Introduces the fundamentals of finite and spectral element methods with emphasis on algorithms and computer implementationProvides practical computational experience with FSELIB-a free library of MATLAB functions and codes Uses the fundamentals of heat and mass transfer as a prototype, then extends the concepts to problems in mechanicsIncludes a concise MATLAB primer in an Appendix
Why another book on the finite element method? There are currently more than 200 books in print with "Finite Element Method" in their titles. Many are devoted to special topics or emphasize error analysis and numerical accuracy. Others stick to the fundamentals and do little to describe the development and implementation of algorithms for solving real-world problems.
Introduction to Finite and Spectral Element Methods Using MATLAB provides a means of quickly understanding both the theoretical foundation and practical implementation of the finite element method and its companion spectral element method. Written in the form of a self-contained course, it introduces the fundamentals on a need-to-know basis and emphasizes algorithm development and computer implementation of the essential procedures.
Firmly asserting the importance of simultaneous practical experience when learning any numerical method, the author provides FSELIB: a software library of user-defined MATLAB functions and complete finite and spectral element codes. FSELIB is freely available for download from http://dehesa.freeshell.org, which is also a host for the book, providing further information, links to resources, and FSELIB updates.
The presentation is suitable for both self-study and formal course work, and its state-of-the-art review of the field make it equally valuable as a professional reference. With this book as a guide, you immediately will be able to run the codes as given and graphically display solutions to a wide variety of problems in heat transfer and solid, fluid, and structural mechanics.
Table of Contents
THE FINITE ELEMENT METHOD IN ONE DIMENSION
Steady diffusion with linear elements
Variational formulation and weighted residuals
Steady diffusion with quadratic elements
Unsteady diffusion in one dimension
HIGH-ORDER AND SPECTRAL ELEMENTS IN ONE DIMENSION
Lobatto interpolation and element matrices
Spectral code for steady diffusion
Spectral code for unsteady diffusion
THE FINITE ELEMENT METHOD IN TWO DIMENSIONS
Convection-diffusion in two dimensions
Code for Laplace's equation with the Dirichlet boundary condition in a disk-like domain
Code for steady convection-diffusion with the Dirichlet boundary condition
Code for Helmholtz's equation with the Neumann boundary condition
Code for Laplace's equation with Dirichlet and Neumann boundary conditions
Bilinear quadrilateral elements
QUADRATIC AND SPECTRAL ELEMENTS IN TWO DIMENSIONS
6-node triangular elements
Grid generation and finite element codes
High-order triangle expansions
High-order node distributions
Modal expansion on the triangle
High-order quadrilateral elements
APPLICATIONS IN SOLID AND FLUID MECHANICS
Plane stress-strain analysis
Finite element methods for plane stress/strain
Finite element methods for plate bending
FINITE AND SPECTRAL ELEMENT METHODS IN THREE DIMENSIONS
Convection-diffusion in three dimensions
4-node tetrahedral elements
High-order and spectral tetrahedral elements
Element grid generation
"[This book] approaches the matter from the more practical side. … It gives a broad, digestible introduction into what everybody wishing to write an FE code needs to know. …This is a hands-on book in that it presupposes the reader to work the examples in MATLAB, for which a primer is provided. The actual work is greatly facilitated by the possibility to freely download software …"
-Monatshefte fur Mathematik, 2007
||September 27, 2016
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