Approach on Centroid Angle–Based Reverse Motion for Hexahedral Mesh of Vector Form Intrinsic Finite Element

Abstract

The virtual reverse motion is a vital procedure of the vector form intrinsic finite-element (VFIFE) method to derive pure nodal deformation. Because the development of VFIFE, especially for hexahedral elements, is still in its infancy, there are no standard criteria for calculation of the pure deformation and the way to implement such calculation could be subjective at present. This study proposes an alternative approach on the reverse motion calculation for the hexahedral mesh based on the centroid-angle transformation. Relying on the fundamental principles of VFIFE, four numerical examples regarding typical cantilever beam structures are provided to illustrate and verify the accuracy and robustness of the presented approach. Compared with the corresponding results from the theoretical solution or finite-element method simulation, satisfactory results were achieved in applied cases relating to various loads, large deformation with rigid body motion, and static and dynamic problems.