DIFFERENTIATION OF FOURIER SERIES IN STRESS SOLUTIONS FOR RECTANGULAR PLATES

Abstract

Certain mathematical conditions of differentiation are necessarily included in a Fourier solution which is based on the hypothesis that a stress function and its partial derivatives can be represented by Fourier series. To illustrate these conditions, a summary of essential theory is followed by examples, using full-range Fourier series and also half-range Fourier series. In these examples of stress solutions it is found that the assigned boundary tractions provide equations sufficient to determine the Fourier coefficients. Additional mathematical conditions, however, are imposed by the hypothesis of termwise differentiation. Unless it can be proved that these additional conditions are fulfilled, the conclusion is that the hypothetical representation by Fourier series may not have sufficient generality to satisfy all required conditions and furnish a solution.