Abstract

One of the effects of creep phenomena in structures is stress relaxation. Owing to this effect, the stiffness of each point is inversely related to the stress at that point, which causes a stress redistribution, a reduction of the maximum stress, and an increment in the displacement field. By contrast, for structural optimization, it is a practical and challenging problem to consider the maximum stress as a failure criterion or objective function. In the present study, the stress relaxation effect was investigated in stress-based topology optimization. The so-called solid isotropic material with penalization method and a nonlinear finite element analysis are utilized for this purpose. The maximum von Mises stress and the total volume of the structure are selected as the objective function and constraint, respectively. The main novelty of this research is to find the optimized topology with the least maximum stress by developing and implementing a time-dependent adjoint method for sensitivity analysis. Implementing the calculated sensitivity for stress-based problems in a gradient-based optimization method, such as the optimality criteria, is quite challenging, and some numerical instabilities in the optimization process are addressed. Several examples are solved with and without considering the stress relaxation effect. The results reveal that the influence of stress relaxation in the reduction of stress concentration makes the optimized layout more similar to the optimized layout obtained by minimizing the compliance for the linear structures.

摘要

结构中蠕变现象的影响之一是应力松弛。由于这种效应，每个点的刚度与该点的应力成反比，这会导致应力重新分布、最大应力减小以及位移场增量。相比之下，对于结构优化，将最大应力视为失效准则或目标函数是一个实际且具有挑战性的问题。在本研究中，研究了基于应力的拓扑优化中的应力松弛效应。为此，利用了所谓的固体各向同性材料和惩罚方法以及非线性有限元分析。分别选择最大 von Mises 应力和结构总体积作为目标函数和约束。这项研究的主要新颖之处是通过开发和实施用于敏感性分析的时间相关伴随方法来找到最大应力最小的优化拓扑。在基于梯度的优化方法（例如最优标准）中实现基于应力的问题的计算灵敏度非常具有挑战性，并且解决了优化过程中的一些数值不稳定性。在考虑或不考虑应力松弛效应的情况下求解了几个示例。结果表明，应力松弛对减少应力集中的影响使得优化布局更类似于通过最小化线性结构的柔度而获得的优化布局。