Finite Elements I

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Finite Elements I

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Author : Alexandre Ern
language : en
Publisher: Springer Nature
Release Date : 2021-02-18

Finite Elements I written by Alexandre Ern and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-18 with Mathematics categories.

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.

Finite Elements

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Author : Richard MacNeal
language : en
Publisher: CRC Press
Release Date : 1993-10-28

Finite Elements written by Richard MacNeal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-28 with Technology & Engineering categories.

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.

Finite Elements In Solids And Structures

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Author : R. Jeremy Astley
language : en
Publisher:
Release Date : 1992

Finite Elements In Solids And Structures written by R. Jeremy Astley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

An introduction to finite elements in their specific and elementary application to solid mechanics and structural analysis. Designed for use as an advanced undergraduate text, it deals mainly with static linear analysis but also includes a brief introduction to dynamic problems.

Finite Element Analysis In Engineering Design

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Author : Rajasekaran S.
language : en
Publisher: S. Chand Publishing
Release Date : 2008

Finite Element Analysis In Engineering Design written by Rajasekaran S. and has been published by S. Chand Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Technology & Engineering categories.

During the past three decades,the finite element method of analysis has rapidly become a very popular tool for computer solution of complex problems in engineering.With the advent of digital computers the finite element method has greatly enlarged the range of engineering problems.The finite element method is very sucessful because of its generality,the formulation of the problem in variational or weighted residual form,discretization of the formulation and the solution of resulting finite element equations.The book is divided into sixteen chapters.In the first chapter,the historical background and the fundamentals of solid mechanics are discussed.The second chapter covers the discrete finite element method or direct stiffness approach to solve trusses which is quite often discussed in computer statics course.These structural concepts are necessary for the basic understanding of the method to a continuum.

Finite Elements For Analysis And Design

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Author : J. E. Akin
language : en
Publisher: Elsevier
Release Date : 2014-06-28

Finite Elements For Analysis And Design written by J. E. Akin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Technology & Engineering categories.

The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material. - Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing - Basic theory has been added in the book, including worked examples to enable students to understand the concepts - Contains coverage of computational topics, including worked examples to enable students to understand concepts - Improved coverage of sensitivity analysis and computational fluid dynamics - Uses example applications to increase students' understanding - Includes a disk with the FORTRAN source for the programs cided in the text

Finite Elements And Approximation

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Author : O. C. Zienkiewicz
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22

Finite Elements And Approximation written by O. C. Zienkiewicz and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Technology & Engineering categories.

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.

Finite Element Methods

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Author : Jonathan Whiteley
language : en
Publisher: Springer
Release Date : 2017-01-26

Finite Element Methods written by Jonathan Whiteley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with Science categories.

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.

An Introduction To The Mathematical Theory Of Finite Elements

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Author : J. T. Oden
language : en
Publisher: Courier Corporation
Release Date : 2011-04-20

An Introduction To The Mathematical Theory Of Finite Elements written by J. T. Oden and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-20 with Technology & Engineering categories.

This introduction to the basic mathematical theory of the finite element method is geared toward readers with limited mathematical backgrounds. Its coherent demonstrations explain the use of these techniques in developing the theory of finite elements, with detailed proofs of the major theorems and numerous examples. 1976 edition.

Theory And Practice Of Finite Elements

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Author : Alexandre Ern
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-29

Theory And Practice Of Finite Elements written by Alexandre Ern and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-29 with Mathematics categories.

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.

Finite Elements

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Author : Eric B. Becker
language : en
Publisher: Prentice Hall
Release Date : 1984

Finite Elements written by Eric B. Becker and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.