DEFLECTION OF NONUNIFORM BEAMS RESTING ON A NONLINEAR ELASTIC-FOUNDATION

The static deflection of a general elastically end restrained non-uniform beam resting on a non-linear elastic foundation subjected to axial and transverse forces, governed by a non-linear fourth order non-homogeneous ordinary differential equation with variable coefficients, is examined. By using the method of perturbation, the governing differential equation is transformed into a set of self-adjoint linear fourth order ordinary differential equations with variable coefficients. It is shown that the deflection of the beam can be expressed in terms of the fundamental solutions of these linear ordinary differential equations. Especially if the coefficients of the linear fourth order ordinary differential equations are in an arbitrarily polynomial form, then the exact solution for the static deflection of the beam can be obtained.