Habashneh Muayad, Movahedi Rad Majid
Department of Structural and Geotechnical Engineering, Széchenyi István University, 9026, Gyor, Hungary.
Sci Rep. 2022 Apr 9;12(1):5989. doi: 10.1038/s41598-022-09612-z.
The aim of this paper is to integrate the reliability-based analysis into topology optimization problems. Consequently, reliability-based topology optimization (RBTO) of geometrically nonlinear elasto-plastic models is presented. For purpose of performing (RBTO), the volume fraction is considered reliable since that the application of (RBTO) gives different topology in comparison to the deterministic topology optimization. The effects of changing the prescribed total structural volume constraint for deterministic designs and changing the reliability index for probabilistic designs are considered. Reliability index works as a constraint which is related to reliability condition added into the volume fraction and it is calculated using the Monte-Carlo simulation approach in the case of probabilistic design. In addition, bi-directional evolutionary structural optimization (BESO) method is utilized to study the effect of geometrically nonlinear elasto-plastic design. The plastic behavior can be controlled by defining a limit on the plastic limit load multipliers. The suggested work's efficiency is demonstrated via a 2D benchmark problem. In case of elastic material, a 2D model of U-shape plate is used for probabilistic design of linear and geometrically nonlinear topology optimizations. Furthermore, a 2D elasto-plastic model is considered for reliability-based design to demonstrate that the suggested approach can determine the best topological solution.
本文旨在将基于可靠性的分析方法融入拓扑优化问题中。为此，提出了几何非线性弹塑性模型的基于可靠性的拓扑优化（RBTO）方法。为了进行RBTO，由于RBTO的应用与确定性拓扑优化相比会给出不同的拓扑结构，因此体积分数被视为可靠的。考虑了改变确定性设计中规定的总结构体积约束以及改变概率设计中可靠性指标的影响。可靠性指标作为一个与添加到体积分数中的可靠性条件相关的约束，在概率设计的情况下使用蒙特卡洛模拟方法进行计算。此外，利用双向进化结构优化（BESO）方法研究几何非线性弹塑性设计的效果。塑性行为可以通过定义塑性极限载荷乘数的限制来控制。通过一个二维基准问题证明了所建议方法的有效性。对于弹性材料，使用U形板的二维模型进行线性和几何非线性拓扑优化的概率设计。此外，考虑一个二维弹塑性模型进行基于可靠性的设计，以证明所建议的方法可以确定最佳拓扑解。
