CAJ | 학술논문

针对等效静载荷法(Equivalent static loads method，ESLM)求解大变形和多变量结构动态非线性优化问题难以收敛与效率较低的不足，结合结构静态线性优化方法与最速下降法(Steepest descent method，SDM)提出一种高效的基于梯度的等效静载荷法(Equivalent static loads method based on gradient，ESLMG)，根据结构动态非线性分析计算得到基于节点位移等效的静态载荷，从而将结构动态非线性优化问题转化为以等效载荷及节点位移为输入条件的结构静态线性优化问题(内层循环)；利用内层循环最优解处的梯度信息，同时结合 SDM 方法更新设计变量(外层循环)；将更新的设计变量值作为下一次迭代内层循环的初始值，直到满足收敛条件为止。该方法在保证算法收敛性的前提下，提高了收敛速度。算例表明，该方法对于处理大变形及多变量结构动态非线性优化问题非常有效，在收敛速度方面相比ESLM方法和数值优化算法具有很大的优势。
침대등효정재하법(Equivalent static loads method，ESLM)구해대변형화다변량결구동태비선성우화문제난이수렴여효솔교저적불족，결합결구정태선성우화방법여최속하강법(Steepest descent method，SDM)제출일충고효적기우제도적등효정재하법(Equivalent static loads method based on gradient，ESLMG)，근거결구동태비선성분석계산득도기우절점위이등효적정태재하，종이장결구동태비선성우화문제전화위이등효재하급절점위이위수입조건적결구정태선성우화문제(내층순배)；이용내층순배최우해처적제도신식，동시결합 SDM 방법경신설계변량(외층순배)；장경신적설계변량치작위하일차질대내층순배적초시치，직도만족수렴조건위지。해방법재보증산법수렴성적전제하，제고료수렴속도。산례표명，해방법대우처리대변형급다변량결구동태비선성우화문제비상유효，재수렴속도방면상비ESLM방법화수치우화산법구유흔대적우세。
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 obtalned 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.