带包边的对称正交铺层复合材料层板分层问题的解析——广义变分解法

ANALYTICAL-GENERALIZED VARIATIONAL METHOD OFSOLUTION FOR DELAMINATIONS OFLAMINATES WITH U-CAP

对于对称正交铺层复合材料层板单向受拉分层问题,本文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。对于包边与不包边这两种情况,本文利用分区广义变分原理代替裂纹表面以外的边界条件,确定奇异应力场的控制量。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简单,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 and adhered with a 'U-cap'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. The govering parameter of singular stress field are determined by the generalized variational priciple for multi-regions, and compared with the solution for delamination of laminates without 'U-cap'.