Dynamic analysis of 3D solid structure using a consecutive-interpolation over polyhedral element mesh

In this study, we investigate the dynamic performance of the three-dimensional solid structures by using the latest development of a consecutive-interpolation scheme. The structure is discretized into finitely arbitrary polyhedral elements. The bounded faces of an element can be non-planar. The interpolation scheme is constructed through twomain steps. The first step uses the piecewise linear shape functions, which are also formulated for arbitrary polyhedral elements. The second step is formulated based on the fact of continuity of the nodal strains, which could only be satisfied by post-processing in the conventionally polyhedral finite element method (PFEM). The natural frequencies of the solid structures are analysed by a dynamic problem. The efficiency of the method is approved by comparing the obtained solutions to those of the conventional finite element method (FEM) using tetrahedral elements and PFEM, which are two methods effectively implemented for complex solids