受分布载荷复合材料层合梁应力分析的一般理论

General Theory on Stress Analysis of Laminated Composite Beam Pressed By Distributed Loading

为了克服层合梁经典理论的缺点 ,提高层间应力的计算精度 ,提出了受分布载荷层合梁应力分析的一般理论。首先根据叠加原理将原始受力状态分解成对称与反对称受力状态。然后用正交完备的三角级数和勒让德级数构造这两种受力状态中每一铺层与层间胶层的位移场 ,并应用广义势能原理确定位移场中的待定系数 ,从而确定层合梁的位移场和应力场。同时 ,单层梁与单层梁之间的胶层被视为各向同性材料并且与其它材料层具有相似的力学特性 ,即具有有限厚度、有限弹性常数。计算结果显示 ,这种解法的收敛性非常好 。

A general theory on stress analysis of laminated compo si te beam pressed by distributed loading is presented for overcoming the defect of classical beam theory and improving the precision of interfacial stress analysi s. By means of the principle of superposition, the loading state of composite l aminated beam is decomposed into symmetric and anti-symmetric states. The Fouri er series and Legendre series are applied to describe the displacement field of each composite ply and glue layer in above states. The principle of generalized potential energy is used to determine the unknown coefficients of the above seri es. In addition, the glue layers are considered to be of finite thickness and fi nite elastic constants in the analysis. The computational results show that the displacements and stresses converge very well, the distributions of transversal shearing stress and transversal normal stress obtained from constitutive equatio n agree with that obtained from equilibrium equation very well.