Finite element approach to the solution of fourth order beam equation

Abstract

Finite element method is a class of mathematical tool which approximates solutions to initial and boundary value problems. Finite element, basic functions, stiffness matrices, systems of ordinary differential equations and hence approximate solutions of partial differential equations which involves rendering the partial differential equation into system of ordinary differential equations. The ordinary differential equations are then numerically integrated. We present a finite element approach in solving fourth order linear beam equation: 2, tt xxxx u c u f x t, which arises in model studies of building structures wave theory. In physical application of waves in building structures, coefficient 2 c, has the meaning of flexural rigidity per linear mass density and f x t, external forcing term. In this paper, we give a solution to the beam equation with 2 c 139 and f x t, 100.