Introduction to the finite element method

The finite element method is a well-established method of analysis extensively used in all
disciplines of engineering. This chapter provides an introduction to the method for the analysis of structures. The derivations presented deal with simple finite elements consisting of
line elements describing two common beam models, namely the Euler-Bernoulli beam and
the Timoshenko beam, readily available in some of the most common finite element analysis
software. In this manner, we will cover some of the key aspects involved in a finite element
derivation and analysis, while minimising the complexity of the numerical model. For the
derivation of more refined and advanced elements, reference should be made to textbooks
dedicated to the finite element method.