Alternative reduced integration avoiding spurious modes for 8-node quadrilateral and 20-node hexahedron finite elements

Integrating the isoparametric 8-node quadrilateral and the 20-node hexahedron elements with Gauss integration based on the 3 point rule produces stiff elements. The excessive stiffness is mainly due to locking phenomenon. One remedy to partly remove locking consists in using reduced integration. Mostly, 2 × 2 or 2 × 2 × 2 integration, respectively, is employed. The lower order integration introduces spurious element modes, however. These modes may deteriorate solutions for finite element models. To overcome this drawback alternative reduced integration procedures are presented. A 5-point rule for the quadrilateral is described. 9-point and 21-point procedures are introduced for the hexahedron. The performance of these procedures is studied by some test problems.