复杂结构的复变函数半解析灵敏度求解方法

项目名称： 复杂结构的复变函数半解析灵敏度求解方法

项目编号： No.51205356

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 机械工程学科

项目作者： 金伟娅

作者单位： 浙江工业大学

项目金额： 25万元

中文摘要： 在复杂结构的梯度优化设计中，精确的灵敏度是正确的优化搜索方向和准确的优化结果的必要保证，高效的灵敏度计算必将提高优化设计的计算效率。申请人提出了高精度、高计算效率的复变函数半解析法，该方法结合了复变函数法和半解析法两者的优点，复变函数法对步长不敏感的优点解决了半解析法由于对步长敏感而导致的严重精度问题,而半解析法高效的计算流程解决了复变函数法计算效率低,所需计算空间大的不足。复变函数半解析法已成功应用在梁单元和平面薄壁板单元结构的灵敏度计算中，结果表明，该方法可将传统的割线灵敏度近似到切线灵敏度，且不失精度和计算效率。但是，复杂结构的灵敏度求解远较梁、平面薄壁板单元复杂得多。本项目拟在前期研究的基础上，研究复变函数半解析法在复杂的材料非线性、几何非线性结构中的算法和精度，并进一步将该方法应用到实际复杂工程结构的尺寸和形状优化设计中，研究其在三维复杂结构的优化设计中的算法、精度和计算效率。

中文关键词： 复变函数半解析法；灵敏度分析；可靠度分析；优化设计；半解析法

英文摘要： In gradient optimization design for complex structures, accurant sensitivities are necessary for correct optimizatin search direction and accurate optimization result. High computational efficiency of sensitivities improves speed of optimization. The applicant proposed Complex Variable Semi-analytical method (CVSAM) with hign accuracy and computational efficiency. This method combines the advantages of complex variable method and semi-analytical method.The advantage that complex variable method is not sensitive to the step size resolves the accurate problem of semi-analytical method. Meanwhile, the computational efficiency of semi-analytical method resolves low computational efficiency and large computational space requirement of complex variable method. The CVSAM has been successfully applied to sensitivity analysis for beam and plane elements. The result shows it obtains very accurate sensitivity with high computational efficiency. However,sensitivity analysis for complex structrues is more complicated than simple beam and plane elements. The research of the project will focus on computational arithmetic and accuracy of sensitivity analysis by the CVSAM in complex material nonlinear and geometric nonlinear structures. Further research will apply CVSAM in the dimensional and shape optimization of a complex 3-D

英文关键词： Complex variable semi-analytical method；sensitivity analysis；reliability analysis；optimization design；semi-analytical method