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基于考虑横向剪切变形直角坐标下矩形中厚扁壳的几何方程、本构关系、平衡方程,建立了关于三个中面位移和两个中面转角为独立变量的矩形中厚扁壳小挠度屈曲的基本微分方程。该方程可退化为矩形中厚板屈曲的基本微分方程,从而说明本文推导过程的正确性及一般性。文中矩形中厚扁壳小挠度屈曲的基本微分方程是一组耦合的变系数二阶偏微分方程,对常曲率扁壳使用双重三角级数并将其作为广义坐标对该方程组进行解耦,进一步建立中厚扁壳小挠度屈曲的特征方程,并得到了简支矩形中厚壳屈曲的临界荷载表达式,最后获得了其屈曲的临界荷载曲线及其相应的临界荷载值。该临界荷载曲线及其相应的临界荷载值可以退化为矩形中厚板的临界荷载曲线及临界荷载值。结果表明:本文提出的算法求解过程简便,矩形中厚扁壳临界荷载收敛较快。
Based on the geometrical equation, constitutive relation and equilibrium equation of the rectangular thick shell with rectangular coordinates in the transverse shear deformation, the small deflection of the medium thick shell with respect to the three mid-plane displacements and two mid-plane turns as independent variables is established Buckling of the basic differential equations. The equation can be degenerated into the basic differential equation of rectangular plate buckling, which shows that the derivation of this paper is correct and general. In this paper, the basic differential equation of the small deflection buckling of a rectangular thick shell is a coupled set of second-order partial differential equations with variable coefficients. The system uses a double trigonometric series of constant curvature flat shells and decouples this system as a generalized coordinate , The characteristic equation of small deflection buckling of medium-thick flat shell is further established, and the critical load expression of buckling of medium thick shell with simple support is obtained. Finally, the critical load curve of buckling and its corresponding critical load are obtained. The critical load curve and its corresponding critical load can degenerate into the critical load curve and the critical load of the rectangular plate. The results show that the algorithm proposed in this paper is simple and easy to solve, and the critical load of the rectangular medium-thick shallow shell converges rapidly.