基于p型有限元法和围线积分法计算复合型应力强度因子

传统有限元法由于采用低阶插值计算应力强度因子时,需要划分的网格数较多,收敛速度较慢,得到的应力强度因子精度不足。p型有限元法在网格确定时通过增加插值多项式的阶数来提高计算精度,具有网格划分少、收敛速度快、精度高、自适应能力强等特点。本文采用基于p型有限元法的有限元计算软件StressCheck计算得到应力场和位移场,并由围线积分法导出混合型应力强度因子(SIFs)。通过几个经典算例,分析了围线的选择对计算精度的影响,计算了不同裂纹长度、不同裂纹角度和裂纹在应力集中区域不同位置时的应力强度因子。并将数值结果、理论解与文献中其他数值计算方法所得的部分结果进行了对比分析,结果表明自由度数不大于7000时,导出的应力强度因子相对误差最大不超过1.2%,数值解表现出较高的精度及数值稳定性。

Extraction of stress intensity factors based on p-version finite element method and contour integral method

Due to the low order interpolation,the traditional finite element method needs to divide more grids and it has lower convergence rate when calculating the stress intensity factor(SIFs),the accuracy of the obtained stress intensity factor is insufficient.By increasing the order of interpolation polynomial on fixed grids,the p-version finite element method(FEM)needs less grids and has faster convergence rate,higher precision and strong adaptability.In this paper,the commercial finite element analysis software StressCheck based on the p-version FEM is adopted to calculate the displacement and stress fields and the contour integral method(CIM)is employed to extract the mixed-mode stress intensity factor(SIFs).The influence of contour’s selection for the accuracy is analyzed,and the stress intensity factors of crack with different lengths,different angles and different positions in the stress concentration region are calculated through several benchmark problems.Numerical results are compared with analytical solution and others obtained by numerical methods in literatures.The maximum relative error of derived stress intensity factors is less than 1.2%while the degrees of freedom(DOFs)is less than 7,000,and the numerical solution shows higher precision and strong numerical stability.