The Method Of Complex Variable For Rectangular Plate Problem

This paper presents a new method for constructing the exact solution of the rectangular plates acting with moments along the boundaries based on the new general solution formula of the equilibrium equation. After a briefly historical and developing retrospect of the theory of plates and shells are introduced, this paper gives a deflection function of the rectangular plates which is written as the sum of a special solution and two simple Fourier series, which are the solutions of the homogeneous equation of the equilibrium equation and come from theory of complex variable.Several of the rectangular plates boundary-value problems are solved by presented method. Such as the bending problem of the rectangular plate with four simply supported boundaries, three simply supported boundaries and one built-in boundary, the two neighboring simply supported boundaries and two neighboring built-in boundaries. All of these plates are under various loads, and acting with non-vanishing moments along three boundaries.The Gibbs'Phenomenon often appears in the exact solutions of the rectangular plates and makes several solutions fail on the boundaries. The Gibbs'Phenomenon is studied in this paper. This paper presents a method how to escape from the Gibbs'Phenomenon by finite polynomial.