Optimization of geometrically non‐linear structures based on a multi‐point approximation method and adaptivity

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Abstract
Presents an approach for optimal design of geometrically non‐linear structures, using adaptive mesh refinement (AMR). The optimization technique adopted is based on the multi‐point approximation method. The finite element method is used for the structural analysis. Reformulation of the optimal design problem is applied to circumvent complications caused by the non‐linear behaviour of the structure. The latter may lead to bifurcations, limit points and/or significant reduction of the structural stiffness for individual intermediate designs generated by an optimization algorithm. Discretization errors are controlled using AMR. To reduce computational costs, the requested global and local discretization errors are not taken as fixed values but are specified on the basis of the current status of the optimization process. In the beginning relatively large errors are accepted, while as the process progresses discretization errors are reduced. The method is applied to thin‐walled structures with geometrically non‐linear behaviour.

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