Application of the finite element method to solving the duffing equation of ground motion

Abstract

In this paper, we applied the Galerkin Finite Element Method to solve a damped, externally forced, second order ordinary differential equation with cubic nonlinearity known as the Duffing Equation. The Galerkin method uses the functional minimization technique which sets the equation in systems of algebraic equations to be solved. Various simulation on the effect of change on some parametric values of the Duffing equation are shown.

Keywords: Galerkin Finite Element Method, stiffness matrix, Duffing Equation, shape functions, basis functions, weight functions.