A direct determination of weight functions for arbitrary three-dimensional cracks – a combined analytical and numerical approach
A direct determination of weight functions for arbitrary three-dimensional cracks – a combined analytical and numerical approach
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DOI：
10.1023/b:frac.0000045716.79450.9f
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发表时间：
2004-09
影响因子：
2.5
通讯作者：
Y. Sumi
中科院分区：
文献类型：
--
作者：
Y. Sumi
本文提出了一种确定任意三维弹性体裂纹应力强度因子权函数的解析与数值相结合的方法。对于给定的结构几何形状，定义了权函数后，任意载荷条件下的应力强度因子可由权函数与牵引矢量的简单内积得到。传统的权函数定义方法有两种：一种是用裂纹体位移场特征函数展开式的超奇异项来定义，另一种是用位移场相对于裂纹虚延伸的变化量来定义。本文应用Maxwell-Betti功的互等定理，对任意三维裂纹极限边缘附近的裂纹面受三种力偶作用的原问题和辅助问题，定义了应力强度因子的权函数。在本配方中，可以通过使用通用有限元代码结合解析表达式的凝聚点附近，超奇点存在的重量函数计算。二维和三维的说明性的例子证实了该方法的有效性。
A combined analytical and numerical method is proposed for the determination of the weight functions of stress intensity factors of cracks in an arbitrary three-dimensional elastic body. Having defined the weight functions for a given geometry of a structure, the stress intensity factors for arbitrary loading conditions can be obtained by a simple inner product of the weight function and a traction vector. Traditionally weight functions are defined in the two ways; the one is defined by the hyper-singular term of the eigen-function expansion of the displacement field of a cracked body, and the other is defined by the variation of displacement field with respect to a virtual extension of a crack. In the present paper, the weight functions for stress intensity factors are defined by applying the Maxwell-Betti's reciprocal theorem to an original problem and the auxiliary problems subjected to three kinds of force-couples acting on the crack surfaces near the limiting periphery of an arbitrary three-dimensional crack. In the present formulation, weight functions can be calculated by using a general-purpose finite element code combined with analytical expressions near the condensation point, where hyper-singularities exist. The validity of the method is confirmed by two- and three-dimensional illustrative examples.