基于非线性分析的加肋板肋条位置无网格优化

在加肋板无网格模型中,肋条的位置对各种工况下加肋板受力性能的影响至关重要.文章基于一阶剪切变形和移动最小二乘法理论提出一种考虑非线性影响的加肋板无网格模型,并利用遗传算法优化肋条位置.首先,采用离散节点分别对平板和肋条进行离散,得到加肋板的无网格离散模型;其次,通过冯·卡门大挠度理论得到非矩形板几何非线性问题的弯曲控制方程;再次,通过哈密顿原理得到加肋非矩形板自由振动问题的控制方程;最后引入遗传算法,以肋条的位置为设计变量、非矩形加肋板中心点挠度最小或自振频率最大为目标函数,对肋条位置进行优化.在考虑了几何非线性影响的肋条位置优化过程中,肋条位置改变时只需重新计算位移转换矩阵,避免了网格重构.本文以全局荷载下单肋条菱形板为例与理论解进行对比,进行有效性验证.再以板的中点挠度最小和自振频率最大为优化目标,对局部荷载作用下不同形状、不同肋条布置方式的加肋板进行优化,分析方法的收敛性及稳定性.

THE OPTIMIZATION OF RIBS POSITION BASED ON STIFFENED PLATES MESHLESS MODEL WITH NONLINEARITY

In the stiffened plate's meshless model, the ribs' position is critical to the mechanical performance of the stiffened plate under various working conditions. Based on the first-order shear deformation theory and the moving-least square approximation, a meshless model of the stiffened non-rectangular plate considering nonlinearity is proposed and the position of the ribs is optimized based on the genetic algorithm. Firstly, the meshless model of the stiffened plate is obtained by discretizing the plate and ribs with discrete nodes. Secondly, the bending governing equation for the geometrically nonlinear problem of the stiffened non-rectangular plate is derived from the Von Karman large deflection theory. Then, the governing equation for the free vibration problem of the stiffened non-rectangular plate is derived from the Hamilton principle. Finally, the genetic algorithm is introduced with the position of the ribs as the design variable and the minimal deflection or the maximal natural frequency of the center point of the non-rectangular stiffened plate as the objective function to optimize the position of ribs. In the process of ribs' position optimization considering the influence of geometric nonlinearity, only the displacement transformation matrix needs to be recalculated when the ribs' position changed, and the mesh reconstruction is totally avoided.In this paper, first taking the single-rib rhombus plate under global load as an example, the comparison with the theoretical results is carried out and the validity of the method is verified. Then, taking the minimum center point deflection and the maximum natural frequency of the stiffened plate as the optimization objective, the stiffened plates with different shapes and different rib' arrangements under local load were optimized, and then the convergence and stability of the proposed method were studied.