Analysis of 2D contact problems under cyclic loads using IGABEM with Bezier decomposition

Abstract

Non-uniform rational B-splines (NURBS) are a convenient way to integrate CAD software and analysis codes, saving time from the operator and allowing efficient solution schemes that can be employed in the analysis of complex mechanical problems. In this paper, the Isogeometric Boundary Element Method coupled with B´ezier extraction of NURBS and conventional BEM are used for analysis of 2D contact problems under cyclic loads. A node-pair approach is used for the analysis of the slip/stick state. Furthermore, the extent of the contact area is continuously updated to account for the nonlinear geometrical behavior of the problem. The Newton-Raphson’s method is used for solving the non-linear system. A comparison to analytical results is presented to assess the performance and efficiency of the proposed formulation. Both BEM and IGABEM show good agreement with the exact solution when it is available. On most examples, they are equivalent with some advantage for IGABEM, though the former is slightly more accurate in some situations. This is probably due to the smoothness of NURBS not being able to describe sharp edges on tractions. As expected, IGABEM incurs in higher computational cost due to the basis being more complex than conventional Lagrangian polynomials.