含椭圆分层复合材料层板三维问题的三角级数能量解法

根据叠加原理将含有椭圆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。然后利用双三角级数构造满足层板分层区位移边界条件的位移模态。最后 ,应用最小势能原理确定位移解。计算结果收敛 ,挠度收敛尤为迅速。

METHOD OF STATE DECOMPOSITION AND TRIGONOMETRIC SERIES ON ELLIPTICAL DELAMINATION IN COMPOSITE LAMINATE

The transverse loading state of a laminate with elliptical 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 caused by the additional shear loading acting on the delamination surfaces;thus a simple mechanics model about delamination area is established. Then, a trigonometric series is applied to describe the displacement mode satisfying the boundary conditions. At last, the principle of minimum potential energy is used to determine the unknown coefficients of the above series. The convergence tests are carried out. From the computational results, it can be shown that all of the displacement components are convergent and the deflection converges more rapidly.