A scaled boundary isogeometric formulation for the elasto-plastic analysis of solids in boundary representation

Abstract

This contribution deals with the nonlinear analysis of boundary represented solids with elasto-plastic material behavior based on the so-called scaled boundary isogeometric formulation (SB-IGA). The proposed approach combines the features of the scaled boundary finite element method and isogeometric analysis. Based on the original boundary representation of the CAD model, a formulation is provided where the geometrical description of the boundary is sufficient to define the entire surface. The domain is parameterized by a radial scaling parameter emanating from a scaling center and a parameter in circumferential direction along the boundary. Non star-shaped domains are tackled by standard sub-structuring. Here, conforming discretizations are considered for the two-dimensional case. According to the isogeometric paradigm, NURBS basis functions are employed for the approximation of the solution. The displacement response is derived based on a multiplicative decomposition of the approximation in circumferential and radial scaling direction. The boundary value problem is solved with the Galerkin method. The Newton–Raphson iterative scheme is employed to obtain the nonlinear response. Several benchmark tests demonstrate the accuracy and computational efficiency of the formulation.