This book is intended for teaching the Finite Element (FE) method. It combines essential theory and exercises that are supported by a set of fourteen dedicated tutorials using relatively easy-to-use open-source CAD, FE and other numerical analysis codes so a student can gain understanding and experience practical analysis. These codes are all freely available on-line.
The theory covers fundamentals of the finite element method. Element stiffness for one dimensional bar and beam, two dimensional and three-dimensional continuum elements are derived based on energy and variational methods, and an introduction given to plate and shell elements. Linear, nonlinear and transient dynamic solution methods are covered for both mechanical and field analysis problems with a focus on heat transfer. Other important topics include element integration, assembly, loads, boundary conditions and contact. Constitutive modelling is important, and one chapter is devoted to introduce elasticity, hyperelasticity and plasticity.
The second half of the book presents one chapter on using the tutorials containing information on code installation and getting started, with general hints on meshing, modelling and analysis. This is then followed by the application tutorials covering linear, nonlinear and dynamic mechanical analysis, steady state and transient heat analysis, field analysis, fatigue, buckling and frequency analysis, a hydraulic pipe network analysis, and lastly two tutorials on Computational Fluid Dynamics (CFD) theory and simulation. In each tutorial links to relevant theory in the book are made and exercises suggested for further study.
For these tutorials open-source codes FreeCAD, CalculiX, FreeMAT and OpenFOAM are used which have capabilities comparable to many commercial products. CalculiX is a comprehensive FE package covering linear, nonlinear and transient analysis for mechanical and field problems. FreeCAD is primarily a powerful CAD modelling code that includes good finite element meshing and is fully integrated with CalculiX. FreeMAT is used in three tutorials for numerical analysis demonstrating algorithms for explicit FE and CFD analysis. And OpenFOAM is applied to more sophisticated CFD flow simulations.
The primary aim of this book is to provide a unified text covering theory and practice, so a student can learn and experiment with these versatile and powerful analysis methods. It should be of value to both finite element courses and for student self-study.
Anthony Pickett undertook postgraduate research in composites analysis at the University of Surrey and RAE Farnborough, followed by nearly twenty-five years industrial work as scientific director with ESI GmbH developing and applying FE codes for crash, impact, process and mechanical simulation of metal and composite structures. From 2002 he was a professor at Cranfield University and since 2007 has continued research and teaching of advanced composites and analysis at IFB (Institute of Aircraft Design) at the University of Stuttgart, Germany.