Analysis of Infinite Elastic Thick Plate Subjected to Loads Symmetrical to Axis of Revolution and to Middle Plane

概要

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We make a stress analysis on the above problem by means of a couple of stress functions with subsequent Fourier-Bessel expansion of the given loads on the boundary, and we obtain the same result as obtained by means of Hankel transformation. First, stress functions and their stress components are obtained for a general loading condition. Next we perform, for example, a numerical calculation and photoelastic experiment in a case similar to the condition of punching a thick plate. In the course of our calculation, we expand the part of hyperbolic functions of integrand contained within the stress functions expressed in infinite integrals by Taylor's law. Thus, integrating by terms, we obtain each stress component. By making use of the fact that the boundary conditions are satisfied asymptotically in the mode of a damped oscillation with an increase in terms, we are able to obtain an approximate solution sufficiently accurate for practical use.
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