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In finite element analysis, piecewise linear shape functions are often powerful and quite simple to construct and implement, which are very popular in the finite method using conventionally tetrahedral and hexahedral elements. Recently, the piecewise linear shape functions have been presented for arbitrary polyhedral elements (PFEM). The new interpolation scheme is relied on the well-known hierarchical shape functions of tetrahedral element. The proposed method shows its flexibility, simplicity and accuracy in the solid mechanics problems. However, due to the nature of linear interpolants, the obtained strains are constant within sub-domains of the polyhedral element and across the elements. Therefore, we apply the consecutive interpolation scheme to further improve the performance and accuracy of PFEM. The scheme was firstly developed for 2D problem domains discretized into linear triangular elements. In this study, it is implemented for 3D polyhedral elements with star-convex arbitrary number of vertices, edges and the facets can be non-planar. The scheme is constructed based on the fact of the continuity of strain across the discretized nodes of the problem domains. The present consecutive shape functions are formulated by using average derivatives of the nodal displacements and the piecewise linear shape functions of PFEM. As a result, the newly formulated shape functions are high-order polynomials over linear polyhedral elements. The numbers of static and dynamic numerical examples using the new consecutive interpolants were carried out to prove the rationality, feasibility, accuracy and performance of the present method.

PFEM, 3D polyhedral elements, consecutive interpolation scheme.