基于XIGA的开孔功能梯度板材料分布多目标优化

MULTI-OBJECTIVE OPTIMIZATION OF MATERIAL DISTRIBUTION FOR FUNCTIONALLY GRADE PLATES WITH CUTOUTS BASED ON XIGA

为解决开孔功能梯度板多目标优化问题,提出了一种将扩展等几何分析方法(XIGA)和以材料分布变化的求解模式。针对开孔结构功能梯度板的力学计算,引入三阶剪切变形理论,并采用扩展等几何分析方法。为提高数值精度,在孔边界区域做四叉树自适应高斯积分。在材料属性描述中,以B样条函数代替传统的功能梯度材料分布函数。优化过程中,以描述材料分布的控制点作为设计变量,建立第一自然频率最大、板质量最小和屈曲临界参数最大的多目标优化问题,其中优化算法选用NSGA-II算法。通过算例表明了算法的有效性。

To solve the multi-objective optimization problem of functionally graded plates with cutouts,a method integrating extended isogeometric analysis(XIGA)and material distribution variation is proposed.For the mechanical calculation of functionally graded plates with cutouts,the third-order shear deformation theory is introduced,and the extended geometric analysis is adopted.To improve the numerical accuracy,the quadtree adaptive gauss integral is used in the hole boundary region.The B-spline function is used to replace the traditional functional grade material distribution function in the description of material properties.In the optimization process,the control points describing material distribution are taken as design variables to establish multi-objective optimization problems with the largest first natural frequency,the smallest plate mass and the largest buckling critical parameters.The NSGA-II algorithm is selected as the optimization algorithm.The effectiveness of the proposed algorithm is demonstrated by some examples in this paper.