厚圆柱扁壳位移型基本方程及控制方程分析

Displacement Fundamental Equations and Analysis of Governing Equations of Thick Cylindrical Shallow Shells

基于考虑横向剪切变形的厚壳位移型基本方程及扁壳基本假定,建立了以5个中面位移为5个独立变量的厚扁壳及厚圆柱扁壳位移型基本方程。对厚圆柱扁壳进行了动力分析,首先引入3个辅助位移函数,同时运用柯西-黎曼条件,将5个二阶微分方程变形为1个二阶和2个四阶过渡微分方程;然后引入另一辅助位移函数,建立其解耦的控制微分方程;最后利用4个辅助位移函数求出5个位移分量。结果表明,厚扁壳的位移型基本方程退化为厚圆柱扁壳及薄圆柱扁壳的位移型方程是正确的,且所推导的方程具有通用性。

The displacement fundamental equations of the thick shallow shells and thick cylindrical shallow shells concerning five independent variables, ie five middle surface displacements were established based on the displacement fundamental equations of the thick shells by transverse shearing deformation and basic hypothesis on shallow shells. Authors analyzed thick cylindrical shallow shells＇ dynamic characteristics by introducing three assistant displacement functions, ie authors converted five second-order differential equations into a second-order differential equation and two fourth-order transition differential equations using Cauchy-Riemann condition, and then introduced another assistant displacement functions to build its decoupled governing differential equations and obtained five displacement components through four assistant displacement functions. The displacements of equations of thick shallow shells degenerate to the displacement equations of the thick cylindrical shallow shells and thin cylindrical shallow shells, which are proved to be right and demonstrate the generality of derived equations.