An adaptive isogeometric analysis meshfree collocation method for elasticity and frictional contact problems

A collocation method has been recently developed as a powerful alternative to Galerkin's method in the context of isogeometric analysis, characterized by significantly reduced computational cost, but still guaranteeing higher-order convergence rates. In this work, we propose a novel adaptive isogeometric analysis meshfree collocation (IGAM-C) for the two-dimensional (2D) elasticity and frictional contact problems. The concept of the IGAM-C method is based upon the correspondence between the isogeometric collocation and reproducing kernel meshfree approach, which facilitates the robust mesh adaptivity in isogeometric collocation. The proposed method reconciles collocation at the Greville points via the discretization of the strong form of the equilibrium equations. The adaptive refinement in collocation is guided by the gradient-based error estimator. Moreover, the resolution of the nonlinear equations governing the contact problem is derived from a strong form to avoid the disadvantages of numerical integration. Numerical examples are presented to demonstrate the effectiveness, robustness, and straightforward implementation of the present method for adaptive analysis.