Design sensitivity analysis method for multidisciplinary shape optimisation problems with linear and non-linear responses

A method to solve shape and size optimisation problems with linear and non-linear responses has been studied taking advantage of statistical methodologies. A nested optimisation procedure has been fixed. The global optimisation problem is decomposed in several subproblems where each non-linear response is locally approximated with a first degree polynomial function identified by the definition and execution of an experimental plan. The approximating functions so obtained are used to evaluate the design sensitivity coefficients required by the optimisation procedure. The numerical results obtained during the optimisation process to verify exactly the value of the non-linear responses are used to verify and to improve the approximating function accuracy. The non-linear design sensitivity analysis method so defined has been used to solve a multidisciplinary shape optimisation problem involving a real 3D automotive structure.