Karman型正交异性矩形薄板非线性弯曲的统一求解方法

本文对Karman型四边支承正交异性薄板在5种不同边界条件下的几何非线性弯曲进行了统一分析。所设的位移函数均为梁振动函数。它们精确地满足边界条件，利用Galerkin方法和位移函数的正交属性，转换控制方程为非线性代数方程。用“稳定化双共轭梯度法”求解稀疏矩阵线性方程组以及“可调节参数的修正迭代法”求解非线性代数方程组，最后给出了相应的数值结果。

A General Method for Nonlinear Bending of von Karman-type Orthotropic Rectangular Thin Plates

A general method for the bending of Karman-type orthotropic rectangular thin plates is presented under 5 different boundary conditions. The beam vibration functions that have orthogonal property may accurately satisfy the boundary conditions. Governing nonlinear partial differential equations are transferred to an infinite set of system of nonlinear algebraic equations containing Fourier coefficients by Galer-kin method. Large scale of sparse matrix linear equations have been solved by Biconjugate Gradients Stabilized Method and nonlinear algebraic equations solved by parameter-regulated iterative procedures. Numerical results of deflection and stress are obtained for different composite materials.