Improved eight-node non-conforming hexahedral element for structures of various shapes

A previous 8-node 24-degree-of-freedom hexahedral element H8i9 is modified to improve its performance in structures of various shapes, especially in plates and shells. First, the complicated correction coefficients for non-conforming modes required by the patch test are reduced to constant values independent of the element. Second, the element strain field is enhanced with bilinear modes by the introduction of a trilinear non-conforming mode. Third, the iterative regularization used to address the ill-conditioned stiffness matrix is replaced by a special 9-point integration rule. Benchmark tests demonstrate that the new element H8ij10 outperforms the previous version, particularly with a notable improvement in coarse-mesh accuracy in plate and shell issues.