双材料V型切口应力强度因子的加料有限元分析

Enriched finite element analysis of stress intensity factors of bi-material V-notch

应用Williams本征函数展开和线性变换求解V型切口端部渐进位移场。将该位移场加入常规等参单元位移模式中,构造双材料V型切口加料单元和过渡单元的位移模式,推导加料有限元方程。建立带V型缺口双材料三点弯曲梁试件和直角界面端平面问题的加料有限元模型,求解有限元方程可直接得到应力强度因子。计算结果与用其他方法得到的数据吻合,验证了方法的正确性,可用于双材料V型切口结构断裂特性计算分析。

The V-notch asymptotic displacement field was derived through an approach based on the Williams＇ series expansion and linear algebraic transforms. By incorporating the displacement expressions to the common isoparametric elements,the enriched and transition element displacement model were obtained,and then the enriched finite element equation was derived consequently. The enriched finite element model for a V-notched bi-material three-point bending beam and an orthogonal bonded materials interface end plane problem were constructed. The stress intensity factors can be solved directly from the finite element equation. Comparisons between the results and the published data computed with other algorithm indicate that the present method is correct and can be used to analyze the fracture property of the V-notched bi-material structure.