摘要
灵敏度分析在结构优化设计和可靠性分析中起着至关重要的作用。针对特征值敏度的解析法在有限元分析中不足,本文提出了一种基于半解析的伴随变量特征值敏度分析方法,用有限差分法代替了常规的解析求导。另外,针对导数矩阵稀疏性的特点提出了一种新颖的存储方法,并将这种方法应用于伴随变量法涉及到的导数矩阵存储,节省了存储空间。最后将本文提出的伴随变量方法与常见的解析法敏度分析方法进行对比,证实本文方法在精确性和计算效率上得到了较大的提高,且非常适合于大型结构的敏度分析。
The sensitivity analysis is very significant in structural optimization design and reliability analysis. To overcome the shortcomings of the analytical eigenvalue sensitivity method in the finite element analysis, a semi- analytical adjoint variable method is proposed, in which the finite difference method has been adopted instead of the analytical derivative. In addition, a new method is developed to store the sparse derivative matrix, which is applied to the proposed adjoint variable method to save the computational memory. Finally, a comparison is made between a general analytical method and the proposed semi-analytical adjoint variable method, it is found that the accuracy and computational efficiency has been improved greatly, and also the proposed method is suitable for large-scale structural sensitivity analysis.
出处
《机械科学与技术》
CSCD
北大核心
2013年第8期1221-1224,1229,共5页
Mechanical Science and Technology for Aerospace Engineering
关键词
结构特征值
设计敏度分析
半解析法
伴随变量
稀疏矩阵的存储
computational efficiency
finite difference method
matrix algebra
sensitivity analysis
structuraleigenvalue
design sensitivity analysis
semi-analytical method
adjoint variable
sparse matrix storage
