Analysis of an Infinite Elastic Thick Plate Subjected to Loads Symmetrical to Axis of Revolution

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 propose a new method for a numerical calculation of stress components. First, stress functions are obtained for a general loading condition. Next, stress functions and stress components are obtained for a typical example, and then we perform a numerical calculation of stress components. 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 Maclaulin law. Thus, integrating by terms, we obtain each stress component. Then, we solve the simultaneous linear algebraic equations with four unknowns so as to satisfy the boundary conditions at two given points on the boundary. The result will show that we are able to obtain an approximate solution in finite terms sufficiently accurate for practical use.
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