含界面裂纹Reissner板弯曲问题分析的奇异单元

首先,采用特征函数渐近展开法,推导了Reissner板弯曲界面裂纹尖端附近位移场渐近展开的前两阶显式表达式,并利用所获得的位移场渐近表达式构造了一种可用于Reissner板弯曲界面裂纹分析的奇异单元。然后,将该奇异单元与外部的常规有限单元相结合,开展了含界面裂纹Reissner板弯曲断裂问题的数值分析。奇异单元可以较好地描述裂纹尖端附近的内力场与位移场,其优势是它与常规单元进行连接时不需要使用过渡单元,并且可以直接给出应力强度因子等断裂参数的高精度数值结果。最后,通过两个数值算例验证了本文方法的有效性。

A singular element for Reissner plate bending problem with interface cracks

On the basis of Reissner''s plate theory,the expressions of the first two order asymptotic displacement field around the tip of an interface crack are derived using William''s eigenfunction series expansion method.And using the deduced generalized displacement field,a novel displacement-mode singular finite element is constructed,which can well depict the characteristic of displacement and singular internal force fields around the crack tip.One advantage of this method is thattransition elements are not required between the singular element and the conventional finite element.Moreover,the stress intensity factors can all be determined directly by the coefficients of the asymptotic series terms.Finally,two numerical examples are analysed to demonstrate the performance of the present method.