A material derivative approach in design sensitivity analysis of three-dimensional contact problems

A shape design sensitivity analysis (DSA) and the optimization of a three-dimensional (3-D) contact problem is proposed using a material derivative approach. A penalty-regularized contact variational equation is differentiated with respect to the shape design parameter. A die shape DSA is also carried out by defining a design velocity field at rigid-body geometry. The material derivative that is consistent with the frictional return-mapping scheme is derived by using nonassociative plasticity. A linearized design sensitivity equation is solved without iteration by using a meshfree method at each converged load step. In order to improve the convergence behavior of the contact problem, a C2-continuous contact surface is constructed from the scattered set of particles. The accuracy and efficiency of the proposed method is shown using two-dimensional and 3-D design examples of the DSA and optimization process.