基于遗传算法的弹性地基加肋板肋梁无网格优化分析

RIB MESHLESS OPTIMIZATION OF STIFFENED PLATES RESTING ON ELASTIC FOUNDATION BASED ON GENETIC ALGORITHM

基于遗传算法及一阶剪切理论,提出一种弹性地基上加肋板肋条位置优化的无网格方法.首先,通过一系列点来离散平板及肋条,并用弹簧模拟弹性地基,从而得到加肋板的无网格模型;其次,基于一阶剪切理论及移动最小二乘近似原理导出位移场,求出弹性地基加肋板总势能;再次,根据哈密顿原理导出结构的弯曲控制方程,并通过完全转换法处理边界条件;最后,引入遗传算法和改进遗传算法,以肋条的位置为设计变量、弹性地基板的中心点挠度最小值为目标函数,对肋条位置进行优化达到地基板控制点挠度最小的目的.以不同参数、载荷布置形式的弹性地基加肋板为例,与ABAQUS有限元结果及文献解进行比较.研究表明,采用所提出的无网格模型可有效求解弹性地基上加肋板弯曲问题,结果易收敛,同时基于遗传算法与改进混合遗传算法所提出的无网格优化方法均可有效优化弹性地基加肋板肋条位置,后者计算效率相对较高,只进行了三次迭代便可获得稳定的最优解,此外在优化过程中肋条位置改变时只需要重新计算位移转换矩阵,又避免了网格重构.

Based on the genetic algorithm and the first-order shear deformation theory,a meshless method is proposed to optimize the position of ribs of the stiffened plate resting on elastic foundation.Firstly,the meshless model of the stiffened plate is obtained by discretizing the plate and ribs with a series of points and by simulating the elastic foundation with springs.Secondly,the displacement field is approximately obtained based on the first-order shear deformation theory and the moving-least square approximation,and the total potential energy of the stiffened plate resting on the elastic foundation is derived.Then,the boundary conditions are dealt with the full transformation method,and the governing equation of the structure is derived from the Hamilton principle.Finally,the genetic algorithm and the improved genetic algorithm are introduced with the location of ribs as the design variable and the minimal deflection of the center point of the stiffened plate as the objective function.The arrangement of ribs is optimized to achieve the minimum center point deflection of the stiffened plate resting on the elastic foundation.Taking some ribbed plates resting on elastic foundation with different parameters and load distribution as the numerical examples,the comparison with the finite element results given by ABAQUS is carried out.The results show that the proposed meshless model can effectively analyze the bending problem of stiffened plate on elastic foundation.Meanwhile,the meshless optimization method based on the genetic algorithm and the improved genetic algorithm both can effectively optimize the position of the ribs of the stiffened plate on elastic foundation,the latter is relatively efficient,and the stable optimal solution can be obtained after only three iterations.Additionally,when the position of the rib changes during the optimization process,only the displacement transformation matrix needs to be recalculated,and the mesh reconstruction is totally avoided.