A polyhedral element formulation based on the scaled boundary method for the analysis of nonlinear problems in solid mechanics

Abstract

AbstractIn this contribution a numerical element formulation for the nonlinear analysis of solids is proposed. The element is defined by a polyhedron with an arbitrary number of polygonal faces. It is based on the scaling concept, which is adopted from the so‐called scaled boundary finite element method (SBFEM). The SBFEM is a semi‐analytical formulation to analyze problems in linear elasticity. Within this method the fundamental concept is to scale the domain's boundary with respect to a scaling center in order to describe the interior domain. The present element formulation employs the scaling concept twice and in contrast to SBFEM, uses a numerical approximation for the displacement response in both scaling directions. This makes it suitable for the analysis of geometrically and physically nonlinear problems. The advantages of the proposed element formulation is its high flexibility in mesh generation. It avoids the hanging node problems as arbitrary element geometries are possible. For example, using Octree algorithms, a fast and reliable mesh generation can be achieved. In case of curved boundaries the element formulation allows a precise representation of the geometry even with coarse meshes. Some numerical examples are presented to evaluate the accuracy of the proposed numerical method against analytical solutions, and a comparison to standard element formulations is given as well.