A hexahedron element formulation with a new multi-resolution analysis

Abstract

A multiresolution hexahedron element is presented with a new multiresolution analysis (MRA) framework. The MRA framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on element domain of a basic node shape function. The basic node shape function is constructed from shifting to other seven quadrants around a specific node of a basic isoparametric element in one quadrant and joining the corresponding node shape functions of eight elements at the specific node. The MRA endows the proposed element with the resolution level (RL) to adjust structural analysis accuracy. As a result, the traditional 8-node hexahedron element is a monoresolution one and also a special case of the proposed element. The meshing for the monoresolution finite element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the solid mathematical basis. The simplicity and clarity of shape function construction with the Kronecker delta property and the rational MRA enable the proposed element method to be more rational, easier and efficient in its implementation than the conventional mono-resolution solid element method or other MRA methods. The multiresolution hexahedron element method is more adapted to dealing with the accurate computation of structural problems.