脱层屈曲的高阶摄动解

High Order Perturbation Solution of Delamination Buckling

本文用摄动法求解了三维复合材料中有纤维搭桥的圆形脱层的屈曲问题。搭桥纤维被简化为连续分布于脱层面上的线性弹簧。用Taylor级数展开法确定了每一级摄动方程用Bessel函数表达的解析解,给出了脱层屈曲临界载荷、挠度曲线与脱层半径、搭桥因子等的封闭关系式。根据这一结果并考虑脱层只能向一个方向挠曲的约束条件,可以进一步探讨脱层屈曲的特征。

Axisymmetric buckling of a circular delamination bridged by linear fibers in 3D composites was studied by perturbation method. The through thickness fibers were assumed to provide linear restoring traction resisting the deflection of the delaminated layer. The analytic solution of each order perturbation equation in form of Bessel＇s function was obtained by an alternative proccedure based on Taylor＇s series expand. The closed form solutions of the critical load and the deflection contour line of the delamination buckling decided by delamination radius and the bridging factor were obtained. Based on the result, with the deflections permitted in one direction only, the characteristics can be further verified for delamination buckling.