Higher-Order Hexahedral Finite Elements for Structural Dynamics: A Comparative Review

Abstract

The finite element method (FEM) is widely used in many engineering applications. The popularity of FEM led to the development of several variants of formulations, and hexahedral meshes surged as one of the most computationally effective. After briefly reviewing the reasons and advantages behind the formulation of increasing order elements, including the serendipity variants and the associated reduced integration schemes, a systematic comparison of the most common hexahedral formulations is presented. A numerical benchmark was used to assess convergency rates and computational efficiencies when solving the eigenvalue problem for linear dynamic analysis. The obtained results confirmed the superior performances of the higher-order brick element formulations. In terms of computational efficiency, defined as the ratio between achievable accuracy and computational execution time, quadratic or cubic formulations exhibited the best results for the stages of FE model assembly and solution computation, respectively.