The global galerkin finite element method as applied to the 1d beam equation: a systems approach

Abstract

The paper focuses on the finite element solution of the fourth-order differential for an EulerBernoulli beam. In this approach the point point loads and concentrated moments are treated in a natural way as part of the system of external forces and are included in the differential equation during the definition of the problem. The Galerkin formulation is then developed over the entire domain before the domain is discretised into a collection of elements to facilitate the evaluation of the integrals to obtain the coefficients of the global set of algebraic equations. This results in the Global Galerkin Finite Element (GGFEM) formulation. The GGFEM can be seen as a systems or holistic approach to the finite element solution of the problem