对称正交铺层复合材料层板分层(剥离)问题的解析——广义变分解法

ANALYTICAL-GENERALIZED VARIATIONAL METHOD OF SOLUTION FOR DELAMINATIONS OF LAMINATES

对于对称正交铺层复合材料层板单向受拉分层问题,本文在引入混合边界条件的前提下,根据穆什海里什维利的求解各向同性平面问题与列赫尼兹基的求解各向异性平面问题的复变函数方法,得到了满足所有基本方程、裂纹表面边界条件与层间连续条件的应力场、位移场的本征展开式。进而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,本方法前期准备工作很少,计算节省机时,结果收敛迅速。

In this paper, the delamination solution of composite laminates, orthogonally and symmetrically stacked under axial tension is given.First of all, the eigen function expansions of stress and displacement fields, satisfying all of the basic equations, boundary conditions on crack surfaces and conditions of continuities between different plies are derived. Furthermore, the stress intensity factors as the coefficients of leading terms in the above expansions are determinsd by the generalized variational principle for multi-regions, to satisfy the boundary conditions.There are only line integrals in the variational equations due to the previous satisfaction of all basic equations.The computations show that this method of solution has the advantages of rapid convergency and time -saving.