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为促进和推广扩展有限元在实际复杂问题中的应用,提出一种适用于扩展有限元非连续区域积分的简易积分方案。利用基于该积分方案的扩展有限元程序,结合粘聚裂纹模型实现了对三点弯梁开裂过程的模拟。结果表明,由此积分方案得出的结果与常规分片积分法方案得到的结果以及已有研究结果十分吻合。与已有积分方案相比,此简易积分方案既能保证精度和收敛性,同时无需复杂的分片积分过程,也无需考虑零能模式的控制措施,大大地降低了建模的复杂性和成本。
In order to promote and popularize the application of extended finite element in practical complex problems, a simple integral scheme suitable for expanding integral of finite element discontinuous area is proposed. Using the extended finite element program based on the integral scheme, combined with the cohesive crack model, the simulation of the cracking process of the three-point bending beam was realized. The results show that the result obtained by this integral scheme is in good agreement with the results obtained by the conventional piecewise integral method and the existing research results. Compared with the existing integral scheme, this simple integral scheme can ensure the accuracy and convergence without the need of complicated slice integral process and without considering the control of zero-energy mode, thus greatly reducing the complexity and cost of modeling .