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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。
Numerical analysis of functionally graded materials is usually modeled as a gradient distribution of material parameters such as elastic modulus in space, which leads to more complex stress fields and presents some difficulties in numerical solution. The higher-order meshless method can reflect the stress field more accurately, however, the excessive integration points lead to low computational efficiency. In this paper, the second-order uniform meshless method, which was originally developed for homogeneous materials, is applied directly to functionally graded materials. The numerical results show that it significantly reduces the number of integration points required while still maintaining the high accuracy and high convergence of the higher-order meshless method, thereby significantly improving the computational efficiency of the meshless method for analyzing functionally graded materials.