薄い平板の撓みの方程式の省略項に就いて : 一樣に加壓される圓板の撓みの計算に對する應用

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The equilibrium equations of thin elastic plates, the lateral deflections of which have magnitudes comparable to the respective plate thicknesses, as will be seen in the case of deformation after buckling or under normal pressure of some extent, have been given by Th. von Karman. [Eq's (1.1)-(1.3)]. These equations are not fully correct for the reasons: (1) that in the equilibrium equation for the direction normal to the plane of the plate, components of forces resulting from the gradient of stress components are neglected, and only the terms due to the changes of curvature are considered, and (2) that in the equations of equilibrium for the plane of the plate, the difference between the state after deformation and that before deformation is not taken into consideration. In this paper, starting from the results derived by R. Kappus for the case of finite deformations of three-dimensional elastic bodies, the author obtained more accurate forms of the equilibrium equations of thin plates as the following: [numerical formula] [numerical formula] [numerical formula] where the strees resultants T_1, S_1, T_2 and the shearing forces normal to the neutral surface N_1, N_2 are expressed in terms of the displacements u, v, w by the ordinary relations. The results obtained above were applied to the case of a finite deformation of a plane circular plate subjected to normal pressure, and the relation between the pressure p and the deformation at the center of the plate f is given in equation (2.26), which describes the experimental results with more accuracy than the existing formula (2.25). The additional terms in the equation for the z direction, which are neglected in the conventional theory, are not negligibly small, as was illustrated in this example, but the additional terms in the equations for the x, y directions can be reasonably neglected in this case.
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薄い平板の撓みの方程式の省略項に就いて : 一樣に加壓される圓板の撓みの計算に對する應用

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