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Theory and Practice of Finite Elements

Author: Alexandre Ern

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 531

ISBN-13: 1475743556

This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.

The Finite Element Method: Theory, Implementation, and Applications

Author: Mats G. Larson

Publisher: Springer Science & Business Media

Published: 2013-01-13

Total Pages: 403

ISBN-13: 3642332870

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This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.

The Finite Element Method

Author: Patrick Ciarlet

Publisher: John Wiley & Sons

Published: 2023-08-29

Total Pages: 404

ISBN-13: 1786307685

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The finite element method, which emerged in the 1950s to deal with structural mechanics problems, has since undergone continuous development. Using partial differential equation models, it is now present in such fields of application as mechanics, physics, chemistry, economics, finance and biology. It is also used in most scientific computing software, and many engineers become adept at using it in their modeling and numerical simulation activities. This book presents all the essential elements of the finite element method in a progressive and didactic way: the theoretical foundations, practical considerations of implementation, algorithms, as well as numerical illustrations created in MATLAB. Original exercises with detailed answers are provided at the end of each chapter.

Practical Finite Element Analysis

Author: Nitin S. Gokhale

Publisher: FINITE TO INFINITE

Published: 2008

Total Pages: 27

ISBN-13: 8190619500

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Highlights of the book: Discussion about all the fields of Computer Aided Engineering, Finite Element Analysis Sharing of worldwide experience by more than 10 working professionals Emphasis on Practical usuage and minimum mathematics Simple language, more than 1000 colour images International quality printing on specially imported paper Why this book has been written ... FEA is gaining popularity day by day & is a sought after dream career for mechanical engineers. Enthusiastic engineers and managers who want to refresh or update the knowledge on FEA are encountered with volume of published books. Often professionals realize that they are not in touch with theoretical concepts as being pre-requisite and find it too mathematical and Hi-Fi. Many a times these books just end up being decoration in their book shelves ... All the authors of this book are from IITÂ€Â™s & IISc and after joining the industry realized gap between university education and the practical FEA. Over the years they learned it via interaction with experts from international community, sharing experience with each other and hard route of trial & error method. The basic aim of this book is to share the knowledge & practices used in the industry with experienced and in particular beginners so as to reduce the learning curve & avoid reinvention of the cycle. Emphasis is on simple language, practical usage, minimum mathematics & no pre-requisites. All basic concepts of engineering are included as & where it is required. It is hoped that this book would be helpful to beginners, experienced users, managers, group leaders and as additional reading material for university courses.

Theory And Practice Of Finite Elements

Author: Alexander Ern

Publisher:

Published: 2005-01-01

Total Pages: 548

ISBN-13: 9788181283627

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The Finite Element Method

Author: Zhangxin Chen

Publisher: World Scientific

Published: 2011

Total Pages: 349

ISBN-13: 9814350567

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A fundamental and practical introduction to the finite element method, its variants, and their applications in engineering.

Practical Guide to Finite Elements

Author: Steven Lepi

Publisher: CRC Press

Published: 1998-03-03

Total Pages: 550

ISBN-13: 9780824700751

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Assuming only basic knowledge of mathematics and engineering mechanics, this lucid reference introduces the fundamentals of finite element theory using easy-to-understand terms and simple problems-systematically grounding the practitioner in the basic principles then suggesting applications to more general cases. Furnishes a wealth of practical insights drawn from the extensive experience of a specialist in the field! Generously illustrated with over 200 detailed drawings to clarify discussions and containing key literature citations for more in-depth study of particular topics, this clearly written resource is an exceptional guide for mechanical, civil, aeronautic, automotive, electrical and electronics, and design engineers; engineering managers; and upper-level undergraduate, graduate, and continuing-education students in these disciplines.

Fundamentals of Finite Element Analysis

Author: Ioannis Koutromanos

Publisher: John Wiley & Sons

Published: 2018-02-12

Total Pages: 724

ISBN-13: 1119260086

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An introductory textbook covering the fundamentals of linear finite element analysis (FEA) This book constitutes the first volume in a two-volume set that introduces readers to the theoretical foundations and the implementation of the finite element method (FEM). The first volume focuses on the use of the method for linear problems. A general procedure is presented for the finite element analysis (FEA) of a physical problem, where the goal is to specify the values of a field function. First, the strong form of the problem (governing differential equations and boundary conditions) is formulated. Subsequently, a weak form of the governing equations is established. Finally, a finite element approximation is introduced, transforming the weak form into a system of equations where the only unknowns are nodal values of the field function. The procedure is applied to one-dimensional elasticity and heat conduction, multi-dimensional steady-state scalar field problems (heat conduction, chemical diffusion, flow in porous media), multi-dimensional elasticity and structural mechanics (beams/shells), as well as time-dependent (dynamic) scalar field problems, elastodynamics and structural dynamics. Important concepts for finite element computations, such as isoparametric elements for multi-dimensional analysis and Gaussian quadrature for numerical evaluation of integrals, are presented and explained. Practical aspects of FEA and advanced topics, such as reduced integration procedures, mixed finite elements and verification and validation of the FEM are also discussed. Provides detailed derivations of finite element equations for a variety of problems. Incorporates quantitative examples on one-dimensional and multi-dimensional FEA. Provides an overview of multi-dimensional linear elasticity (definition of stress and strain tensors, coordinate transformation rules, stress-strain relation and material symmetry) before presenting the pertinent FEA procedures. Discusses practical and advanced aspects of FEA, such as treatment of constraints, locking, reduced integration, hourglass control, and multi-field (mixed) formulations. Includes chapters on transient (step-by-step) solution schemes for time-dependent scalar field problems and elastodynamics/structural dynamics. Contains a chapter dedicated to verification and validation for the FEM and another chapter dedicated to solution of linear systems of equations and to introductory notions of parallel computing. Includes appendices with a review of matrix algebra and overview of matrix analysis of discrete systems. Accompanied by a website hosting an open-source finite element program for linear elasticity and heat conduction, together with a user tutorial. Fundamentals of Finite Element Analysis: Linear Finite Element Analysis is an ideal text for undergraduate and graduate students in civil, aerospace and mechanical engineering, finite element software vendors, as well as practicing engineers and anybody with an interest in linear finite element analysis.

Finite element theory and its application with open source codes

Author: Anthony Pickett

Publisher: Anthony Pickett

Published: 2020-11-10

Total Pages: 366

ISBN-13:

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This book combines essential finite element (FE) theory with a set of fourteen tutorials using relatively easy-to-use open source CAD, FE and other numerical analysis codes so a student can undertake practical analysis and self-study. The theory covers fundamentals of the finite element method. Formulation of element stiffness for one dimensional bar and beam, two dimensional and three dimensional continuum elements, plate and shell elements are derived based on energy and variational methods. Linear, nonlinear and transient dynamic solution methods are covered for both mechanical and field analysis problems with a focus on heat transfer. Other important theoretical topics covered include element integration, element assembly, loads, boundary conditions, contact and a chapter devoted to material laws on elasticity, hyperelasticity and plasticity. A brief introduction to Computational Fluid Dynamics (CFD) is also included. The second half of this book presents a chapter on using tutorials containing information on code installation (on Windows) and getting started, and general hints on meshing, modelling and analysis. This is then followed by tutorials and exercises that cover 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 CFD simulation. In each case theory is linked with application and exercises are included for further self-study. For these tutorials open source codes FreeCAD, CalculiX, FreeMAT and OpenFOAM are used. CalculiX is a comprehensive FE package covering linear, nonlinear and transient analysis. One particular benefit is that its format and structure is based on Abaqus, so knowledge gained is relevant to a leading commercial code. FreeCAD is primarily a powerful CAD modelling code, that includes good finite element meshing and modelling capabilities and is fully integrated with CalculiX. FreeMAT is used in three tutorials for numerical analysis demonstrating algorithms for explicit finite element and CFD analysis. And OpenFOAM is used for other 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.

Introduction to the Finite Element Method and Implementation with MATLAB®

Author: Gang Li

Publisher: Cambridge University Press

Published: 2020-07-30

Total Pages: 525

ISBN-13: 110857386X

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Connecting theory with numerical techniques using MATLAB®, this practical textbook equips students with the tools required to solve finite element problems. This hands-on guide covers a wide range of engineering problems through nine well-structured chapters including solid mechanics, heat transfer and fluid dynamics; equilibrium, steady state and transient; and 1-D, 2-D and 3-D problems. Engineering problems are discussed using case study examples, which are solved using a systematic approach, both by examining the steps manually and by implementing a complete MATLAB®code. This topical coverage is supplemented by discourse on meshing with a detailed explanation and implementation of 2-D meshing algorithms. Introducing theory and numerical techniques alongside comprehensive examples this text increases engagement and provides students with the confidence needed to implement their own computer codes to solve given problems.