用扩展有限元方法来分析含裂纹板时剪切闭锁问题消除

摘要

A method for the modeling of cracks in plates using the extended finite element method is pre-sented, this method is based on traditional finite element method, the standard displacement fields are en-riched with discontinuous fields and the near tip asymptotic fields which present the crack, thus this allows for crack geometries are independent of the finite element mesh topology, and greatly facilitates the sim-ulation of crack growth. Using mixed interpolation (MITC4) which solves the problem of Reissner plates can avoid the phenomenon of shear locking. Using the interaction integral can derive mixed-mode stress inten-sity factors. Finally, a series of numerical examples illustrated the accuracy and utility of this method.%文章介绍了扩展有限元计算含裂纹板问题的基本方法，该方法以常规有限元为基础，通过在位移场中增加反映裂纹面的不连续函数及反映裂尖局部特性的裂尖渐近位移场函数，体现裂纹的存在，从而使裂纹与有限元模型相互独立，方便了裂纹扩展的模拟。采用求解 Reissner 板问题的混合插值单元 MITC4，可以有效地避免剪切闭锁现象。通过相互作用能量积分确定混合模型的应力强度因子。最后，通过一系列的数值算例验证了该方法的正确性。