高阶剪切变形理论下两邻边铰支两邻边夹紧复合材料层板的几何非线性分析

首先用虚位移原理推导出以位移形式表达的Reddy型高阶剪切变形理论的复合材料层板的非线性控制方程。选定的5个位移函数均满足两邻边铰支两邻边夹紧边界条件。用Galerkin方法把无量纲化之后的控制方程组转化为非线性代数方程组。稳定化双共轭梯度法用于求解稀疏线性方程组,可调节参数的修正迭代法用于求解非线性代数方程组。最后求出了不同复合材料的挠度和弯矩值并同Kirchhoff及Reissner-Mindlin板的结果进行了比较。

GEOMETRICALLY NONLINEAR ANALYSIS OF LAMINATED COMPOSITE PLATES WITH TWO ADJACENT EDGES SIMPLY SUPPORTED AND THE OTHER TWO ADJACENT EDGES CLAMPED USING HIGH-ORDER SHEAR DEFORMATION THEORY

Based on Reddy抯 high-order shear deformation theory, geometrically nonlinear governing equations of composite laminated plates are obtained in the form of displacements by the virtual displacement principle. All five-displacement functions satisfy the boundary conditions that two adjacent edges simply supported and the other two adjacent edges clamped. Galerkin抯 method is used to transfer non-dimensionalized governing equations to an infinite set of nonlinear algebraic equations. Linear equations of sparse matrix are solved by Biconjugate Gradients Stabilized Method and nonlinear algebraic equations are solved by parameter-regulated iterative procedures. Numerical results of deflection and bending-moment are presented and compared with that of Kirchhoff and Reissner-Mindlin plate theory for different composite materials.