复合材料层合梁分层问题中应力强度因子与守恒积分的解析变分解法

ANALYTICAL-GENERALIZED VARIATIONAL METHOD ABOUT SOLUTION OF SIF AND CONSERVATIVE INTEGRAL FOR DELAMINATIONS OF LAMINATE BEAM

利用虚功原理导出了涉及两种不同介质的守恒积分表达式以及守恒积分J_Ⅰ与应力强度因子K_Ⅱ的关系式。对于对称正交铺层复合材料层合梁的分层问题,在利用分区广义变分原理确定了应力强度因子K_Ⅱ以及应力与位移本征展开式中的所有待定系数的基础上,进一步求出守恒积分值。最后,作为验证,由J_Ⅰ求出K_Ⅱ,并与由解析变分方法求出的K_Ⅱ相比较。计算表明,本方法前期准备工作少,计算节省机时,结果收敛迅速;沿不同积分路径求出的守恒积分保持恒定,并且用两种方法求出的K_Ⅱ具有很好的一致性。

: In this paper, the formula of conservative integral with the relationship between J1 -integral and the stress intensity factor (SIF)KⅡ in two dissimilar media is derived by using the principle of virtual-work. For the delamination of composite laminate beam stacked orthogonally and symmetrically with four plies under transverse loading, the magnitudes of J1 -integral along different paths are obtained on the basis of the determination of the SIF and all of the coefficients in the expansions. According to the relationship between J1-integral and SIF,KⅡ, can also be determined and compared with those determined by generalized-variational principle. The computational results show that this method has the advantages of simple preparation, rapid convergency and time-saving, the magnitudes of J1- integral along different paths keep constant accurately and the SIFs obtained by direct variational method and by indirect J1-integral method agree with each other satisfactorily.