关键词: 等效静载荷法, 结构动态非线性优化, 梯度分析, 最速下降法

Abstract: Combined with structure static linear optimization and the steepest descent method(SDM), an equivalent static loads method based on gradient(ESLMG)is proposed to overcome the disadvantages of difficulty to achieve convergence and low efficiency of equivalent static loads method(ESLM) when solving large deformation and multi-variable structure nonlinear dynamic optimization, equivalent static loads based on node displacement are calculated according to structure nonlinear dynamic analysis and then structural dynamic nonlinear optimization problem will be transformed into structure static linear optimization problem with the obtained equivalent loads and node displacement as input conditions, which is called inner iteration. The design variables are updated efficiently according to the method of SDM and the gradient information of optimal solution, which is called outer iteration. The updated variables are used as the initial value of next iteration until convergence condition is satisfied. The proposed method can improve the convergence speed under the premise of algorithm convergence. Numerical examples show that the method is very effective for dealing with large deformation and structure dynamic nonlinear multivariable optimization problem, and it has great advantage compared with ESLM and numerical optimization algorithms in terms of convergence rate.

Key words: equivalent static loads method, gradient analysis, steepest descent method, structure nonlinear dynamic optimization