OPTIMAL ROBUST DESIGN OF NOVEL MATERIALS: PROBLEMS OF STABILITY AND VIBRATIONS

A numerical method for the optimal design of thin anisotropic laminates is presented, layer thicknesses and lamination angles being the design variables. An optimal solution is pursued with respect to frequency domain objectives, e.g. fundamental frequency and Euler critical load. A special feature of the method is the semi-analytical second order design sensitivity that is computed with the aid of a Rayleigh-Ritz analysis approach. A modified sequential quadratic programming scheme is then introduced, where standard quasi-Newton approximations are avoided by an exact calculation of the Hessian matrix. Furthermore, the robustness of the method with respect to scatter in material properties such as mass density and elastic moduli is assessed. A stochastic extension of the Rayleigh-Ritz approach is developed on this purpose that allows the location of those regions in the design space that are most sensitive to physical parameter randomness. This allows the use of a modified objective function that penalizes sensitive solution.