Optimum shape design of incompressible hyperelastic structures with analytical sensitivity analysis

This paper is focused on the structural shape optimization of incompressible hyperelastic structures. An analytical sensitivity is developed for the rubber like materials. The whole shape optimization process is carried out by coupling a closed geometric shape in R2 with boundaries, defined by B-splines curves, exact sensitivity analysis and mathematical programming method (S.Q.P: sequential quadratic programming). Design variables are the control points coordinate. The objective function is to minimize Von-Mises stress, constrained to the total material volume of the structure remains constant. In order to validate the exact Jacobian method, the sensitivity calculation is performed: numerically by an efficient finite difference scheme and by the exact Jacobian method. Numerical optimization examples are presented for elastic and hyperelastic materials using the proposed method.