Seismic optimal design of frame based on sensitivity analysis

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Journal of Vibration and Shock ›› 2012, Vol. 31 ›› Issue (17) : 99-106.

论文

Seismic optimal design of frame based on sensitivity analysis

LIU Qi-mao, YAN Liu-bin

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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.