含矩形内部分层的复合材料层板的状态分解-片条合成能量解法

METHOD OF STATE DECOMPOSITION AND SLICE COMPOSITION ON RECTANGULAR DELAMINATION IN COMPOSITE LAMINATE

根据叠加原理将含有矩形内部分层的层板在横向载荷作用下的受力状态进行分解，从而将分层问题归结为在分层表面上的附加剪切载荷作用下层板附加位移与附加应力的分析，并据此建立了一个仅包含分层区的力学模型。进而在层板分层区中切取平行于边界的切片，将切片视为含分层的层合梁，其位移模态以相应层合梁的附加位移模态来表示。这样，可构造层板分层区内满足位移边界条件的位移场。最后，应用最小势能原理确定位移幅值的闭合解。计算结果表明，挠度幅值远远大于中面位移幅值。

The transverse loading state of a laminate with rectangular delaminations is divided using the principle of superposition, so that the problem of delamination can be reduced to the analysis about the additional displacements and stresses which are caused by the additional shear loading acting on the delamination surfaces; then a simple mechanics model about delamination area is established. The laminate sections parallel to the boundary of delamination area can be regarded as laminated beams with delaminations, the displacements of which can be expressed by the analytical solutions of additional displacements in the above beams. By this way, the additional displacement fields satisfying the displacement boundary condition of delamination area can be established. Finally, a closed form solution of additional displacements is obtained by the principle of minimum potential energy. The above results are compared with the convergent solutions obtained by the method of trigonometric series. It shows that