Hexahedral Solid Element with Rotational Degrees of Freedom Based on a Novel Trail-Correction Displacement Interpolation Scheme

Abstract

To address the issue of incompatible nodal parameters between finite elements of different dimensions, this paper introduces a new interpolation formula, named “trial-correction” displacement interpolation, utilizing trilinear and cubic interpolations. This interpolation method is applied to construct an 8-node hexahedral solid element (Solid-H8-TC) with rotational degrees of freedom, featuring 6 nodal parameters including 3 translational and 3 rotational displacements. The element successfully passed the patch test and demonstrated convergence. Subsequent numerical examples show that the Solid-H8-TC element achieves a numerical accuracy of over 99% as the mesh is refined. Furthermore, the Solid-H8-TC element can be directly combined with shell elements, effectively resolving the compatibility issues of nodal parameters between finite elements of different dimensions. Lastly, the trial-correction displacement interpolation method employed in this study exhibits excellent scalability and provides a new theoretical basis for finite element analysis of plane, beam, and shell structures.