A 6-node pentahedron (or wedge) element with linear shape functions. This element does not have rotational degrees of freedom at its nodes.

References

1. Abaqus Theory Manual - Triangular, Tetrahedral, and Wedge Elements

Element Geometry

The 6-node pentahedron is formulated as an isoparametric element such that element geometry is inconsequential. The local isoparametric coordinate axes are $\xi,\eta,$ & $\gamma$.

Where:

$0≤\xi≤1$

$0≤\eta≤1$

$-1≤\gamma≤1$

Degrees of Freedom

The 6-node pentahedron formulation contains three degrees-of-freedom (DoFs) at each node:

1. x-translation
2. y-translation
3. z-translation

There are six nodes defined for this formulation. These nodes are numbered from 1 to 6 in a counter-clockwise direction, bottom surface first, then top surface. This element formulation does not contain rotational degrees of freedom.

The local stiffness matrix is formulated with the following degree-of-freedom order:

$\begin{bmatrix}x_1 & y_1 & z_1 & x_2 & y_2 & z_2 & ..... & x_6 & y_6 & z_6 \end{bmatrix}$

Where:

$x_k=$ X-translation at node $k$