超大规模变量结构敏度求解技术研究

摘要

The sensitivity analysis plays a critical role in super large-scale optimization problem.The analytic method for sensitivity analysis has been investigated deeply,and the analytical expression of differential stiffness matrix is derived for shell elements and the displacement constraints sensitivity is obtained by using virtual displacement method.The method was programmed based on the HAJIF system with FORTRAN language.Validation examples showed that the proposed method has a high reliability in solving super large-scale optimization problem,and the efficiency of the present method is almost 70 times of that of the differential method.%针对超大规模变量结构优化中的敏度求解问题,深入系统地研究了全解析法高效位移敏度求解理论,推导了壳单元微分刚度矩阵的解析表达式,引入虚位移法解决了结构刚度矩阵求逆运算,进而给出了位移敏度全解析表达式.采用科学高效的程序流程组织方法在HAJIF系统平台上开发了超大规模变量结构位移敏度快速求解模块.与差分法和半解析法的对比结果表明:本文算法敏度结果具有较高的可靠性;超大规模变量位移敏度算例测试表明本文算法效率约为差分法的70余倍,敏度结果一致性较好,所开发的模块能够高效可靠的解决超大规模变量位移敏度求解问题.