Optimization of a hyper-elastic structure with multibody contact using continuum-based shape design sensitivity analysis

In this paper, a continuum-based shape design sensitivity formulation is pr esented for a hyper-elastic structure with multibody frictional contact. A nearly incompressible constraint is treated using the pressure projection m ethod that projects a hydrostatic pressure into a lower order space to avoi d a volumetric locking. The variational formulation for multibody frictiona l contact is developed using a penalty method that regularizes the solution of the variational inequality. The material derivative of continuum mechan ics is utilized to develop the continuum-based shape design sensitivity ana lysis for the hyper-elastic constitutive relation and penalized contact for mulation. The sensitivity equation is solved at each converged load step us ing the same tangent stiffness of response analysis due to the path depende ncy of the sensitivity of the frictional contact problem. A very accurate a nd efficient sensitivity results are shown through shape optimization of a windshield wiper.