3D Elements

In ATLAS the following Finite Elements (FE) are available :

  • ELE_TYPE = 1 tet4 : 4-noded tetrahedral element;

  • ELE_TYPE = 2 hex8 : 8-noded hexahedral element with a fully standard integration;

  • ELE_TYPE = 3 hex8sr : 8-noded hexahedral element with a selective-reduced integration;

The local stiffness matrix of the element \(\mathbf{K}_{e}\) is defined by the following integral over the element volume \(V_{e}\) :

\(\mathbf{K}_{e} = \int_{V_{e}} \mathbf{B}^{T} \mathbf{D} \mathbf{B} dV\)

where \(\mathbf{B}\) collects the derivatives of the shape functions and \(\mathbf{D}\) is the elasticity matrix.

The next sections show how this integral is computed for the different types of FE.