项目名称: 一种全新的结构修改重分析方法及其应用
项目编号: No.11472014
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: 陈璞
作者单位: 北京大学
项目金额: 68万元
中文摘要: 结构修改重分析在计算固体力学的研究与实践中大量存在,如材料非线性、结构拓扑优化、施工模拟等,然而目前已有的重分析算法均无法满足需求,当遇到大量修改的情形往往会失效。针对这个问题,本项目在目前流行的高效的稀疏矩阵求解方案基础上,提出一种全新的结构局部修改重分析直接方法。该方法的基础是修改后刚度矩阵三角分解式的更新,申请人等的研究发现,结构的局部修改只影响刚度矩阵三角分解中的少部分矩阵元素。与结构修改重分析直接法中传统的Sherman-Morrison-Woodbury公式相比,本项目提出的方法在大规模问题局部大量修改时具有极高的计算效率,并且与现在广泛使用的有限元方法的稀疏矩阵求解方案兼容,实现相对简单,方便推广和应用。这一研究及其应用有望极大地提高结构修改重分析的能力,无论是规模还是效率。从而提高材料非线性、结构拓扑优化、施工模拟等有限元计算的效率。
中文关键词: 有限元;结构修改;图分裂;稀疏矩阵
英文摘要: Reanalysis for structural modifications exists widely in the research and practice of computational solid mechanics, such as material nonlinear problem, structural topological optimization, construction sequence analysis, etc. However, the existing reanalysis methods are usually not efficient if the number of the modifications in terms of element or rank is large. To address this problem, a new direct reanalysis method for local structural modifications, based on popular efficient sparse matrix solvers, will be studies in this project. The basis of this method is to update the triangular factor after modifying. The applicants' recent studies show that local structural modifications only affect part of the factors in triangular factorization. To compare with the traditional reanalysis method, Sherman-Morrison-Woodbury formulas, the proposed method is much more efficient for large number of modifications. Moreover, this new method is completely compatible with the present row-format sparse matrix solver and can be easily implemented and popularized. This study is expected to greatly improve the ability of reanalysis for modifications both in scale and efficiency.
英文关键词: finite element;structural modification;graph partition;sparse matrix