Abstract
Structural optimization of crash-related problems usually involves nonlinearities in geometry, material, and contact. The Equivalent Static Load (ESL) method provides a method to solve such problems. It has previously been extended to employ an individual Finite Element model describing the deformed geometry at each considered time step under the name Difference-based Equivalent Static Load (DiESL) method. This paper demonstrates how an appropriate selection of the time steps in each cycle can further improve the convergence behavior of the DiESL method. It is shown that the adaptive selection of time steps leads to better objective values and more reliable convergence to the presumed global optimum. Furthermore, the DiESL extension enables the adaption of path-dependent structural properties of the original nonlinear problem like material stiffness in each linear auxiliary load case. In this paper, an adaption of the Young’s modulus on element level in the linear auxiliary problem corresponding to the local plasticization in the nonlinear dynamic problem is successfully implemented. Here, the test examples indicate that an observable improvement can only be obtained if neither the elements in the elastic nor in the plastic range are dominating the structure’s behavior.
Highlights
Linear static response structural optimization is highly efficient and is embedded in a considerable number of applications commonly used during the design process in industry
It has been shown that the Difference-based Equivalent Static Load (DiESL) method enables a significant increase in approximation quality for displacements and strains from nonlinear dynamic problems while simultaneously providing faster convergence
Three criteria are used to evaluate the influence of the extensions on the DiESL method’s performance: the average number of cycles required for convergence, the number of multi-start runs converging to the global optimum, and the resulting average objective value
Summary
Linear static response structural optimization is highly efficient and is embedded in a considerable number of applications commonly used during the design process in industry. Many commercial codes such as MSC NASTRAN, Altair OptiStruct, or VRAND GENESIS are available in this area, enabling sizing, shape, and topology optimization in an acceptable amount of time. In contrast to the well-established optimization based on linear analysis, the real challenge in optimization is the optimization of highly nonlinear dynamic systems. We restrict ourselves to the use of commercial crash solvers for the nonlinear dynamic analysis to ensure that the proposed DiESL method can be applied to real automotive crash problems
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