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本文针对工程中常用几何尺度的矩形底四边简支常曲率双曲扁薄壳的内力分析,为工程设计人员提供出快捷而能保证工程设计上应有精确度的近似计算方法。根据双曲扁壳的工作特点及这些特点在其基本微分方程中的反映,本文提出一套近似程度相当高的计算公式,可以用来直接算出扁壳在均布荷载作用下的位移和内力。当壳体取α,β座标系统时,在α方向:径向位移 W=-q/Eδk_2~2(1-e~(-ξ)cosξ), 弯矩 M_1=qC_1~2/2e~(-ξ)sinξ,在β方向:径向位移 W=-q/Eδk_1~2(1-e~(-η)cosη), 弯矩 M_2=qC_2~2/2e~(-η)sinη,上列式中:C_1=0.76■,C_2=0.76■,ξ=α′/C_1,η=β′/C_z,而α′和β′分别为所计算之点距平行于β方向和α方向的最近边界的距离;扁壳的薄膜内力公式为.T_1=-q/k_1K_(T_1),T_2=-q/k_2K_(T_2),S=-q/■=K_S。文内附有常用几何尺度双曲扁壳的K_(T_1)、K_(T_2)及K_S数值表。此外, 本文还提出了双曲扁壳在集中荷载作用下,内力T_1、T_2及S的近似计算公式。本文所提出的近似计算方法,能满足工程设计上的要求, 因此可以在工程设计中推广采用。
This paper aims at the internal force analysis of the simple curved hyperbolic double-curvature thin shell with four simple supports at the bottom of the rectangle, which is commonly used in engineering, and provides engineering engineers with an approximate calculation method that can ensure the accuracy of engineering design. According to the work characteristics of the hyperbolic flat shell and the reflection of these characteristics in its basic differential equations, this paper proposes a set of calculation formula with a fairly high degree of approximation, which can be used to directly calculate the displacement and internal force of the flat shell under uniform load. When the shell takes the α,β coordinate system, in the α direction: radial displacement W=-q/Eδk_2~2(1-e~(-ξ)cosξ), bending moment M_1=qC_1~2/2e~( - ξ) sin ξ, in the direction of β: radial displacement W = -q/Eδk_1~2(1-e~(-η)cosη), bending moment M_2=qC_2~2/2e~(-η)sinη, Where: C_1=0.76■, C_2=0.76■, ξ=α′/C_1, η=β′/C_z, and α′ and β′ are the nearest edges of the calculated distance parallel to the β direction and the α direction, respectively. The distances; the internal force formula of the thin-shelled shell is .T_1=-q/k_1K_(T_1), T_2=-q/k_2K_(T_2), S=-q/■=K_S. The K_(T_1), K_(T_2) and K_S tables of commonly used geometrical hyperbolic flat shells are attached. In addition, an approximate formula for the internal forces T_1, T_2, and S of the hyperbolic flat shell under concentrated loading is also proposed. The approximate calculation method proposed in this paper can meet the requirements of engineering design, so it can be used in engineering design.