplex as the convex combinations of $k+1$ points, e.g. a triangle is a $2$-simplex.
Definition
As a triangle $K$ ...
- 321
4
votes
Accepted
2D Heat equation solved with finite element method converges in skewed way
The problem was that the LHS of the weak form was wrong, the correct one is:
$$
-\int u_{x} v_{x} + u_{y} v_{y} dxdy
$$
Instead of
$$
-\int (u_{x}+u_{y}) (v_{x}+v_{y})dxdy
$$
Thanks to whpowell96 for ...
4
votes
Energy conservation in the solution of the Helmholtz equation
Mathematically, you have the Diriclet energy:
$$
E = \int (-|\nabla\psi|^2+k^2|\psi|^2-f\psi^*-f^*\psi)d^Dx
$$
whose minimisation gives you the Helmholtz equation. The natural energy current would be:
...
- 141
3
votes
Accepted
Mass Matrix of Tetra10 Element
Generally speaking, denoting $(\phi_i)_i$ the basis functions, the Mass matrix entries are
$M_{ij} = \int_{\Omega} \pmb\phi_i \cdot \pmb\phi_j $
With 10 nodes, I assume you are dealing with the degree ...
- 321
2
votes
Accepted
finding weak form of nonlinear differential equation for FEM simulation
First notice that
$$
(k_3 - k_1)\sin(u)\cos(u)(u')^2 + (k_1\cos^2(u) + k_3\sin^2(u))u'' = ((k_1\cos^2(u) + k_3\sin^2(u))u')' + (k_1 - k_3)\sin(u)\cos(u)(u')^2.
$$
I choose to rearrange our equation so ...
- 1,567
2
votes
Accepted
Determination of the domain of nonlinearity in a Neo-Hook solid model (Finite elements)
Since your $\lambda_{11}$ is close to unity, it means that your response will be close to linear, because your strain is small. You have not provided enough strain for the non-linearity to kick-in.
I ...
- 519
1
vote
Pretension a truss mechanism (using the direct stiffness method)
So presumably you intend to pretension the truss members using some other
prescribed loading condition?
When you say you want to account for the effects of this pretension, I assume
you are thinking ...
- 5,864
1
vote
how to solve a coupled nonlinear partial differential equations(Boundary Value Problem)
Closing eyes about the dynamics of the PDE, it is possible to write the finite difference and finite element formulations of the PDE.
In FEM, you can consider both $\theta$ and $\phi$ as unknowns and ...
- 131
1
vote
Geometrically nonlinear finite element problem and mesh distortion
In FEA, the basis functions are defined over a reference element, here a unit square. This is a "function basis factory" of sorts, as you then write a global basis restricted to a given ...
- 321
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