面向多孔点阵材料与结构动力学特性分析的等几何流形元法研究

Periodic and porous lattice material and structure, as high-strength and light-weight multifunctional material, is of great potential applications, and thus are widely used in high-tech fields such as aerospace and warship/submarine fields at home and abroad. During the service, the lattice materials and structures inevitably endure dynamic loads such as vibration and impact. Therefore, to predict the dynamic characteristics of lattice materials and structures efficiently, the study of calculation method is of great scientific significance and application value. With the demand of structural dynamic characteristics analysis and optimization design of lattice materials and structures, and avoiding that current methods cannot predict the structural frequency and strength of lattice structures effectively, this project is proposed to develop novel and efficient isogeometric manifold method to analyze the dynamic characteristics of lattice materials and structures. In this project, theoretical derivation, numerical calculation and confirmatory experiments are employed for the analysis to obtain the final numerical model of dynamic characteristics analysis of porous lattice material and structure. For the efficient dynamic analysis of lattice material and structure, new isogeometric manifold elements, mesh generation technique and the solving of dynamic equilibrium equations are studied to form the theory of isogeometric manifold method. New method can provide a novel and efficient tool for the prediction of dynamic characteristics and structural optimization design of lattice material and structure.

具有周期性和多孔性的点阵材料与结构，是极具应用潜力的轻质高强多功能材料，在国内外航空航天、舰船/潜艇等诸多高科技领域受到了广泛关注与应用。点阵结构在服役过程中，不可避免的承受振动、冲击等动态载荷，研究其动力学特性高效预测的计算方法具有重要的科学意义和应用价值。本项目基于点阵材料与结构动力学特性分析与结构优化设计的需求，针对现有方法无法准确并高效预测多孔点阵结构频率、强度等动力学特性的问题，发展适用于点阵材料与结构动力学特性高效分析的等几何流形元法。项目采用理论推导、数值计算和验证性实验相结合的方法，开展针对点阵结构高效分析的等几何流形单元、网格划分与动力学方程求解的研究，最终获得多孔点阵材料与结构动力学特性分析的数值计算模型，据此形成点阵结构动力学特性分析的等几何流形元理论，实现对点阵结构动力学特性的高效准确分析，最终为多孔点阵材料与结构的动力学特性预测与优化设计提供理论基础和技术支撑。

具有周期性和多孔性的点阵材料与结构，是极具应用潜力的轻质高强多功能材料，在国内外航空航天、舰船/潜艇等诸多高科技领域受到了广泛关注与应用。点阵结构在服役过程中，不可避免的承受振动、冲击等动态载荷，研究高性能的点阵结构以及其动态特性与高效的数值仿真分析方法具有重要的科学与应用价值。本项目主要研究了新型点阵结构的静动态特性，对适用于点阵结构数值分析的计算方法开展了系统的研究。在项目资助下，课题组设计了新型的二维与三维的轻质承载点阵结构，并通过增材制造技术制备了性能可靠的点阵结构，验证了设计的可行性。尤其对于三维点阵结构，通过样条插值的方式修正了点阵结构的设计，优化静动力学特性的同时，得到了该点阵结构的网格生成技术，发展了点阵结构的数值仿真技术。新型二维与三维点阵结构在轻量化水平与承载特性方面较传统结构具有明显优势，可为点阵结构在航空航天轻量化结构中的应用奠定基础。课题组还提出了新型三维手性多功能点阵结构的设计方法，给出了其细观本构模型与高精度数值计算方法，开展了实验表征研究，验证了新型结构特有的拉扭耦合特性。针对点阵结构或复杂拓扑结构的动力学分析，课题组开展高精度数值计算方法的研究，针对等几何单元与有限元单元的动力学时域分析开展了研究，获得了高精度的数值计算方法，可为点阵结构的动力学特性高精度计算提供直接的仿真分析技术。在项目资助下，课题组在Journal of the Mechanics and Physics of Solids, Composite Structures, Extreme Mechanics Letters, International Journal of Mechanical Science, Computers & Structures, Computational Mechanics等期刊上发表SCI论文14篇，申请发明专利2项。