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In this paper we suggest two modified one-point Gauss integration rules forthe Q1 bi- or trilinear element. The modifications both stabilize the hourglassmodes of the one-point rule, and one of them is accurate also on severelydistorted elements. We investigate the performance of the integration rules forthe hexahedron element, and combine standard one-point integration of thevolumetric terms with the modified rules for the isochoric terms to handle nearincompressible situations.

Modified midpoint integration rule for the trilinear element in large deformation elasticity