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本文采用弹性力学的位移解法研究对称斜交铺层复合材升层板在平面变形情况下的分层问题,得到了满足所有基本方程,层间连续条件与裂纹表面静力边界条件的位移场与应力场的本征展开式。然后利用分区广义变分原理代替裂纹表面以外的边界条件,确定位移场与应力场表达式中的待定系数,进而确定裂纹尖端附近奇异应力场的控制量——广义应力强度因子。由于所有基本方程预先得以满足,在变分方程中只有线积分而无面积分。计算表明,本文方法前期准备工作简便,计算节省机时,结果收敛迅速。
In this paper, the displacement problem of symmetrical skew plies composite laminates under plane deformation is studied by using the displacement solution method of elastic mechanics. The displacement field and the displacement field that satisfy all the basic equations, the continuity between layers and the static boundary condition of crack surface are obtained Intrinsic Expansion of Stress Field. Then the partitioned generalized variational principle is used to replace the boundary conditions outside the crack surface to determine the undetermined coefficients in the displacement field and stress field expression, and then the control amount of singular stress field near the crack tip - generalized stress intensity factor is determined. Since all of the basic equations are satisfied in advance, there is only a linear integral with no area in the variational equation. The calculation shows that the preparation of the method in this paper is simple, the result is fast convergence when calculating the saving time.