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本文从研究扁壳的挠度和内力的混合函数的重调微分方程出发,利用力的变分原理,得到了均布荷载下双曲抛物面浅壳挠度和内力的精确解,分析了结构初始曲率及扭率对其刚度的影响,从而建立了关于弯曲曲率和扭率两个判别条件.当结构初始弯曲曲率小于其判别值的下界时,结构可视为双曲扭壳,当结构的初始扭率大于其判别值上界时,则可忽略弯曲效应,视结构为无矩状态,对于这两种情况计算误差均不大于百分之一.
In this paper, based on the study of the retuned differential equation of the mixed function of the deflection and internal force of the shallow shell, the exact solution of the shallow shell deflection and the internal force of the hyperbolic paraboloid under uniformly distributed loads is obtained by using the variational principle of the force. The initial curvature of the structure is analyzed. The influence of the twist rate on its stiffness has established two criteria for the bending curvature and the torsion ratio. When the initial bending curvature of the structure is lower than the lower bound of its discriminant value, the structure can be considered as a hyperbolic twisted shell when the initial torsional rate of the structure is When it is larger than the upper bound of the discriminant value, the bending effect can be neglected, and the apparent structure is a momentless state. The calculation error is not more than one percent for both cases.