  In this paper we suggest two modified one-point Gauss integration rules for
the Q1 bi- or trilinear element. The modifications both stabilize the hourglass
modes of the one-point rule, and one of them is accurate also on severely
distorted elements. We investigate the performance of the integration rules for
the hexahedron element, and combine standard one-point integration of the
volumetric terms with the modified rules for the isochoric terms to handle near
incompressible situations.
