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First, I would like to mention that orthotropic materials have 9 parameters, and not 12, as can be implied from your question. The simplest approach would be to compute the arithmetic/geometric mean …

You take an arbitrary volume $V$ and use the translational and rotational equilibrium equations over it. They read \begin{align*} \int\limits_A \mathbf{t}\mathrm{d}A + \int\limits_V \mathbf{f} \mathrm …

It is not true that a third-degree polynomial gives you the exact solution always. For example, for a cantilever beam with a uniform load, you get a fourth-order solution in the displacement.

if you need a program with 3D capabilities I would suggest Elmer, that provides a graphical user interface and is easy to use. If 2D capabilities are enough, I would suggest Agros that has a really ni …

In general, no. For displacements, you have the following system of coupled differential equations: $$(\lambda + 2\mu)\nabla\nabla\mathbf{u} - \mu\nabla\times\nabla\times\mathbf{u} + \mathbf{f} = \r …

This seems to be more of a Physics question than a Computational Science one. Due to the symmetry of your problem, you can conclude that the solution is of the form $$\mathbf{u} = u_r \hat{\mathbf{e …

To understand what you are doing you need to dance along with all those many concepts and equations. There is no shortcut there. If you are asking about an explicit expression for the local stiffness …

I am guessing that RFEM uses Euler- Bernoulli beam theory. In that case, you need elements that have continuous derivatives. This is achieved using Hermite interpolation where you end up with cubic po …

The elastic energy stored in your solid is computed as $$\Pi = \int_\Omega \sigma : \epsilon\, \mathrm{d}\Omega\, ,$$ where $\sigma$ is the stress tensor, $\epsilon$ is the strain tensor, and $:$ is t …

You could also take advantage of the symmetry of the problem. As an added advantage you end up with a mesh with half the elements. I would just consider half of the beam and add roller constraints on …

Let us consider the uncoupled mechanical problem. Hence, we have 10 unknowns $\{\rho, \mathbf{v}, \underline{\underline{\sigma}}\}$, assuming that the stress and strains are symmetric (this might not …

Regarding your first question. One option would be to try to use what is commonly done in laminates for Kirchoff-Love plates, I would not know how good is that approximation, though. Another option, …

First, let us properly describe the boundary conditions of your problem. You have the following: Fixed/encastre. The left hole is fixed and displacements are zero there. These boundary conditions are …

TL;DR: as answered by @BillGreene as a comment a model with plasticity is nonlinear. Even when the stresses are not high enough the solution process is probably different from a linear one. Regarding …

There are two main ways to write stress/strain tensors as 6 components vectors: Voigt notation, that is the most common; and Mandel-Kelvin notation, that has the advantage of writing stress and stra …