A NURBS enhanced polygonal element formulation based on the scaled boundary method for the analysis of solids in boundary representation

Abstract

AbstractThe contribution is concerned with a numerical element formulation for the nonlinear analysis of solid in boundary representation. Its results in a polygonal element with an arbitrary number of sides. Straight edges are possible as well as curved edges, which are described by e.g. Non‐Uniform Rational B‐Splines (NURBS). The element formulation is based on the so‐called scaled boundary finite element method (SBFEM). The basic idea is to scale the domain's boundary with respect to a scaling center in order to describe the interior domain. In contrast to SBFEM, the proposed method makes use of a numerical aproximation for the displacement response in scaling direction. This enables the analysis of geometrically and physically nonlinear problems in solid mechanics. The interpolation at the boundary in circumferential direction is independent of the interpolation in scaling direction. So, different basis functions can be used for each direction, e.g. NURBS basis functions in circumferential and Lagrange basis functions in radial direction. The advantage of the presented element formulation is the flexibility in mesh generation. The avoidance of so‐called hanging node problems as arbitrary element geometries are possible. For example, using Quadtree algorithms, a fast and reliable mesh generation can be achieved. Furthermore, in connection with trimming algorithms, the element formulation allows a precise representation of the geometry even with coarse meshes. Some benchmark tests are presented to evaluate the accuracy of the proposed numerical method against analytical solutions.