【摘要】 在扩展有限元的框架内,本文发展了一种构造裂尖单元位移场的方法。整个裂纹沿程两侧的非连续位移场只通过富集变换的阶梯函数表征,在裂尖单元,通过调整形函数使得非连续性严格地消失于裂纹尖端。在避免混合区单元引入不满足单位分解的附加位移项的同时,实现了裂纹尖端单元位移场部分非连续特性的表达。还对裂尖单元的形函数调整原则进行了分析,以平面四节点单元为例提出了两种调整方式。文中裂尖单元中含有曲折裂纹的算例说明了本文方法的有效性和适用性。更多还原

【Abstract】 An approximate construction method is developed for crack-tip elements in the frame of extended finite element method.Only the shifted Heaviside functions are introduced to represent the discontinuous displacement field along the whole crack.In crack-tip elements,the standard shape functions are modified to ensure the discontinuity vanish at the crack tip strictly.The partly discontinuous field is achieved and no extra displacement terms are added to the partly-enriched elements.Rules for the modification of the shape functions of crack-tip elements are analyzed.Two kinds of modification based on the proposed method are applied to 4-node bilinear element.The numerical example for zigzag-crack-tip elements demonstrates the validation and efficiency of the proposed method.更多还原