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 引用本文: 高效伟, 郑保敬, 刘健. 功能梯度材料动态断裂力学的径向积分边界元法[J]. 力学学报, 2015, 47(5): 868-873.
Gao Xiaowei, Zheng Baojing, Liu Jian. DYNAMIC FRACTURE ANALYSIS OF FUNCTIONALLY GRADED MATERIALS BY RADIAL INTEGRATION BEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 868-873.
 Citation: Gao Xiaowei, Zheng Baojing, Liu Jian. DYNAMIC FRACTURE ANALYSIS OF FUNCTIONALLY GRADED MATERIALS BY RADIAL INTEGRATION BEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 868-873.

功能梯度材料动态断裂力学的径向积分边界元法

• 摘要: 采用径向积分边界元法分析功能梯度材料动态断裂力学问题. 该方法使用与弹性模量无关的弹性静力学开尔文基本解作为问题的基本解,在导出的边界-域积分方程中含有由材料的非均质性和惯性项引起的域积分,通过径向积分法将域积分转化为等效的边界积分,得到只含边界积分的纯边界积分方程;从而建立只需边界离散的无内部网格边界元算法. 采用候博特方法求解关于时间二阶导数的系统离散的常微分方程组. 最后通过数值算例验证本文方法的精度和有效性.

Abstract: In this paper, the radial integration boundary element method is presented to analyze dynamic fracture mechanics problems of functionally gradient materials. The fundamental solutions for homogeneous, isotropic and linear elastic solids are used to derive the boundary-domain integration equations by weighted residual method and this approach leads to domain integrals appearing in the resulting integral equations. The radial integral method (RIM) is employed to transform the domain integrals into boundary integrals and thus the boundary-only integral equations formulation can be achieved. The Houbolt method is utilized to solve the resulted system of time-dependent algebraic equations from the discretization. Numerical results are given to demonstrate the efficiency and the accuracy of the present method.

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