Finite Elements

Author : Nitin S. Gokhale
Publisher : FINITE TO INFINITE
Page : 27 pages
File Size : 55,5 Mb
Release : 2008
Category : Engineering
ISBN : 9788190619509

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Practical Finite Element Analysis by Nitin S. Gokhale Pdf

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 IIT€™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.

Author : Alexandre Ern,Jean-Luc Guermond
Publisher : Springer Nature
Page : 325 pages
File Size : 51,9 Mb
Release : 2021-03-22
Category : Mathematics
ISBN : 9783030563417

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Finite Elements I by Alexandre Ern,Jean-Luc Guermond Pdf

This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.

Author : Richard MacNeal
Publisher : CRC Press
Page : 554 pages
File Size : 46,6 Mb
Release : 1993-10-28
Category : Technology & Engineering
ISBN : 0824791622

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Finite Elements by Richard MacNeal Pdf

In this work, MacNeal examines why finite elements sometimes fail and how element designers have corrected their failures. It includes quantitative analyses of failure modes and illustrations of possible side effects found in proposed remedies, providing a practical understanding of finite element performance. The book is designed to enable users and practitioners to identify and circumvent the major flaws of finite elements, such as locking, patch-test failure, spurious models, rigid-body failure, induced anisotropy and shape sensitivity.

Author : Alexandre Ern,Jean-Luc Guermond
Publisher : Springer Nature
Page : 417 pages
File Size : 40,5 Mb
Release : 2021-03-29
Category : Mathematics
ISBN : 9783030573485

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Finite Elements III by Alexandre Ern,Jean-Luc Guermond Pdf

This book is the third volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume III is divided into 28 chapters. The first eight chapters focus on the symmetric positive systems of first-order PDEs called Friedrichs' systems. This part of the book presents a comprehensive and unified treatment of various stabilization techniques from the existing literature. It discusses applications to advection and advection-diffusion equations and various PDEs written in mixed form such as Darcy and Stokes flows and Maxwell's equations. The remainder of Volume III addresses time-dependent problems: parabolic equations (such as the heat equation), evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear hyperbolic equations (scalar conservation equations, hyperbolic systems). It offers a fresh perspective on the analysis of well-known time-stepping methods. The last five chapters discuss the approximation of hyperbolic equations with finite elements. Here again a new perspective is proposed. These chapters should convince the reader that finite elements offer a good alternative to finite volumes to solve nonlinear conservation equations.

Author : Jacob Fish,Ted Belytschko
Publisher : Wiley-Blackwell
Page : 319 pages
File Size : 53,9 Mb
Release : 2007-06-12
Category : Computers
ISBN : 0470035803

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A First Course in Finite Elements by Jacob Fish,Ted Belytschko Pdf

Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations. Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements: Adopts a generic approach to the subject, and is not application specific In conjunction with a web-based chapter, it integrates code development, theory, and application in one book Provides an accompanying Web site that includes ABAQUS Student Edition, Matlab data and programs, and instructor resources Contains a comprehensive set of homework problems at the end of each chapter Produces a practical, meaningful course for both lecturers, planning a finite element module, and for students using the text in private study. Accompanied by a book companion website housing supplementary material that can be found at http://www.wileyeurope.com/college/Fish A First Course in Finite Elements is the ideal practical introductory course for junior and senior undergraduate students from a variety of science and engineering disciplines. The accompanying advanced topics at the end of each chapter also make it suitable for courses at graduate level, as well as for practitioners who need to attain or refresh their knowledge of finite elements through private study.

Author : Ted Belytschko,Wing Kam Liu,Brian Moran,Khalil Elkhodary
Publisher : John Wiley & Sons
Page : 834 pages
File Size : 41,5 Mb
Release : 2014-01-07
Category : Science
ISBN : 9781118632703

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Nonlinear Finite Elements for Continua and Structures by Ted Belytschko,Wing Kam Liu,Brian Moran,Khalil Elkhodary Pdf

Nonlinear Finite Elements for Continua and Structures p>Nonlinear Finite Elements for Continua and Structures This updated and expanded edition of the bestselling textbook provides a comprehensive introduction to the methods and theory of nonlinear finite element analysis. New material provides a concise introduction to some of the cutting-edge methods that have evolved in recent years in the field of nonlinear finite element modeling, and includes the eXtended Finite Element Method (XFEM), multiresolution continuum theory for multiscale microstructures, and dislocation- density-based crystalline plasticity. 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. Key features: Presents a detailed and rigorous treatment of nonlinear solid mechanics and how it can be implemented in finite element analysis Covers many of the material laws used in today’s software and research Introduces advanced topics in nonlinear finite element modelling of continua Introduction of multiresolution continuum theory and XFEM Accompanied by a website hosting a solution manual and MATLAB® and FORTRAN code Nonlinear Finite Elements for Continua and Structures, Second Edition is a must-have textbook for graduate students in mechanical engineering, civil engineering, applied mathematics, engineering mechanics, and materials science, and is also an excellent source of information for researchers and practitioners.

Author : Alexandre Ern,Jean-Luc Guermond
Publisher : Springer Science & Business Media
Page : 531 pages
File Size : 44,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475743555

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Theory and Practice of Finite Elements by Alexandre Ern,Jean-Luc Guermond Pdf

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.

Author : Dietrich Braess
Publisher : Cambridge University Press
Page : 348 pages
File Size : 47,8 Mb
Release : 2007-04-12
Category : Mathematics
ISBN : 9781139461467

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Finite Elements by Dietrich Braess Pdf

This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

Author : Susanne Brenner,L. Ridgway Scott
Publisher : Springer Science & Business Media
Page : 369 pages
File Size : 48,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475736588

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The Mathematical Theory of Finite Element Methods by Susanne Brenner,L. Ridgway Scott Pdf

A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide

Author : Mohamed Gadala
Publisher : Cambridge University Press
Page : 631 pages
File Size : 44,7 Mb
Release : 2020-07-09
Category : Mathematics
ISBN : 9781107194083

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Finite Elements for Engineers with ANSYS Applications by Mohamed Gadala Pdf

Covering theory and practical industry usage of the finite element method, this highly-illustrated step-by-step approach thoroughly introduces methods using ANSYS.

Author : Mats G. Larson,Fredrik Bengzon
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 48,8 Mb
Release : 2013-01-13
Category : Computers
ISBN : 9783642332876

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The Finite Element Method: Theory, Implementation, and Applications by Mats G. Larson,Fredrik Bengzon Pdf

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.​

Author : O. C. Zienkiewicz,Robert Leroy Taylor
Publisher : Butterworth-Heinemann
Page : 482 pages
File Size : 40,6 Mb
Release : 2000
Category : Continuum mechanics
ISBN : 0750650559

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The Finite Element Method: Solid mechanics by O. C. Zienkiewicz,Robert Leroy Taylor Pdf

Author : O. C. Zienkiewicz,K. Morgan
Publisher : Courier Corporation
Page : 356 pages
File Size : 55,8 Mb
Release : 2013-04-22
Category : Technology & Engineering
ISBN : 9780486318011

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Finite Elements and Approximation by O. C. Zienkiewicz,K. Morgan Pdf

A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises. Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher order finite element approximation, mapping and numerical integration, variational methods, and partial discretization and time-dependent problems. A survey of generalized finite elements and error estimates concludes the text.

Author : Daniele Boffi,Franco Brezzi,Michel Fortin
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 55,9 Mb
Release : 2013-07-02
Category : Mathematics
ISBN : 9783642365195

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Mixed Finite Element Methods and Applications by Daniele Boffi,Franco Brezzi,Michel Fortin Pdf

Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.

Author : Jonathan Whiteley
Publisher : Springer
Page : 232 pages
File Size : 54,5 Mb
Release : 2017-01-26
Category : Science
ISBN : 9783319499710

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Finite Element Methods by Jonathan Whiteley Pdf

This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.