ADVANCES IN STRUCTURAL OPTIMIZATION INCLUDING NONLINEAR MECHANICS

It is common practice to base both, topology optimization as well as a subsequent shape optimization, on linear elastic structural response. But the value of optimization results in the design of structures strongly depends on the relevance of the underlying mechanical model. For example a key question is how good the level of the chosen kinematic relation or the underlying material model are able to represent the real behavior of the structure. Furthermore the quality of the numerical methods in order to determine the structural response and its sensitivity plays an important role. The more the mechanical model is simplified by assumptions, e.g. neglecting nonlinear effects or by approximating the in general 3D structural layout and stress state by 1D or 2D models, the less meaningful and the more sensitive the optimization results may be. To obtain a realistic design by structural optimization it may be essential to base the optimization on a more realistic physical behavior, e.g. to consider geometrically and materially non- linearities. The present study addresses these aspects and extends the formulation into the nonlinear structural regime. This may include either large deformations and stability phenomena or material nonlinearities. Moreover in view of gradient solution methods, the sensitivity analysis has to be adapted to these extended problems. Depending on the kind of the mechanical problem different methods for the sensitivity analysis are applied. For path-dependent problems, like elastoplasticity, a variational approach turns out to be suitable while for problems with pure geometrically nonlinear behavior a discrete approach is favorable. The present optimization procedures are demonstrated by examples showing rather the principle features of the enhancements then real practical design problems.