无需分片积分的扩展等参有限元法模拟混凝土裂缝扩展

Crack Growth Simulation in Concrete Beam Based on Extended Isoparametric Finite Element Method Under Quadrature Without Sub-area

针对有限元方法在模拟裂缝时的缺点,采用扩展有限元方法进行了混凝土梁的开裂模拟。采用统一的富集函数表示非连续场,避免了混合单元的出现,且此格式下的富集自由度具有特定意义。在非连续单元积分时,采用简易积分方案,在满足精度的基础上,减少了建模的复杂性。最后基于等参单元模型,运用扩展有限元方法进行了混凝土梁在位移加载下的裂缝扩展模拟,并与已有研究成果进行了比较,结果比较吻合。表明此模型在简化计算下保证了精度和收敛性。

Aiming at the drawback of FEM in modeling crack, an extended finite element method for modeling the fracture of a concrete beam is studied. Unified enrichment function is adopted in the approximation of discontinuous field, in which mixing element is avoided and the enrichment freedom has specific significance. A simple integration scheme is used for numerical quadrature of discontinuous zones. This scheme can reduce the complication with acceptable accuracy. At last, based on isoparametric element, crack growth in a concrete beam under displacement loading is simulated. The results agree well with those obtained from other methods. This scheme guarantees accuracy and convergence and simplifies procedure.