Shape optimization of thin walled structures governed by geometrically nonlinear mechanics

This paper introduces a structural optimization strategy that combines FE-based parametrization with nonlinear kinematics in order to optimize the shape of thin shell structures. The optimization is based on gradient based strategies where the required derivatives are formulated by the adjoint approach. The applied solution algorithm combines the well known nonlinear path following strategies with the design update procedure of the shape optimization. This results in robust and flexible methods that require only a minimum of system evaluations. The proposed optimization goals improve the load carrying behavior of the structure and minimize displacements and stresses. It is shown that such efficient designs also exhibit an improved limit load. This contribution illustrates the application of the proposed method by several shape optimization problems. The presented results prove the exceptional performance of the optimized designs even if the optimal design is disturbed by unavoidable imperfections. It is shown that the application of nonlinear kinematics in the shape optimization of thin shell structures allows for a much more realistic system response and gradient data. The proposed approach is applicable to all kind of optimization strategies like topology, sizing or material optimization, respectively.