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基于直角坐标下考虑横向剪切变形情况下厚圆柱扁壳的几何方程、物理方程、平衡微分方程,建立了以3个中面位移和2个中面转角为独立变量的中厚圆柱扁壳弯曲的位移型基本微分方程。因该方程可退化为薄圆柱扁壳弯曲的基本微分方程,说明了其推导过程的正确性及一般性。此外,厚圆柱扁壳的位移型基本微分方程是一个10阶微分方程,对其使用双重三角级数进行了求解,进一步建立了厚圆柱扁壳小挠度弯曲的基本方程;然后应用MATLAB工具对简支矩形底厚圆柱扁壳弯曲的双重三角级数型基本方程进行求解;最后运用MATLAB工具分析厚圆柱扁壳,给出了3个中面位移和2个中面转角的解析解及挠度变化曲线。结果表明:双重三角级数法适用于任何形式的分布载荷,3个中面位移和2个中面转角的收敛性较好;级数的收敛性还取决于载荷的形式,其中均布载荷收敛性最好。
Based on the geometrical equation, physical equation and equilibrium differential equation of the thick cylindrical shell under transverse shear deformation in rectangular coordinates, a medium-thick cylindrical shell with three mid-plane displacements and two mid-plane turns as independent variables was established Of displacement basic differential equations. Because this equation can degenerate into the basic differential equation of the thin cylindrical shell, it shows the correctness and generality of its derivation. In addition, the displacement-type basic differential equation of a thick cylindrical shell is a 10-order differential equation, which is solved by using double trigonometric series. The basic equations of small deflection bending of a thick cylindrical shell are further established. Then, Finally, using MATLAB tool to analyze the thick cylindrical shell, the analytical solutions and deflection curves of three mid-plane displacements and two mid-plane rotations are given. . The results show that the double trigonometric series method is suitable for any form of distributed loads. The convergence of three medium-surface displacements and two mid-surface rotations is better. The convergence of series is also dependent on the form of the load, in which the uniform load convergence The best sex.