Efficient isoparametric trimmed-hexahedral elements with explicit shape functions

In this study, we develop isoparametric trimmed-hexahedral (TH) elements with explicit shape functions for finite element analysis using trimmed meshes. TH elements are placed at the boundary of a trimmed mesh generated by cutting a regular hexahedral mesh with a geometric surface. Master TH elements are defined based on the marching cubes algorithm for an isoparametric mapping from the reference coordinates to the physical coordinates. Shape function values at the support points of master TH elements are precomputed by solving Laplace's equation with appropriate boundary conditions. Explicit shape functions for master TH elements are constructed by interpolating the precomputed shape function values at the support points of master TH elements. The present explicit shape functions satisfy the required properties of FEM, and significantly reduce the computational cost compared with the previously developed polyhedral shape functions.