多参量断裂力学广义杂交/混合裂纹有限元法

通过研究广为人知的断裂力学单变量八节点位移裂纹QPE元和Akin族奇异单元法，本文运用经典局部裂纹解析解，与非协调假设应力杂交-混合元列式方法相结合，提出用于分层各向异性材料的多变量半解析假设应力奇异广义杂交／混合裂纹有限元法，能克服现有位移裂纹元法的域应力分布精度低和高次单元所需计算容量大的局限性，互为补充，更有利于结构裂纹扩展分析和应用研究。文中设计了一个半解析奇异裂纹平面单元，各向同性材料板算例验证了退化二次八节点协调位移裂纹元及六节点非协调奇异应力裂纹元，说明采用稀疏及加密单元网格，两类裂纹单元分别从上下逼近收敛于实验和理论参考解，可得到吻合程度较好的1／√r奇异应变和应力分量以及应力强度因子值，表明了本文奇异裂纹单元理论的优越性。

Two Variant Semi-analytical Generalized Hybrid/Mixed Crack Finite Element Procedure for Computational Fracture Mechanics in Multi-Layered Domains

Through studying the renowned second order compatible displacement quarter-point element(QPE)for cracks and Akin's compatible singular element family,this paper continues to modify the two-variable assumed stress generalized hybrid/mixed element(GH/ME) model according to linear fracture mechanics,and proposes for the corresponding lower order incompatible generalized hybrid/mixed singular crack finite element, computing procedure with both nonconforming displacements and singular strain functions enhanced,in order to increase the rate of numerical convergences in multilayered anisotropic hard and brittle domains with cracks,and to decrease the required computational storage bandwidths and capacities. The suggested incompatible hybrid/mixed singular crack element technique,a complementary one to other compatible displacement crack elements,possesses field singularities of stresses/strains too,and does not need to fix the singular point at elemental nodes when applying to mixed crack propagations. Benchmark numerical evaluation of (singular) stress components and stress intensity factors in an isotropic tension plate proves that the mentioned crack finite elements work and approach to the reference solution of an opening crack mode upwards and downwards. However,its insensitivities to mesh distortion and coordinate invariance should be further improved for better convergence to the actual singular stress fields around corners and cracks.