基于比例边界有限元广义形函数方法模拟混凝土裂纹扩展问题

本文提出了考虑侧面荷载存在的比例边界有限元广义形函数。该广义形函数具有自然满足单元交界面连续性的优点,采用该方法研究了混凝土黏聚裂纹的扩展问题。在裂纹扩展步中采用线性渐进叠加假设,在断裂过程区,裂尖单元以及非裂尖单元中的黏聚力采用广义形函数以等效荷载的形式统一施加在单元节点上,比以往的插入界面单元或者特解方法来模拟断裂过程区的黏聚力更为简便。另外,本文采用多边形比例边界有限元网格重划分技术对混凝土裂纹扩展问题进行数值模拟,并通过两个典型算例进行了验证。对裂纹扩展路径、荷载-位移曲线以及黏聚力分布进行了分析比较,并对网格敏感性进行了研究,结果表明采用SBFEM广义形函数方法模拟混凝土黏聚裂纹扩展具有准确性和高效性。

Crack propagation modelling in concrete based on scaled boundary finite element generalized shape function

The new scaled boundary finite element shape function (generalized shape function) is proposed considering the side-face loads. The advantage of the generalized shape function that naturally satisfying the continuity of the interface of the element is verified. The generalized shape function method is used to study the cohesive crack propagation in concrete. In the crack propagation step,the linear asymptotic superposition assumption is adopted. In the fracture process zone,the cohesive tractions in the crack tip element and the non-crack tip elements are uniformly applied to the element node in the form of equivalent load, which is more convenient than the previous interface element method to simulate the cohesive tractions in the fracture process zone. Polygon SBFEM remeshing technology is used to simulate the concrete crack propagation problem, and the results of two typical examples are presented. The crack propagation path,load-displacement curve and cohesion distribution are analyzed and compared,and the mesh sensitivity is also studied. The results show that the SBFE generalized shape function method is accurate and efficient for modelling concrete crack propagation.