杨绿峰, 徐 华, 李 冉, 彭 俚. 广义参数有限元法计算应力强度因子[J]. 工程力学, 2009, 26(3): 48-054.
引用本文: 杨绿峰, 徐 华, 李 冉, 彭 俚. 广义参数有限元法计算应力强度因子[J]. 工程力学, 2009, 26(3): 48-054.
YANG Lu-feng, XU Hua, LI Ran, PENG Li. THE FINITE ELEMENT WITH GENERALIZED COEFFICIENTS FOR STRESS INTENSITY FACTOR[J]. Engineering Mechanics, 2009, 26(3): 48-054.
Citation: YANG Lu-feng, XU Hua, LI Ran, PENG Li. THE FINITE ELEMENT WITH GENERALIZED COEFFICIENTS FOR STRESS INTENSITY FACTOR[J]. Engineering Mechanics, 2009, 26(3): 48-054.

广义参数有限元法计算应力强度因子

THE FINITE ELEMENT WITH GENERALIZED COEFFICIENTS FOR STRESS INTENSITY FACTOR

  • 摘要: 应力强度因子是结构断裂分析中的重要物理量。工程应用中常采用奇异单元,利用裂尖奇异区内特定直线上的其他物理量间接计算,并拟合裂尖处应力强度因子的值。该文在改进Williams级数位移场的基础上,根据广义参数有限元法建立了含有裂尖广义应力强度因子作为待定参数的Williams宏单元(简称W单元),导出了奇异区单元的广义参数位移模型和W单元计算格式,并据此直接计算裂尖处的应力强度因子。结合算例分析了W单元的径向离散比例因子、径向离散网格数和级数项数等重要参数对计算精度的影响,并给出了它们的建议值。算例表明:断裂分析的广义参数W单元与通常使用的奇异单元相比,不仅简便实用,而且计算精度高、收敛快。

     

    Abstract: The stress intensity factor (SIF) is an important parameter for structural fracture analysis. The conventional finite element method (FEM) with singular elements was often adopted for SIF calculation in engineering applications, in which displacement or stress components had to be used to attain the SIF at points locating along specified lines in singular domain around the crack tip. In this paper, the Williams series is modified and a Williams macro element is presented for SIF calculation on the basis of the method of finite element with generalized degrees of freedom (FEDOFs). The displacement model for FEDOFs is derived in the singular domain, based on which the SIF near the crack tip can be obtained directly. The influence of some important parameters in the Williams element on the precision of computing results is examined and discussed. The recommended values for these parameters, including the ratio factor of radial discretization, the number of radial discretizing mesh and terms of series, are given based on detailed parametric study. Examples show that the Williams element with Generalized DOFs is more convenient and accurate for SIF analysis than the conventional FEM with singular element.

     

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