Development of Sensitivity Analysis and Reanalysis mothods for Nonlinear

在这个研究项目的起点上，仅仅是为了开发非线性结构反应的灵敏度分析和重分析方法。然而，从实用的角度来看，结构优化也包括应用所开发的方法。首先，在有限元框架内建立了弹塑性结构响应的灵敏度分析方法。对于弹塑性结构行为的重分析，采用了泰勒级数展开法。计算了桁架结构、框架结构和板结构的弹塑性反应灵敏度。应用该方法得到的再分析解与精确解吻合较好。此外，还发现荷载放大系数的灵敏度在重分析中起着重要作用，从而使单元的精确屈服成为可能。本文还建立了梁柱和加筋板屈曲后弹性行为的灵敏度分析方法。梁柱采用有限元方法，加筋板采用解析法。结果表明，在载荷控制下进行分析时，重分析解与屈曲载荷附近的精确解有很大不同，并将所提出的方法应用到优化设计中。然后，对考虑屈曲的桁架结构和考虑弹性板屈曲的加筋板进行了优化设计，验证了该方法的有效性。

At the starting point of this research project, only the development of methods for sensitivity analysis and reanalysis for nonlinear structural responses were aimed. However, from the practical point of view, structural optimization was also included applying the developed methods.At the beginning, the method of sensitivity analysis was developed for elastoplastic structural responses in the framework of the finite element method. For reanalysis of elastoplastic structural behavior, Taylor's series expansion method was applied. The sensitivities of elastoplastic responses of truss, frame and plate structures were calculated. The reanalysis solutions applying the proposed method were found to be in good agreement with the exact solutins. It was also found that the sensitivities of load magnification factors which enables exact yielding of elements play an important role in reanalysis.The methods of sensitivity analysis for post-buckling elastic behavior were also developed for beam-columns and stiffened plates. The finite element methods was applied for beam-columns, and the analytical method for stiffened plates. It was found that the reanalysis solution is largely different from the exact solution near the buckling load when the analysis is performed under load control.At the end, the developed methods were incorporated into the optimal design procedure. Then, the optimization of truss structure allowing yielding and that of stiffened plates allowing elastic panel buckling were performed, and the usefulness of the proposed method was demonstrated.