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本文讨论了一种新的有限元法在计算线弹性断裂力学应力强度因子 K_1上的应用。这种有限元法,允许在每个单元上,其相应的插值多项式具有不同的阶次。取多项式阶次在1～8范围内变化,作应变能释放率数值计算,结果表明:即使计算网格划分得很粗糙,随着插值多项式阶次 p增加,也能得到计算结果是强单调收敛的。取不同多项式阶次的平均近似值,可使应力计算逐点收敛。这种只需增加阶次,而使 K_1因子计算结果具有强单调收敛的特性,为计算应力强度因子提供了一种新方法。这一方法的主要优点在于:无需精确的网格或特殊的程序,就能达到足够的计算精度。
This paper discusses the application of a new finite element method in the calculation of the linear elastic fracture mechanics stress intensity factor K_1. This finite element method allows the corresponding interpolation polynomials to have different orders on each cell. Taking the polynomial order varying within the range of 1-8, the strain energy release rate is calculated numerically. The results show that even if the calculation grid is divided very rough, as the interpolation polynomial order p increases, the calculation result is also a strong monotonic convergence. of. Taking the average approximation of different polynomial orders, the stress calculation can be converged point by point. This only needs to increase the order, and makes the calculation result of K_1 factor have strong monotonic convergence, which provides a new method for calculating the stress intensity factor. The main advantage of this method is that it can achieve sufficient computational accuracy without the need for precise grids or special programs.