大挠度剪切理论下复合材料夹层圆柱扁壳的广义傅里叶级数解法

APPLICATION OF GENERALIZED DOUBLE FOURIER SERIES TO PROBLEMS ON SHEAR THEORY OF SANDWICH SHALLOW SHELL WITH COMPOSITE LAMINATE FACES

大挠度剪切理论下复合材料夹层圆柱扁壳的稳定性控制方程是一组非线性高阶常系数偏微分方程，其中包含四个独立的函数，它们分别为横向挠度ｗ、参考曲面的法线转角Φｘ、Φｙ和应力函数Ｆ。本文中将这四个独立的函数表示为广义傅里叶级数，选用了两个变量分离的梁本征函数之积构成广义傅里叶级数的通项，通过梁本征函数中的待定常数使所选级数预先满足简支、固支或弹性支持边界条件。然后把以广义傅里叶级数表示的独立函数代入控制方程中便将这个非线性高阶常系数偏微分方程转化为非线性代数方程组，这样便可以寻求不同的通用程序进行求解。从而为复合材料叠层、夹层板壳在复杂边界条件下的弯曲、振动和稳定问题的求解探索出了一种通用的、有效的方法。

The governing equations of laminatefaced sandwich cylindrical shallow shells based on the firstorder shear theory with large deflection are highorder partial differential equations. Four dependent functions are involved. They are the deflection w, the rotations of the normal to the undeformed median surface Φx, Φy and the force function F. In the present paper these dependent functions are expressed as generalized double Fourier series with beam eigenfunctions as general terms. These series are chosen so that various boundary conditions are satisfied. By substituting these expressions into the highorder partial differential governing equations, they become a set of algebraic equations. Here is developed a universal and effective method to solve the problems on the shear theory of laminated or sandwich thinwalled structures with large deflection.