基于X-SBFEM的裂纹体非网格重剖分耦合模型研究

扩展有限元法利用了非网格重剖分技术,但需要基于裂尖解析解构造复杂的插值基函数,计算精度受网格疏密和插值基函数等因素影响。比例边界有限元法则在求解无限域和裂尖奇异性问题优势明显,两者衔接于有限元法理论内,可建立一种结合二者优势的断裂耦合数值模型。该文从虚功原理出发,利用位移协调与力平衡机制,提出了一种断裂计算的新方法X-SBFEM,达到了扩展有限元模拟裂纹主体、比例边界有限元模拟裂尖的目的。在数值算例中,通过边裂纹和混合型裂纹的应力强度因子计算,并与理论解对比,验证了该方法的准确性和有效性。

STUDY ON THE COUPLING MODEL OF CRACK WITHOUT REMESHING BASED ON X-SBFEM

The extended finite element method (XFEM) without remeshing has to adopt complex interpolation function based on analytic solution in the crack tip. Besides, the computational accuracy is affected by mesh density and interpolation function. The scale boundary finite element method (SBFEM) has great advantage in solving problems characterized by stress singularity and infinite domain. Because both methods are combined into the finite element theory, a fracture numerical coupling model with the advantages of the two methods can be established. Based on the principle of virtual work, a new fracture numerical method called X-SBFEM is proposed by taking advantage of the displacement coordination and the force balance mechanism. In this method, the crack body is simulated by XFEM and the crack tip is simulated by SBFEM. During the numerical evaluation, this algorithm is validated by calculating the stress intensity factors of cracks, which is compared with the theoretical solution.