Symmetry analysis of an elastic beam with axial load

Abstract: We construct the closed form solution of an elastic beam with axial load using Lie symmetry method. A beam with spatially varying physical properties such as mass and second moment of inertia is considered. The governing fourth order partial differential equation with variable coefficients which is not amenable to simple methods of solution, is solved using Lie symmetry. We incorporate boundary conditions and then compare with the numerical solution.