Finite

Today, I intend to explain the last of the finite element equation methods : the weighted residual methods Among them, the most widely used Galerkin's method will be explained. Assuming there is a differential equation $Du(x)=f(x)$ for $u(x)$, and the approximate solution for $u$ is denoted as $\hat u$, then since $u \ne \hat u$, $Du(x)=f(x)$ is satisfied, but $D\hat u - f \ne 0$. This is referr..

The book(Darly L.Logan - A First Course in the Finite Element Method) explains the principle of virtual work as follows. If a deformable body in equilibrium is subjected to arbitrary virtual (imaginary) displacements associated with a compatible deformation of the body, the virtual work of external forces on the body is equal to the virtual strain energy of the internal stresses. In other words,..

Three main ways to derive finite element equations. 1. Direct method or Direct equilibrium method for structural analysis problems 2. Energy Methods and principle of virtual work 3. Weighted Residual Methods Of the three methods, the direct method is the simplest and can clarify the physical understanding of the FEM. However, it is limited to finding the stiffness matrix of a one-dimensional ele..

I remembered that in my previous post(13_Pendulums) I said that I would explain the Finite Element Method(FEM) later. 13_Pendulums There are a lot of interesting examples in the RADIOSS example, so I'll be working through them for a while. In this post, I'll going to perform a Pendulums example. There was also an example file in HyperMesh's installation path. However, due to the diffe finite-ele..

There are a lot of interesting examples in the RADIOSS example, so I'll be working through them for a while. In this post, I'll going to perform a Pendulums example. There was also an example file in HyperMesh's installation path. However, due to the different versions, the example in the previous post was slightly different. In this example, we're dealing with a gravitational contact with no lo..