结构优化半解析灵敏度及误差修正改进算法

提出结构半解析灵敏度分析及其针对刚体位移的误差修正方法的改进算法, 构建灵敏度分析与误差修正项可分离形式. 该方法实现简便, 数值精度不受摄动步长与单元数目的影响. 首先从总体角度推得静力问题的误差修正半解析灵敏度分析方法, 提出了位移误差修正灵敏度列式, 并给出算法实施途径; 然后将此思路推广于自振频率、屈曲临界载荷问题, 提出了相应的计算步骤. 随后, 给出梁单元与壳单元误差修正项的具体推导方法, 并分别使用两种单元构建有限元模型进行算例测试. 结果表明, 该方法适用于多种分析类型, 数值精度不受单元数目与摄动步长的影响. 由于灵敏度分析与误差修正项可以分开计算, 该方法支持将误差修正项直接叠加于灵敏度求解结果进行误差修正, 使已有灵敏度分析程序得到充分利用. 尤其对于复杂工程结构的优化设计, 特别是形状优化设计以及尺寸、形状混合优化设计, 相比于原误差修正方法, 实现更为简便, 效率有所提升, 能为半解析灵敏度分析方法及其程序实现提供新的思路. 

MODIFIED SEMI-ANALYTICAL SENSITIVITY ANALYSIS AND ITS ERROR CORRECTION TECHNIQUES

Modified semi-analytical sensitivity analysis algorithm and its error correction term method are presented, where the sensitivity analysis terms and the error correction term can be separated. The method can facilitates program implementation and the accuracy of the method won’t be influenced by perturbation step length and number of elements. Firstly, a modified semi-analytical sensitivity analysis technique with its error correction term is presented for static displacement, which is based on global structure equations of the sensitivity analysis, and its program implementations are provided. Then, the modified method is implemented on other analysis tasks including natural frequency and linear buckling analysis. Consequently, the error correction terms of both beam elements and shell elements are derived. Then, the specific deducing process of error correction terms concerning beam and shell elements is described. Next, the modified method is verified by typical finite element models with beam and shell elements. The results highlight the applicability of the modified method to various analysis types mentioned above, and the accuracy is not influenced by the number of elements and perturbation step length. Since sensitivity analysis parts and error correction term can be computed respectively, the error correction term can becomputed independently and added directly to the results of sensitivity analysis, which can make full use of existing sensitivity analysis programming. This modified method can help complex engineering structural design. Especially, compared to the original semi-analytical sensitivity analysis and error correction methods, the computational efficiency of the modified method is enhanced with respect to shape optimization design variables or shape combined with size optimization, which can provide new ideas for sensitivity analysis and its program implementation.