Meshless shape design sensitivity analysis and optimization for contact problem with friction

In this paper, a continuum-based shape design sensitivity formulation for a frictional contact problem with a rigid body is proposed using a meshless method. The contact condition is imposed using the penalty method that regu larizes the solution of variational inequality. The shape dependency of the contact variational form with respect to the design velocity field is obta ined. The dependency of the response with respect to the shape of the rigid body is also considered. It is shown that the sensitivity equation needs t o be solved at the final converged load step for the frictionless contact p roblem, whereas for the frictional contact case the sensitivity solution is needed at the converged configuration of each load step because the sensit ivity of the current load step depends on that of the previous load step. T he continuum-based contact formulation and consistent linearization is crit ical for accurate shape design sensitivity results. The accuracy of the pro posed method is compared with the finite difference result and excellent ag reement is obtained for a door seal contact example. A design optimization problem is formulated and solved to reduce the contact gap opening successf ully in a demonstration of the proposed method.