层合板一个新的高阶理论解析解

本文以复合材料的Reddy高阶理论为基础,引进一个位移函数Φ,将原来求解的微分方程组转化为一个高阶微分方程,得到了四边简支情况下的Navier型解,和一对边简支另一对边任意情况下的Levy型解.文中列举了算例进行比较,其数值结果和文献上已有结果相吻合,表明本文采用的解法是可靠的.Reddy高阶理论未知数不多,但精度比一阶剪切变形理论要好,计算时无需用剪切修正系数,计算较为简单.

An Analytical Solution of Rectangular Laminated Plates by Higher-Order Theory

On the basis of the Reddy.s higher-order theory of composites,this paper introduces a displacement function 5 into it and transforms its three differential equations for symmetric cross-ply composites into only one eight-order differential equation generated by the displacement-function.When a proper 5 is chosen,both solutions are obtained,namely,the Navier-type solution of simply supported rectangular laminated plates and the Levy-type solution with the boundary condition where two opposite edges are simply supported and remains are arbitrary.The numerical examples show that the present results concide well with the existing results in the references,thus validating that the present solving method is reliable.The higher-order theory of Reddy is simpler in calculation but has higher precision than the first-order shear deformation theory because the former has fewer unknows than the latter and requires no shear coefficients.