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本文推导了含边缘裂纹各向异性板与单向复合材料板的应力与位移的函数项级数表达式。该级数每一项均满足平衡方程、协调方程与裂纹表面静力边界条件。通过最小势能原理的变分方程来满足其余静力边界条件以确定级数中的待定系数,从而求得应力强度因子。最后,本文给出了长条板拉伸试件、紧凑拉伸试件与三点弯曲试件的计算结果。收敛是迅速的,几乎所有算例都能满足两位收敛。
In this paper, the function term series expressions of stress and displacement of anisotropic plates with edge cracks and unidirectional composite plates are deduced. Each of the series satisfies the equilibrium equation, which reconciles the equations with the crack boundary surface static boundary conditions. Through the variational equation of the principle of least potential energy, the rest of the static boundary conditions are satisfied to determine the undetermined coefficients in the series, so as to obtain the stress intensity factor. Finally, the calculation results of long strip tensile specimens, compact tensile specimens and three-point bending specimens are given in this paper. Convergence is rapid, and almost all the examples can satisfy the two convergence.