Introduction 📖

The Finite Element Method (FEM) is an incredibly popular topic among students but can be difficult to study, let alone to apply in practice.

This article introduces you to the best FEM books to assist your studies, reduce frustration & help you gain some practical knowledge. I saved you some precious time grooming Google – you're welcome! 🙂

General Books on FEM 📚

Introduction to the Finite Element Method

This book provides a systematic approach and simple introduction ot the finite element method, this self-contained book will enable the reader to obtain a clear understanding of the concepts involved in this traditionally complicated methodology.

A First Course in Finite Elements

The text material evolved from over 50 years of combined teaching experience it deals with a formulation and application of the finite element method. A meaningful course can be constructed from a subset of the chapters in this book for a quarter course; instructions for such use are given in the preface.

The course material is organized in three chronological units of one month each: 1) the finite element formulation for one-dimensional problems, 2) the finite element formulation for scalar field problems in two dimensions and 3) finite element programming and application to scalar field problems; and finite element formulation for vector field problems in two dimensions and beams.

In conjunction with the book there will be the access and use of ABAQUS software and MATLAB exercises.

Practical Finite Element Analysis for Mechanical Engineers

"Practical Finite Element Analysis for Mechanical Engineers" by Dominique Madier is a book about the practical aspect of finite element analysis for structural engineers. The objective is to offer the best practical methods and guidelines for the development and validation of finite element models.

It gives to the structural engineers the keys to developing accurate and reliable finite element models by avoiding the most frequent errors. It contains around 100 examples which illustrate the different modeling techniques.

A First Course in the Finite Element Method

Discover a simple, direct approach that highlights the basics you need within A FIRST COURSE IN THE FINITE ELEMENT METHOD, 6E. This unique book is written so both undergraduate and graduate students can easily comprehend the content without the usual prerequisites, such as structural analysis. The book is written primarily as a basic learning tool for students, like you, in civil and mechanical engineering who are primarily interested in stress analysis and heat transfer. The text offers ideal preparation for utilizing the finite element method as a tool to solve practical physical problems.

The Finite Element Method: Its Basis and Fundamentals

The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications.

This edition sees a significant rearrangement of the book’s content to enable clearer development of the finite element method, with major new chapters and sections added to cover:

• Weak forms
• Variational forms
• Multi-dimensional field problems
• Automatic mesh generation
• Plate bending and shells
• Developments in meshless techniques

The Finite Element Method for Engineers

A useful balance of theory, applications, and real-world examples.

The Finite Element Method for Engineers, Fourth Edition presents a clear, easy-to-understand explanation of finite element fundamentals and enables readers to use the method in research and in solving practical, real-life problems. It develops the basic finite element method mathematical formulation, beginning with physical considerations, proceeding to the well-established variation approach, and placing a strong emphasis on the versatile method of weighted residuals, which has shown itself to be important in nonstructural applications.

Finite Element Procedures

Finite element procedures are now an important and frequently indispensable part of engineering analyses and scientific investigations. This book focuses on finite element procedures that are very useful and are widely employed. Formulations for the linear and nonlinear analyses of solids and structures, fluids, and multiphysics problems are presented, appropriate finite elements are discussed, and solution techniques for the governing finite element equations are given.

The book presents general, reliable, and effective procedures that are fundamental and can be expected to be in use for a long time. The given procedures form also the foundations of recent developments in the field.

Practical Books 💻

MATLAB Guide to Finite Elements: An Interactive Approach

This successful textbook explores the numerical implementation of Finite Element Analysis using the computer program MATLAB, which is very popular today in engineering and engineering education. The book contains a short tutorial on MATLAB as well as a systematic strategy for the treatment of finite element methods. Useful to both students and researchers in engineering, it provides various examples and exercises from mechanical, civil and aerospace engineering, as well as from materials science.

The book especially stresses the interactive use of MATLAB, with each example solved in an interactive manner. An extensive solutions manual is provided as well, which includes detailed solutions to all the problems in the book for classroom use. This second edition includes a new brick (solid) element with eight nodes and a one-dimensional fluid flow element. A review of the applications of finite elements in various fields such as fluid flow, heat transfer, structural dynamics, electro-magnetics, is added as well.

Practical Stress Analysis with Finite Elements

Updated with new material, the third edition of this highly popular book is a no-nonsense guide to finite element analysis aimed at beginners. Are you tired of picking up a book that claims to be on "practical" finite element analysis only to find that it is full of the same old theory rehashed and contains no advice to help you plan your analysis? If so then this book is for you! The emphasis of this book is on doing FEA, not writing a FE code.

A method is provided to help you plan your analysis and a chapter is devoted to each choice you have to make when building your model giving you clear and specific advice. Finally nine case studies are provided which illustrate the points made in the main text and take you slowly through your first finite element analyses. The book is written in such a way that it is not specific to any particular FE software so it doesn't matter which FE software you use, this book can help you!

Building Better Products With Finite Element Analysis

This book offers a practical view of finite element analysis (FEA) by reviewing the basics of design analysis from an engineering perspective. It provides practical guidelines for specific design problems, such as setting boundaries, contact points between parts, sheetmetal weldments, plastic components, and other common encounter problems. The book also includes a compilation of data which is invaluable to the beginning as well as experienced design analyst.

Introduction to Finite Element Analysis Using MATLAB (R) and Abaqus

There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB® and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software.

The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MATLAB is a high-level language specially designed for dealing with matrices, making it particularly suited for programming the finite element method, while Abaqus is a suite of commercial finite element software.

Nonlinear Finite Element Analysis 🤯

For those of you who are into nonlinearities! 😉

Nonlinear Finite Elements for Continua and Structures

Nonlinear Finite Elements for Continua and Structures, Second Edition focuses on the formulation and solution of discrete equations for various classes of problems that are of principal interest in applications to solid and structural mechanics. Topics covered include the discretization by finite elements of continua in one dimension and in multi-dimensions; the formulation of constitutive equations for nonlinear materials and large deformations; procedures for the solution of the discrete equations, including considerations of both numerical and multiscale physical instabilities; and the treatment of structural and contact-impact problems.

Nonlinear Finite Element Methods

Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations.

This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.

Introduction to Nonlinear Finite Element Analysis

This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems.

The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms.

FEM for Fluid Dynamics 💦

The Finite Element Method for Fluid Dynamics

The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics. The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations.

The character-based split (CBS) scheme is introduced and discussed in detail, followed by thorough coverage of incompressible and compressible fluid dynamics, flow through porous media, shallow water flow, and the numerical treatment of long and short waves.

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