The Semi-analytical Adjoint Variable Method of Structural Eigenvalue Sensitivity
-
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。Abstract: 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.
-
[1] Keulen F V，Haftka R T，Kim N H．R eview of options for struc-tural design sensitivity analysis．part1: linear systems[J]．Com-puter Methods in Applied Mechanics and Engineering，2005，194:3213～3243 [2] Adelman H M，Haftka R T．Sensitivity analysis of discrete struc-tural systems[J]. AIAA Journal，24(5):823～832 [3] Huan S C，Liang P．A new method of sensitivity analysis of static responses for finite element systems[J]. Finite Elements in Analysis and Design，1998，29:187～203 [4] de Boer H，van Keulen F．R efined semi_analytical design sen-sitivities[J]. International Journal of Solids and Structures，2000，37:6961～6980 [5] Papadrakakis M，Nikolaos D L，Tsompanakis Y．Large scale structural optimization: computational methods and optimization algorithms[J]．Archives of Computational Methods in Engi-neering，2001，8(3):239～301 [6] Tae H L．Adjoint method for design sensitivity analysis of multi-ple eigenvalues and associated eigenvectors [J]. AIAA Jour-nal，2007，45(8):1998～2004 [7] Luo J H，Hae C G．Modal sensitivity analysis of coupled acous-tic-structural systems[J]. Journal of Vibration and Acoustics，1997，119:545～550 [8] Arora J S，Cardoso J B．A variational principle for shape design sensitivity analysis[J]．AIAA，1991，30(2):538～547 [9] Lund E．Finite Element Based Design Sensitivity Analysis and Optimization[D]．Dissertation of Institute of Mechanical Engineering，Aalborg University Special R eport No．23，1994 [10] MD/NASTR AN Design Sensitivity and Optimization User's Guide[M]．MSC．Software Corporation，2010 -
点击查看大图
计量
- 文章访问数: 216
- HTML全文浏览量: 26
- PDF下载量: 7
- 被引次数: 0
下载:
