两邻边铰支两邻边夹紧正交各向异性矩形板的中等大挠度

MODERATE LARGE DEFLECTION OF ORTHOTROPIC RECTANGULAR PLATES WITH TWO ADJACENT EDGES SIMPLY SUPPORTED AND THE OTHER TWO ADJACENT EDGES CLAMPED

利用 Galerkin方法分析了 von- Karm an型两邻边铰支两邻边夹紧正交各向异性矩形板。所设的位移函数为梁振动函数 ,它不仅能精确地满足边界条件 ,而且具有正交的特性 ,从而把复杂的非齐次非线性偏微分方程组化为一组非线性代数方程组。通过非线性方程组的线性化和可调节参数的修正迭代解法找出问题的解。实践证明 ,梁振动函数的收敛很快 ,只须取出级数的前几项即可满足精度要求。

In the paper, von Karman type orthotropic rectangular plates with two adjacent edges simply supported and the other two adjacent edges clamped are analysed by using Galerkin method.The beam vibration functions are taken as displacement functions that may accurately satisfy the boundary conditions, and have orthogonality property.The governing nonlinear partial differential equations are reduced to an infinite set of systems of nonlinear algebraic equations containing Fourier coefficients which have been solved by linearizing iterative procedures. The series of beam vibration functions are rapidly converged. Only a few items of the series may meet the need of accuracy. Numerical results of deflection and stress are obtained for different composite materials.