On the influence of boundary conditions, Poisson’s ratio and material non-linearity on the optimal shape

Design of a boundary in a material and in a structure is in principle an identical problem. However, for structures, we mostly assume the external loads to be given, while in the design for material moduli, the loads are evaluated from forced displacements and the loads are therefore design dependent. In the present study, we shall focus on the in¯uence of these di€erent load assumptions. Also, the in¯uence of PoissonÕs ratio and of material non-linearity will be shown. Based on sensitivity analysis, we also obtain general information. The objective may be the sti€est design, the strongest design or just a design of uniform energy density along the shape. In an energy formulation, it was proven earlier that these three objectives have the same solution, at least within the limits of geometrical constraints, including the parametrization. Without involving stress/strain ®elds, this proof holds good for 3D problems, for power-law non-linear elasticity and for anisotropic elasticity. With this background, the results of a number of in¯uence studies are presented