A generalized shape optimization procedure for the solution of linear partial differential equations with application to multidisciplinary optimization

This paper deals with a technique for finding the solution with the optimum shape for linear partial differential equations, which are the governing equations of several very important effects in structures and machines to be optimized. As a new trend in the science of optimization, applications of multidisciplinary optimization are increasing, where the evaluation of the objective function or the design constraints needs the usage of the results obtained by several disciplines (fluid flow, thermal analysis, contact problems, nonlinear structural analysis). Therefore the meaning of shape must be enlarged as a general multivariable function, representing geometrical form, temperature distribution, as well as pressure or velocity field. For the optimization a genetic type search algorithm is applied. The numerical example of the Reynolds equation for the pressure distribution in hydrodynamic journal bearings is shown. By using this procedure the shape of the gap between the sliding surfaces can be optimized. Several other examples show the efficiency of the method, in multidisciplinary optimization problems.