纤维增强复合材料板壳结构的准周期分析模型与优化设计方法

Accurate analysis and innovate design are crucial to fiber reinforced composite shell structures. Current analytical models over-restrict the deformation mode of unit cells, which leads to inborn errors. Relevant current optimization methods also fail to carried out collaborative optimization on macro geometry and micro stacking sequence. In the present project, the characteristic and difficulties in the analysis of composite structures will be considered, including non-uniformity, discontinuities and singularity. A high-accuracy quasi-periodic model with deformation adaptability will be focused to be developed, while an efficient structure & topology optimization approach will be proposed based on the quasi-periodic model and an explicit geometric description frame.Both analytical and experimental approaches will be carried out in this project. Typical unit cell will be modeled based on experimental observation of micro interface and plying parameters, and quasi-periodic boundary conditions considering relative rotation of boundaries will be applied on the unit cell. The quasi-periodic boundary conditions will ensure the deformation of unit cell meets actual structures. Therefore, the equivalent properties of composite structures are accurately predicted.With the accurate prediction of unit cells, the optimization approach of composite structures will be proposed. The geometry & topology of structures will be adapted by changing a few explicit parameterized surfaces, by which the coupling between manufacturing process, structural geometry and stacking parameters will be considered. The research findings could provide scientific and theoretical foundation for the analysis and design of relevant equipment and products.

实现纤维增强复合材料板壳结构的精准分析与创新设计具有重要科学意义。现有的分析理论均过度限制了复合材料板壳微元的变形，存在天然的分析误差；相关优化设计方法亦难以实现结构几何与纤维铺层的协同优化。本项目将针对具有非均匀、强间断、奇异性特点及难点的复合材料板壳结构，发展具备变形顺应性的高精度准周期分析模型，并建立显式几何描述框架下的结构/拓扑高效优化设计方法。采用理论与实验相结合的研究手段，建立符合实验观测的铺层与界面微结构模型，对板壳微元施加考虑边界平动与相对转动的准周期边界条件，使微元变形更贴合实际，进而准确预测复合材料结构的等效力学性能。基于高精度分析模型，以参数化曲面为基元，调控板壳结构的几何尺寸与拓扑形式，并快速提取结构几何尺寸，实现工艺-几何-铺层耦合参数的高效计算，建立复合材料结构/铺层协同优化设计方法。本项目研究成果有望为相关重大装备及产品的分析与设计提供科学基础与理论支撑。

本项目针对具有广泛应用背景的纤维增强复合材料板壳结构，建立基于准周期边界条件的分析模型，并使用结构几何/拓扑显式描述这一全新框架开展优化理论研究。对代表微元施加上下表面边界自由、四周边界同时发生平动与转动的准周期边界条件，着力解决现有方法难以精确刻画结构变形模式的难点，并建立了界面微结构与铺层参数模型，以提高复合材料板壳结构等效力学性能的预测精度。并基于板壳微元等效刚度的高精度预测，考虑结构宏观几何形态、微观铺层参数与制造工艺的相互耦合，发展了考虑制造约束的复合材料结构拓扑优化设计理论。主要研究内容包括两部分：(一)准周期边界条件下复合材料板壳结构的等效刚度分析模型；(二)基于显式几何基元的复合材料板壳结构几何与拓扑描述方法。. 项目执行期内标注期刊论文成果13篇，其中SCI检索期刊论文9篇，论文成果发表于Composites Part A、International Journal of Mechanical Sciences等相关领域高水平期刊。培养毕业硕士研究生7人。各方面成果指标达到预期指标。