Finite

${\sigma _x}$ and ${\sigma _y}$ is the normal stress, ${\tau _{xy}}$ is the shear stress acts on the x edge in the $y$ direction, ${\tau _{yx}}$ is the shear stress acts on the $y$ edge in the $x$ direction. Represented by the vector column matrix as follows. And general definitions of normal and shear strins as follows. Represented by the vector column matrix as follows. For plane stress, the a..

In this post, I'll conduct a crash analysis of the mid rail using HyperCrash. Model - Material Piecewise linear RHO_I(Initial density) : 7.85e-6 E(Young's modulus) : 206 Nu(Poisson's ratio) : 0.3 Model - Property Shell Thick(shell thickness) : 1.6 Contact interface Stfac(Scale factor for stiffness) : 1 Gapmin(Min. gap for impact activ) : 0.9 Fric(Coulomb friction) : 0.2 Control Card RUN_NAME_NUM..

Continuing from the last post, in this post, I'll analyze the fluid structure coupling example and look at the results. In HyperCrash, load the .rad file. Part It consists of a tank container and meshes for air and water. Property Since hourglass was explained in the previous post(12_S-Beam Crash),I won't go into detail here and will focus only on setting the parameters. Tank container hm(Shell ..

In this post, I will execute the "fluid structure coupling" example found in the RADIOSS guide. The description in the guide is as follows. Solshing inside a fuel tank by simulating the fluid structure coupling. The tank deformation is achieved by appling an impsed velocity on the left corners. Water and air inside the tank are modeled with the ALE formulation. The tank container is described us..

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,..

I solve an example problem using the direct method explained in previous post. The problem as follows. Each element stiffness matrix as follows To expand each element stiffness matrix to the size of the global stiffness matrix, simply add rows and columns of zeros for displacements not related to that element. Assembled in to the global stiffness matrix, as follows. Organized in the form K=KU Gi..

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..

In the previous post, I talked about part and property. Today, I explain to other part in pendulums example Material Just one material for this example. Model - Material Create New - Elastic and Hyperelastic - Linear elastic (1) In reality, for most materials density does not change, but in simulations, we sometimes need to simulate special environments such as high temperature or high pressure,..