4

The primary problem is that the CST approximation has a different displacement response depending on the orientation of mesh elements relative to the applied element loading (you're only allowed to applied forces on the nodes of triangles, so distributed loads must be approximated). You can see the effect of this by looking at only a single triangle ...


2

You can use discontinuous Galerkin methods also for $P_0$ elements. It's true that the gradient in the cell interior is zero, so your formulation will exclusively consist of the jump terms at cell interfaces.


2

The given $$ \int_\Omega v \frac{\partial}{\partial x}\left( \frac{\partial u}{\partial x} + \frac{\partial u}{\partial y}\right) dx dy = 0 $$ becomes $$ \int_\Omega \frac{\partial}{\partial x}\left[v\left( \frac{\partial u}{\partial x} + \frac{\partial u}{\partial y}\right) \right] dx dy - \int_\Omega \frac{\partial v}{\partial x}\left( \frac{\partial u}{\...


2

That depends a lot on the specific numerical method in use, 2D/3D, and application. Common reference problems are likely to have an analytical solution or be verifiable qualitatively by some fundamental principles. I would bring up the common examples I use personally from each category: Wave scattering from a perfect electric conductor (PEC)/dielectric/...


2

If I understand your question correctly you're solving a linear elasticity problem using conjugate gradient and it's preconditioned with a preconditioned AMG solver? It seems to me that this may be overkill for a pretty well behaved problem, and that could be why you don't see much of a speed-up. Just to elaborate a bit. I think it makes more sense to just ...


2

Here is how you want to test this and you need only two elements in the mesh. You want to define your left BC so it will reproduce a constant stress state as follows: assuming $u$ is the displacement in the x-direction and $v$ the displacement in the y-direction, set $u=0$ at the two nodes on this edge and $v=0$ at the bottom node on this edge. The two nodes ...


1

The general form of the equation is $$ \frac{\partial \sigma_{ij}}{\partial x_j} + F_i = \rho \frac{\partial^2 U_i}{\partial t^2} $$ where the stress is given by $$ \sigma_{ij} = \sigma_{ij}(U) = 2 \mu \varepsilon_{ij} + \lambda \varepsilon_{kk} \delta_{ij}, \qquad \varepsilon_{ij} = \varepsilon_{ij}(U) = \frac{1}{2}\left( \frac{\partial U_i}{\partial x_j} + ...


1

I think that the answer by @helloworld922 is misleading. The first image shown in the answer seems to be an effect of the Poisson effect, a contraction in one direction due to loads applied in the other direction. If you want to obtain a state of constant stress in your simulation you need to change the boundary conditions that you are applying, namely: all ...


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