非网格重剖分模拟宏观裂纹体的扩展有限单元法(Ⅰ:基础理论)

基于有限元计算网格,扩展有限单元法通过建立特殊的广义节点插值形式来描述含裂缝体的不连续位移场,避免了有限元法模拟裂缝时需要的网格重划分。进而,本文从虚功原理出发,在有限元法框架内完整地推导了能模拟宏观裂纹力学场的扩展有限元法实现公式,在理论上更全面地考虑了内部裂纹面上分布外载荷及缝内粘连材料刚度的影响,并提出了构建统一的扩展有限单元刚度阵形成模式,保证了与传统有限单元方式的协调一致。文中对方法的实现过程也做了详细阐述,给出了通用的计算公式,确保了算法的可行性。

Extended finite element method for modeling cracks without remeshing(Ⅰ:basic theory)

Within the basic frame of the finite element method(FEM),the extended finite element method(XFEM) for modeling macro-cracks is developed and improved in theory in this paper,in which the special discontinuous displacement field is simulated by applying a generalized nodal interpolation method,as well as cohesive cracks and the effects of loading on crack surfaces can also be efficiently considered in the computation.During its numerical evaluation,this article introduces a unified constructing process of stiffness matrices for various extended finite elements,consistent with the traditional finite element method.In addition,all of the related calculating expressions are presented in detail, and some key factors in the numerical implementation of XFEM are discussed to ensure its feasibility.