Voronoi Polygonal Hybrid Finite Elements and Their Applications

This chapter describes the polygonal hybrid finite element formulation with fundamental solution kernels for two-dimensional elasticity in isotropic and homogeneous solids. The n-sided polygonal discretization is implemented by the Voronoi diagram in a given domain. Then the element formulation is established by introducing two independent displacements, respectively, defined within the element domain and over the element boundary. The element interior fields approximated by the fundamental solutions of problem can naturally satisfy the governing equations and the element frame fields approximated by one-dimensional shape functions are used to guarantee the conformity of elements. As a result, only element boundary integrals caused in the modified hybrid functional are needed for practical computation. Finally, the present method is verified by three examples involving the usage of general and special n-sided polygonal hybrid finite elements.