Construction of generalized shape functions over arbitrary polytopes based on scaled boundary finite element method's solution of Poisson's equation

A general technique to develop arbitrary-sided polygonal elements based on the scaled boundary finite element method is presented. Shape functions are derived from solution of Poisson's equation in contrast well-known Laplace shape that only linearly complete. The application Poisson can be complete up any specific order. retain advantage allowing direct formulation polygons with arbitrary number sides and quadtree meshes. resulting similar where each field variable interpolated by same set parametric space differs integration stiffness mass matrices. Well-established procedures applied developed functions, solve a variety engineering problems including, for example, coupled problems, phase fracture, addressing volumetric locking near-incompressibility limit adopting mixed formulation. Application demonstrated several problems. Optimal convergence rates observed.