# Tag Info

### 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 $K$ ...
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 ...

### 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: ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...

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