复合材料结构分析中的辛有限元分形研究

项目名称： 复合材料结构分析中的辛有限元分形研究

项目编号： No.11472005

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 丁克伟

作者单位： 安徽建筑大学

项目金额： 66万元

中文摘要： 将复合材料结构分析问题导入哈密尔顿体系，建立弱形式的应力与位移混合方程，化复合材料结构分析问题为哈密尔顿正则方程问题，研究分形有限元的求解技术，以及正则方程的辛算法，揭示复合材料结构奇异性问题的理论基础，探索其在层合结构计算中的应用，获得复合材料力学行为的实时变化和分层机理，建立一套全新的基于辛几何的求解辛体系。该项目将给出多种复合材料结构的标准哈密尔顿正则方程, 同时引入辛Household 变换、Givens 变换, 以及隐含和显式重新开始的辛Lanczos 方法。 本项目目的是获取一种新的数值分析方法，提高结构分析的计算效率和计算精度。该算法确有特征保持的优点，特别是在解的稳定性上具有独特的优越性，这是一种新的尝试，具有重要的理论意义和广泛的应用前景。

中文关键词： 分形；辛；有限元；复合材料；结构

英文摘要： The composite structure analysis problem have been introduced into the Hamilton system, set up the weak form of stress and displacement mixed equation, the composite structure analysis for the Hamilton canonical equation problem, research the fractal finite element solution techniques, as well as canonical equation of symplectic algorithm, this project reveals composite structure of the theoretical basis of the singularity problem, explore its application in the calculation of the laminated structure and access to real-time changes of the mechanical behavior of composite materials and layered mechanism, establish a set of new the solution of the symplectic system based on symplectic geometry. The project will provide a variety of composite structures standard Hamilton canonical equations, and at the same time introducing symplectic Household transformation, Givens transformation, as well as implicit and explicit re-start of the symplectic Lanczos method. This project to get a new numerical analysis methods, improve the structure analysis computation efficiency and precision. The algorithm has the advantages of keep characteristics, especially in the stability of the solution has a unique advantage, this is a new attempt, and has important theoretical significance and wide application prospect.

英文关键词： fractal;symplectic;finite element;composite;structure