基于刚度与强度要求的轻质材料与结构拓扑一体化优化设计方法研究

Based on the lack of a systematic research in the world on a multi-scale optimization design of materials and structural topologies based on strength requirements and considering the importance of its systematic research for material and structural creative designs, this project will conduct research on an integrated design methodology of lightweight materials and structural topologies based on stiffness and strength requirements.Firstly, present schemes circumventing the numerical instabilities such as checkerboard patterns and etc., and the technology generating more distinct and smoother structural topologies will be investigated and developed，based on the nodal relative density variables and the finite cell method. A relaxed suitable model formulation of the topology optimization problem in mathematics will be constructed. A measure reducing the number of stress constraints, a high efficient analysis method for structural stress constraints and their sensitivities and optimization strategies will be investigated based on active stress constraints, approximate aggregate stress constraint functions and the surrogate model methodology.Secondly, effective material interpolation schemes on both the macro and meso scales are constructed, the macro structural objective function (compliance etc.) expression will be derived with respect to micro structural base material properties by mathematical derivations, an integrated design methodology of materials and structural topologies will be proposed, and the effect of size scale on optimal materials and structural topologies will be investigated.Finally, a high efficient analysis method for stresses and their sensitivities on the macro and meso scale structures will be given, two hierarchical structural optimization model formulations of materials and structural topologies will be built, and optimization algorithm will be developed based on parallel computing techniques. According to engineering requirements，the innovative developments in the aspects of an integrated design methodology of lightweight materials and structural topologies based on stiffness and strength requirements in the mechanical field will be obtained. The outcomes of this research will be useful for the advancement of designing and manufacturing techniques in the mechanical industry.

基于当前国际上缺乏涉及强度的材料及结构拓扑多尺度优化设计的系统性研究，考虑到它对于结构和材料创新设计的重要意义，本项目进行基于强度和刚度要求的轻质材料与结构拓扑一体化优化设计方法研究。首先，基于有限胞元法和节点密度变量，改进避免数值不稳定性问题的现有方案，构造适定的结构静力拓扑优化问题列式；研究基于主动应力约束、总体凝聚应力约束和代理模型方法的结构应力约束减缩措施、应力约束及其灵敏度的高效计算方法；其次,构建结构和材料的两级材料插值模型, 将宏观结构目标函数(柔顺度等)通过数学推导转换成材料参数的表达式，提出结构拓扑与材料一体化设计方法, 研究微结构尺寸效应；最后, 发展高效的细观和宏观应力及其灵敏度分析方法,构建结构与材料一体化两级优化列式和并行计算优化算法。结合工程需求,在基于强度和刚度要求的材料与结构拓扑一体化优化设计方法方面取得进展。项目成果将会促进机械领域设计和制造技术的发展。

在实际工程应用中,材料和结构的同时设计中具有重要意义。近年来已经见证了不断增长的材料和结构同时设计的研究兴趣。然而该主题的大部分研究工作仅涉及单个约束的材料及结构拓扑多尺度优化设计。基于当前国际上缺乏涉及多约束和强度要求的材料及结构拓扑优化设计的系统性研究，考虑到它们对于结构和材料创新设计的重要意义，本项目进行了基于强度和刚度要求的轻质材料与结构拓扑一体化优化设计方法研究。.首先,研究了位移、柔顺度、频率和应力导数等的分布规律,构建了一种创新性强的可行域调整方案和探索了一种利于结构特性量平稳变化的结构拓扑优化近似模型化方法。而后,开发了具有收敛性和稳健的基于可行域调整的多工况载荷、多约束结构拓扑优化高效算法。将上述技术和高效求解方案推广到了涉及位移、频率和动响应要求及多载荷工况、病态载荷工况和考虑载荷随机的结构拓扑优化问题, 以及考虑位移、频率和动响应要求的结构材料拓扑优化设计问题。构造了单元的应力梯度计算格式,并引进了自适的总体凝聚应力梯度约束函数。建立了基于主动应力约束、应力梯度和总体凝聚应力约束的结构应力约束减缩措施、应力约束及其灵敏度的高效计算公式。再者, 研究了细观结构尺寸效应,构建了等效的轻质材料与结构拓扑一体化两级优化列式、结构柔顺度、频率、位移等性能函数相对于细观和宏观结构变量的灵敏度分析格式和其二次显式近似式。进而发展和完善了基于强度和刚度要求的轻质材料与结构拓扑一体化优化设计理论方法和技术。完成了大量仿真算例和部分方法的实验验证。项目在基于强度和刚度要求的材料与结构拓扑一体化优化设计方法研究方面取得了重要进展。本课题已发表期刊和会议论文21篇, 其中11篇被EI收录, 6篇被SCI收录,获得发明专利和实用新型专利各一项。培养了3名博士和25名硕士研究生，其中一人获得了博士学位,15人获得了硕士学位。项目成果促进了结构优化学科的进步和机械领域设计及制造技术的发展。