The 20-node hexahedron (or brick element) is a 6-sided solid element with quadrilateral shape functions formulated as an isoparametric element. This element is more accurate than the 8-node hexahedron and can be used in a coarser mesh, but at the cost of computation time.

References

1. Abaqus Theory Manual - Isoparametric Continuum Elements
2. Nikishkov, G. P. "Introduction to the Finite Element Method." University of Aizu, Aizu-Wakamatsu 965-8580, Japan. 2007 Lecture Notes

Element Geometry

The 20-node hexahedron is formulated as an isoparametric element such that element geometry is inconsequential. The local isoparametric coordinate axes are $\xi,\eta,$ & $\gamma$. It contains eight vertex nodes and 12 mid-side nodes, none of which have rotational degrees of freedom. The mid-side nodes appear in the final stiffness matrix and are added to the overall model.

Where:

$-1≤\xi≤1$

$-1≤\eta≤1$

$-1≤\gamma≤1$

Degrees of Freedom

The 20-node hexahedron formulation contains three degrees-of-freedom (DoFs) at each node:

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

There are 8 vertex nodes and 12 mid-side nodes defined for this formulation. These nodes are numbered from 1 to 8 in a counter-clockwise direction, bottom surface first, then top surface, vertex nodes first, then mid-side nodes.

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

$\begin{bmatrix}x_1 & y_1 & z_1 & x_2 & y_2 & z_2 & ..... & x_{20} & y_{20} & z_{20} \end{bmatrix}$

Where: