An Evaluation of The Quality of Hexahedral Meshes Via Modal Analysis

Hex-meshes have wide and important applications in scientific computing. Various methods have been proposed to tessellate a shape into a hex-mesh according to certain geometrical quality criteria (e.g. scaled Jacobian), which is usually not directly related to the downstream computing problem. This paper discusses such criteria on the elastic finite element analysis problem via analyzing the result of Modal Analysis performed on different hex-meshes. With the isometric uniform material configuration, the larger the scaled Jacobian (minimal/average) and the number of elements, the smaller are the eigenvalues, which usually indicates better accuracy and stability (condition number). Besides the element quality, singularity placement also affects the accuracy of the solution and is difficult to alter by simple subdivision. Results of this work may serve as a guide in evaluating hexremeshing approaches and choosing appropriate hex-meshes for finite element analysis.