基于等几何分析的变刚度层合结构优化技术

Under the condition of current manufacturing capabilities, it is most likely to produce the most lightweight body structures for products in the areas like aerospace industry with variable-stiffness composite laminates, which are made by means of ply-drop or placing fibers in curvilinear paths. However, the lightweight design of variable-stiffness laminates often fails because of the difficulties encountered in solving the optimization problem with the characteristics of nonlinearity, non-convexity and high-dimensional mixed-integer variables. To address this issue, this project proposes to develop the methodologies for multi-level re-parameterizations and their related optimizations on the basis of gradual convexity improvement, which is achieved in an integrated isogeometric modeling scheme for the structure’s geometry, analysis and optimization problems. Firstly, the project will study the multi-level dimension-adjustable parameterization approaches for design variables on laminate geometry, material and stiffness, based on the hierarchical refinement technique in NURBS, and will study the methods for design variable reduction under the complex manufacturing constraints for the discrete lamination problem. Secondly, the project will elaborate the issues on overcoming the low-efficiency problems at the bottleneck computation steps like high-order Gaussian integration and large deformation evaluation in the isogeometric performance analyses for strength, free vibration and buckling. Finally, the project will put its major effort on developing the methodologies for creating the multi-phase/multi-level distributed optimization models for design of variable-stiffness composite laminates and their coordinated optimization algorithms that search for the global optimal solution. In addition, the project will also develop a prototype software system to validate the proposed methodologies with practical case studies. The successful implementation of the project would greatly elevate the effectiveness of design optimization on more complex laminated structures in industry.

在现有制造条件下，使用铺层递减和曲线纤维变刚度层合结构能够使航空航天等领域产品主体结构到达最大程度的轻量化。然而，变刚度层合结构设计需要求解非线性、非凸和高维离散-连续变量的设计优化问题，往往难于得到充分优化的设计方案。本课题拟在几何-分析-优化一体化的等几何模型基础上，采用面向凸性渐进改善的设计空间重新参数化以及对应的分级优化方法解决该问题。为此，课题首先基于NURBS层次细分技术研究层合板壳中几何、材料和刚度变量的多层次维度可调参数化方法，同时对离散纤维角度铺层问题研究满足复杂制造约束的变量简约方法。其次研究强度、模态和屈曲性能分析中高阶高斯积分和大变形计算等低效率计算环节处理方法。最后研究变刚度层合结构优化中分步/分层/分布优化建模以及全局协调寻优算法。课题将通过开发相关软件原型系统，对研究成果进行检验和应用验证。课题预期成果将使工业界能够对更复杂的层合结构进行更加有效的设计优化。

纤维增强复合材料层合结构具有高的比强度、比刚度和优良的耐热性，广泛应用于航空航天、医疗等众多领域。使用变厚度/变角度铺层方式更能极大限度地达到降成本、减重量目的。然而，这些变刚度层合结构铺层设计面临非线性、非凸和变量多等难点问题。本课题目标是通过合理的设计空间简约参数化和快速的等几何分析实现变刚度层合结构设计方案优化。..为此，本项目开展了若干研究工作。首先，研究了变刚度层合板壳结构参数化建模方法、快速等几何分析方法以及轻量化寻优算法。其次，开发了变刚度层合结构分析优化程序并进行了应用验证工作。本项目在执行上述研究任务的过程中取得了下列主要成果：（1）针对该优化设计中原始设计变量数目巨大、变量约束复杂问题，提出了考虑制造约束的纤维铺层模板和材料铺层参数分布表达的变量简约方法；前者用于变层数的直线纤维铺设问题，后者用于变角度的曲线纤维铺设问题。（2）针对优化搜索对力学性能分析计算效率要求高问题，提出了基于张量分解的层合板壳结构离散方程系数矩阵的快速生成方法。（3）针对变层数直线纤维铺设问题，提出了基于多模板的分块启发式优化搜索算法，确定区域块的最优层数和纤维角度及顺序；针对变角度曲线纤维铺设中非凸优化问题，提出了两级优化框架，第一级搜索层合板最优铺层参数分布，第二级用基于流函数最小二乘法提取优化的纤维轨迹。..本项目在克服层合结构优化设计中变量多、力学分析计算量大、全局寻优困难等难点问题方面取得了一些进展，为相关工业软件开发提供了理论和方法基础。具体进展主要体现在：分区域纤维铺层模板在满足约束条件下减少了离散变量数目；基于张量分解的矩阵生成方法提高了力学分析效率；基于截断层次B样条的自适应铺层参数分布优化方法有较强的全局最优解搜寻能力。

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