基于敏度分析的框架抗震优化

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (17) : 99-106.

论文

基于敏度分析的框架抗震优化

刘齐茂 , 燕柳斌

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Seismic optimal design of frame based on sensitivity analysis

LIU Qi-mao, YAN Liu-bin

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文章历史 +

摘要

针对目前结构抗震优化设计方法存在优化效率低下的问题，提出一种高效的框架抗震优化设计方法。在有限元法和Newmark法基础上导出一种高效的层间相对位移对设计变量一阶和二阶导数的算法，建立显含时间参数，以结构质量最小化为目标，同时满足层间相对位移和设计变量约束的优化数学模型，通过积分型内点罚函数将显含时间参数的不等式约束优化问题转变为一系列不含时间参数的无约束优化问题，利用层间相对位移对设计变量一阶和二阶导数的信息计算罚函数的梯度和海森矩阵，然后利用梯度和海森矩阵构造求解优化设计问题高效有效的优化算法。算例表明本文的抗震优化方法能获得结构的最优设计，具有简单、下降速度快、不需要进行一维搜索等特点。是一种有效和高效的框架抗震二阶优化方法。

Abstract

Currently the seismic optimal design methods of structures are inefficient. This paper develops an efficient seismic optimal design method for the frames. An efficient algorithm of the first and second derivatives of the interstorey drift with respect to design variables is derived based on the finite element method and Newmark method. The time-dependent optimal mathematics model for achieving minimum weight design with interstorey drift and design variable constraints is established. The inequality constraint time-dependent problem is converted into a sequence of appropriately formed unconstrained time-independent problems using the integral inner point penalty function method. The gradient and Hessian matrix of the penalty function can be achieved using the information of the first and second derivatives of the interstorey drift with respect to design variables. Then the efficient and effective optimal algorithm is constructed to solve the optimal design problem using the gradient and Hessian matrix. The example indicates the seismic optimal design method in this paper can obtain the optimum design of the structures. The major advantages of the seismic optimal design method are simplicity, the descent property, the excellent convergence rate near the optimum, and the absence of a line search. It is an efficient and effective seismic second-order optimization method for the frames.