Finite Element Formulation of Beam Elements

Abstract

In this chapter, various types of beams on a plane are formulated in the context of finite element method. The formulation of the beam elements is based on the Euler-Bernoulli and Timoshenko theories. The kinematic assumptions, governing equations via Hamilton’s principle and matrix formulations by using shape functions, are described in detail. In constructing the beam element formulations, the shape functions which are derived from the homogeneous governing equations lead to high-accuracy beam analyses. The theories discussed and derived herewith will be used in the subsequent chapters when we deal with the Isogeometric approach to beams.