对称斜交铺层复合材料层板在平面变形情况下分层问题的解析—广义变解法

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。

ANALYTICAL-GENERALIZED VARIATIONAL METHOD OF SOLUTION FOR DELAMINATION OF LAMINATES IN PLANE WARPING

In this paper, the delamination solution of the angularly and symmetrically stacked composite laminates is given for the plane warping condition.First of all, the eigen function expansions of stress and displacement-fields are derived, for which all of the basic equations, boundary conditions on crack surfaces and conditions of continuities between different plies are satisfied. Furthermore, the govering parameters of the singular stress fields as the coefficient of singular terms in the above expansions are determined by the generalized variational principle for multi-regions, to satisfy the boundary conditions,excluding those along the crack surfaces. There are only line integrals in the variational equations due to the previous satisfactions of all basic equations.The computations show that this method of solution has the advantages of simple preparation, rapid cbnyergency and time-saving.