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.