Shape optimal design using fictitious loads

Implementation aspects of the natural velocity field approach for shape optimal design are discussed. The problem of concern is to find the optimum shape of an elastic body that requires minimizing an objective function subject to stress, displacement, frequency, and manufacturing constraints. In this paper, fictitious loads are applied at certain control nodes on an auxiliary structure, and the deformation produced by these loads is used to update the shape. The use of beam stiffeners in the auxiliary structure leads to smoother shapes. Furthermore, softer material properties in the auxiliary structure result in faster convergence when iterating through the feasibile region. The method is applied in conjunction with both discrete and continuum methods of design sensitivity analysis.