含椭圆形分层层板的状态分解-片条合成能量解法

根据叠加原理将含有椭圆形非穿透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坐标平面的切片,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,且与由双三角级数能量解法所得挠度幅值吻合很好。 

METHOD OF STATE DECOMPOSITION AND SLICE COMPOSITION ONELLIPTICAL DELAMINATION IN COMPOSITE LAMINATE

The transverse loading state of a laminate with elliptical delaminations is decomposed by means of the principle of superposition, so the problem of delamination can be reduced to the analysis of the additional displacements and stresses caused by the additional shear loading acting on the delamination surfaces, and thus a simple mechanics model of the delamination area is established. The laminate sections parallel to the coordinate planes can be regarded as laminated beams with delaminations, the displacements of which can be expressed by the analytical solutions of the additional displacements in the above beams. In this way, the additional displacement fields satisfying the displacement boundary condition of the 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 the deflections acquired from two different ways agree with each other very well and are greater than the in plane displacements by 1~2 order of magnitude.