Time history response derivatives with respect to the design variables are frequently used in optimization design, damage detection, structural control, etc. This paper proposes a substructuring method for efficient calculation of higher order time history response derivatives of large-scale structures. First, the global structure is disassembled into several small substructures and the substructural displacement is projected onto the range space of a few substructural master eigenvectors. Afterwards, the derivative of substructural master eigenvectors of a few substructures containing the design variables are assembled to form the reduced first, second, and higher order sensitivity equations with a size of the number of master eigenvectors. The equivalent eigenvector which relates the slave and master eigenvectors is derived to compensate for the inertial effect of discarded slave eigenvectors. Finally, the first, second, and higher order time history response derivatives of global large-scale structure are efficiently solved from the reduced sensitivity equations by using Newmark- β method. A numerical one-bay plane frame and a numerical highway bridge are applied to verify the accuracy and efficiency of proposed substructuring method.

中文翻译：

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利用子结构法高效计算高阶时程响应导数

关于设计变量的时程响应导数经常用于优化设计、损伤检测、结构控制等。本文提出了一种高效计算大型结构高阶时程响应导数的子结构方法。首先，将全局结构分解为几个小的子结构，并将子结构位移投影到几个子结构主特征向量的范围空间上。然后，将包含设计变量的几个子结构的子结构主特征向量的导数组合起来，以形成主特征向量数量大小的简化一阶、二阶和高阶灵敏度方程。导出关联从属特征向量和主特征向量的等效特征向量以补偿被丢弃的从属特征向量的惯性效应。最后，利用Newmark-β方法从简化的灵敏度方程中有效求解全局大尺度结构的一阶、二阶和高阶时程响应导数。应用数值一湾平面框架和数值公路桥梁验证了所提出的子结构方法的准确性和效率。