Convergence of Analytic Fourier Series Solution for Elastic Bending of Thin Plates

Abstract

In this paper, the convergence of the analytic Fourier series solution of elastic bending of thin plates is studied. Firstly, the original problem is turned into an investigation on the convergence of the Fourier series array with four kinds of variables such as the deflection, rotation, bending moment or torque, and shear force of thin plates, and the concept of integrated convergence of the Fourier series array is proposed. Secondly, the external influences at work, including load condition, length to width ratio and boundary condition, on the convergence of the Fourier series array are disentangled, by which the fusion strategy of the traditional Fourier series method and the traditional numeric method is presented as an effective approach for the improvement in convergence of the analytic Fourier series solution.