功能梯度材料的二阶一致无网格法

QUADRATICALLY CONSISTENT MESHFREE METHOD FOR FUNCTIONALLY GRADED MATERIALS

功能梯度材料的数值分析通常模型化为材料参数如弹性模量在空间的梯度分布,这将导致更为复杂的应力场,给数值求解带来一定困难。高阶无网格法能更精确地反映应力场,然而过多的积分点导致其计算效率低下。该文将原本针对均匀材料发展的二阶一致无网格法直接应用于功能梯度材料。数值结果表明,它大幅度减少了所需的积分点数目,同时仍然保持高阶无网格法的高精度和高收敛性,因而显著改善了无网格法分析功能梯度材料的计算效率。

Functionally graded materials （FGMs） are usually modeled, in numerical analysis, by using a graded distribution of material parameters, such as the Young＇s modulus. This leads to more complicated stress field and poses certain difficulties in numerical simulations. On the other hand, high-order meshfree methods reproduce stress field more accurately. However, they require much more integration points which leads to inefficiency. In this study, the quadratically consistent meshfree method, originally developed for homogeneous materials, was directly applied to FGM. Numerical results show that the number of integration points are dramatically reduced and meanwhile, the high level of accuracy and convergence of high-order meshfree methods are maintained. As a result, the proposed quadratically consistent meshfree method remarkably improves the computational efficiency of meshfree analysis of FGM.