考虑多性能指标的连续体结构拓扑优化设计方法研究

Employing topology optimization, some new-type and more reasonable designs better than the designers’ experience can be obtained, by which much more cost can be reduced, and the improvement on the structural performance can be achieved in practical applications. Structural strength, stiffness and stability are three important factors considered in structural design; and it has important theoretical research value and practical engineering significance to consider them simultaneously in topology optimization of continuum structures. In this project, a topology optimization model for minimizing structural compliance with constraints on the material volume, stress and critical buckling load factors is proposed to conduct a research on topology optimization of continuum structures considering multi-performance index simultaneously. In order to deal with stress constraints more efficiently and accurately, an adaptive cluster selection criterion will be established based on the stress distribution level of current design and permissible value, then corresponding stress aggregation functions are built and updated dynamically according to the design evolution. To achieve an improvement in the quality of the designs, the effect of the penalty factor on the calculated value of buckling load factors, stress, compliance and design evolution process will be analyzed and an adaptive continuation algorithm will be developed. Employing the digital image compression techniques and parallel computing technology, an efficient and robust algorithm is presented. The results of this research work will present theoretical foundation and technical basis for the engineering application of design schemes, and also provide a reliable and practical method for structure concept design. The achievements of this project will benefit science and application fields.

结构拓扑优化方法可以突破工程师经验和认识局限产生新型、更加合理的设计方案，将其应用于实际工程可以降低成本、提高结构性能。强度、刚度和稳定性是结构设计时需要考虑的三个重要指标，在结构拓扑优化中同时予以考虑，具有理论研究价值和工程实际意义。本项目提出材料体积、应力及稳定性约束下连续体结构柔顺度最小化的拓扑优化模型，研究同时考虑强度、刚度及稳定性多性能指标的连续体结构拓扑优化问题。基于应力分布水平及容许值建立自适应群簇选取准则，构建群簇应力聚合函数并随设计演化动态更新，实现局部应力约束的高效处理；通过分析惩罚指数对失稳荷载因子、应力、柔顺度计算值及设计演化过程的影响，建立自适应连续化算法，获得高质量的优化设计；基于数字图像压缩和并行计算技术，建立高效稳定的求解算法。预期研究成果可为拓扑优化的工程应用提供理论基础和技术依据，也为结构概念设计提供一种可靠、切实可行的方法，具有科学意义及应用前景。

材料制造过程中通常会存在缺陷，可能导致结构服役时产生疲劳破坏，在结构拓扑优化模型中考虑疲劳应力约束有利于降低缺陷带来的不利影响。材料强度、结构刚度和稳定性是结构安全设计时需要考虑的三个重要指标，在结构概念设计阶段同时予以考虑有利于降低材料成本，提高结构性能。实际工程结构服役时，荷载方向、幅值均具有不确定性，从而导致确定性荷载作用下的最优设计不再具有最佳的性能。针对以上三个问题，本项目采用理论分析与数值模拟相结合的方法，开展了如下研究工作：首先，采用Murakami提法建立了疲劳强度与缺陷尺寸及位置的关系，研究了两类应力约束下结构柔顺度最小化问题，探究了疲劳应力约束和von Mise屈服应力约束对优化设计结果的影响；其次，研究了同时考虑应力和稳定性约束的结构柔顺度最小化问题，证实了同时考虑这三类指标的必要性以及提出算法的有效性；最后，采用Gauss-Seidel激活相方法研究了不确定荷载作用下多材料连续体结构拓扑优化设计，探究了荷载幅值和方向不确定性等参数对优化设计结果的影响，获得了比确定性提法鲁棒性更好的优化设计结果。