FINITE ELEMENT DISCRETIZATION OF THE BEAM EQUATION

A beam is a structural element or member designed to support loads applied at various points along the element. Beams make up a structure which is an assembly of a number of elements. Beams undergo displacement such as deflection and rotations at certain important location of a structure such as centre of a bridge or top of a building. I haveanalysed numerically a two dimensional beam equation with one degree of freedom of the form  using finite element method. The positive constant has the meaning of flexural rigidity per linear mass density,  the beam deflection and  is the external forcing term. This involved discretization of the beam equation employing Galerkins technique which yields a system of ordinary differential equations.