用高阶剪切变形理论分析复合材料层板的中等大挠度

Analysis of Moderate Large Deflection of Composite Laminated Plates Using Higher-Order Shear Deformation Theory

根据 Reddy的高阶剪切变形理论 ,用虚位移原理推导出以位移形式表达的复合材料层板的非线性控制方程及相应的边界条件。所有的位移函数均满足三边铰支一边夹紧边界条件。用 Galerkin方法把无量纲化之后的控制方程转化为一组非线性代数方程组。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。

Based on the Reddy′s higher order shear deformation theory, geometrically nonlinear governing equations and their boundary conditions of composite laminated plates are obtained in the form of displacements by the virtual displacement principle. The boundary conditions in which three edges are simply supported and one edge is clamped are satisfied by all displacement functions. Galerkin′s method is used to transfer dimensionless 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 for different composite materials.