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

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.