Modified Fourier transform method and its application for solving the problem of large deformations of a beam

A modification of the Fourier transform method, which makes feasible transforming products of two functions and/or their derivatives, is described. By application of this method, some kinds of nonlinear differential equations can be transformed and solved. In this paper, the solution of the problem of bending a beam with fixed supports, under continuous transversal loading is given. Equations of the large deformations theory are used. The mutual influence between the deflection and the axial force is taken into account. The problem is mathematically described by a system of three nonlinear differential equations, with the appropriate boundary conditions. The solution is obtained by making use of an iterative procedure, based on the modified Fourier transform method.