Equilibrium Finite Element Formulations

Author : J. P. Moitinho de Almeida,Edward A. Maunder
Publisher : John Wiley & Sons
Page : 315 pages
File Size : 42,7 Mb
Release : 2017-03-20
Category : Technology & Engineering
ISBN : 9781118424155

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Equilibrium Finite Element Formulations by J. P. Moitinho de Almeida,Edward A. Maunder Pdf

A comprehensive treatment of the theory and practice of equilibrium finite element analysis in the context of solid and structural mechanics Equilibrium Finite Element Formulations is an up to date exposition on hybrid equilibrium finite elements, which are based on the direct approximation of the stress fields. The focus is on their derivation and on the advantages that strong forms of equilibrium can have, either when used independently or together with the more conventional displacement based elements. These elements solve two important problems of concern to computational structural mechanics: a rational basis for error estimation, which leads to bounds on quantities of interest that are vital for verification of the output and provision of outputs immediately useful to the engineer for structural design and assessment. Key features: Unique in its coverage of equilibrium – an essential reference work for those seeking solutions that are strongly equilibrated. The approach is not widely known, and should be of benefit to structural design and assessment. Thorough explanations of the formulations for: 2D and 3D continua, thick and thin bending of plates and potential problems; covering mainly linear aspects of behaviour, but also with some excursions into non-linearity. Highly relevant to the verification of numerical solutions, the basis for obtaining bounds of the errors is explained in detail. Simple illustrative examples are given, together with their physical interpretations. The most relevant issues regarding the computational implementation of this approach are presented. When strong equilibrium and finite elements are to be combined, the book is a must-have reference for postgraduate students, researchers in software development or numerical analysis, and industrial practitioners who want to keep up to date with progress in simulation tools.

Author : J. P. Moitinho de Almeida,Edward A. Maunder
Publisher : Wiley
Page : 0 pages
File Size : 42,7 Mb
Release : 2017-02-08
Category : Technology & Engineering
ISBN : 1118926226

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Equilibrium Finite Element Formulations by J. P. Moitinho de Almeida,Edward A. Maunder Pdf

A comprehensive treatment of the theory and practice of equilibrium finite element analysis in the context of solid and structural mechanics Equilibrium Finite Element Formulations is an up to date exposition on hybrid equilibrium finite elements, which are based on the direct approximation of the stress fields. The focus is on their derivation and on the advantages that strong forms of equilibrium can have, either when used independently or together with the more conventional displacement based elements. These elements solve two important problems of concern to computational structural mechanics: a rational basis for error estimation, which leads to bounds on quantities of interest that are vital for verification of the output and provision of outputs immediately useful to the engineer for structural design and assessment. Key features: Unique in its coverage of equilibrium – an essential reference work for those seeking solutions that are strongly equilibrated. The approach is not widely known, and should be of benefit to structural design and assessment. Thorough explanations of the formulations for: 2D and 3D continua, thick and thin bending of plates and potential problems; covering mainly linear aspects of behaviour, but also with some excursions into non-linearity. Highly relevant to the verification of numerical solutions, the basis for obtaining bounds of the errors is explained in detail. Simple illustrative examples are given, together with their physical interpretations. The most relevant issues regarding the computational implementation of this approach are presented. When strong equilibrium and finite elements are to be combined, the book is a must-have reference for postgraduate students, researchers in software development or numerical analysis, and industrial practitioners who want to keep up to date with progress in simulation tools.

Author : Klaus-Jürgen Bathe
Publisher : Klaus-Jurgen Bathe
Page : 1056 pages
File Size : 51,6 Mb
Release : 2006
Category : Engineering mathematics
ISBN : 097900490X

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Finite Element Procedures by Klaus-Jürgen Bathe Pdf

Author : Barna Szabó,Ivo Babuška
Publisher : John Wiley & Sons
Page : 337 pages
File Size : 46,8 Mb
Release : 2011-03-21
Category : Technology & Engineering
ISBN : 9781119993483

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Introduction to Finite Element Analysis by Barna Szabó,Ivo Babuška Pdf

When using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided? Whenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential part of any modelling effort. Giving users of finite element analysis (FEA) software an introduction to verification and validation procedures, this book thoroughly covers the fundamentals of assuring reliability in numerical simulation. The renowned authors systematically guide readers through the basic theory and algorithmic structure of the finite element method, using helpful examples and exercises throughout. Delivers the tools needed to have a working knowledge of the finite element method Illustrates the concepts and procedures of verification and validation Explains the process of conceptualization supported by virtual experimentation Describes the convergence characteristics of the h-, p- and hp-methods Covers the hierarchic view of mathematical models and finite element spaces Uses examples and exercises which illustrate the techniques and procedures of quality assurance Ideal for mechanical and structural engineering students, practicing engineers and applied mathematicians Includes parameter-controlled examples of solved problems in a companion website (www.wiley.com/go/szabo)

Author : Rajasekaran S.
Publisher : S. Chand Publishing
Page : 643 pages
File Size : 46,8 Mb
Release : 2008
Category : Technology & Engineering
ISBN : 9788121923149

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Finite Element Analysis in Engineering Design by Rajasekaran S. Pdf

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.

Author : Klaus-Jürgen Bathe,John Tinsley Oden,Edward L. Wilson
Publisher : MIT Press (MA)
Page : 1120 pages
File Size : 41,5 Mb
Release : 1977
Category : Mathematics
ISBN : WISC:89034014308

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Formulations and Computational Algorithms in Finite Element Analysis by Klaus-Jürgen Bathe,John Tinsley Oden,Edward L. Wilson Pdf

Author : Erasmo Carrera,Maria Cinefra,Marco Petrolo,Enrico Zappino
Publisher : John Wiley & Sons
Page : 569 pages
File Size : 45,9 Mb
Release : 2014-07-29
Category : Mathematics
ISBN : 9781118536650

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Finite Element Analysis of Structures through Unified Formulation by Erasmo Carrera,Maria Cinefra,Marco Petrolo,Enrico Zappino Pdf

The finite element method (FEM) is a computational tool widely used to design and analyse complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another. Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same 'fundamental nucleus' that comes from geometrical relations and Hooke's law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements. It also covers 1D and 2D FEs that make use of 'real' physical surfaces rather than ’artificial’ mathematical surfaces which are difficult to interface in CAD/CAE software. Key features: Covers how the refined formulation can be easily and conveniently used to analyse laminated structures, such as sandwich and composite structures, and to deal with multifield problems Shows the performance of different FE models through the 'best theory diagram' which allows different models to be compared in terms of accuracy and computational cost Introduces an axiomatic/asymptotic approach that reduces the computational cost of the structural analysis without affecting the accuracy Introduces an innovative 'component-wise' approach to deal with complex structures Accompanied by a website hosting the dedicated software package MUL2 (www.mul2.com) Finite Element Analysis of Structures Through Unified Formulation is a valuable reference for researchers and practitioners, and is also a useful source of information for graduate students in civil, mechanical and aerospace engineering.

Author : M Moatamedi,Hassan A. Khawaja
Publisher : CRC Press
Page : 154 pages
File Size : 41,9 Mb
Release : 2018-07-20
Category : Mathematics
ISBN : 9780429841613

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Finite Element Analysis by M Moatamedi,Hassan A. Khawaja Pdf

Finite element analysis has become the most popular technique for studying engineering structures in detail. It is particularly useful whenever the complexity of the geometry or of the loading is such that alternative methods are inappropriate. The finite element method is based on the premise that a complex structure can be broken down into finitely many smaller pieces (elements), the behaviour of each of which is known or can be postulated. These elements might then be assembled in some sense to model the behaviour of the structure. Intuitively this premise seems reasonable, but there are many important questions that need to be answered. In order to answer them it is necessary to apply a degree of mathematical rigour to the development of finite element techniques. The approach that will be taken in this book is to develop the fundamental ideas and methodologies based on an intuitive engineering approach, and then to support them with appropriate mathematical proofs where necessary. It will rapidly become clear that the finite element method is an extremely powerful tool for the analysis of structures (and for other field problems), but that the volume of calculations required to solve all but the most trivial of them is such that the assistance of a computer is necessary. As stated above, many questions arise concerning finite element analysis. Some of these questions are associated with the fundamental mathematical formulations, some with numerical solution techniques, and others with the practical application of the method. In order to answer these questions, the engineer/analyst needs to understand both the nature and limitations of the finite element approximation and the fundamental behaviour of the structure. Misapplication of finite element analysis programs is most likely to arise when the analyst is ignorant of engineering phenomena.

Author : Ted Belytschko,Wing Kam Liu,Brian Moran,Khalil Elkhodary
Publisher : John Wiley & Sons
Page : 834 pages
File Size : 43,5 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 : Eugenio Oñate
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 51,7 Mb
Release : 2010-02-25
Category : Technology & Engineering
ISBN : 9781402087332

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Structural Analysis with the Finite Element Method. Linear Statics by Eugenio Oñate Pdf

STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 1 : The Basis and Solids Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elastic foundations, stress smoothing, error estimation and adaptive mesh refinement techniques, among others. The text concludes with a chapter on the mesh generation and visualization of FEM results. The book will be useful for students approaching the finite element analysis of structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis. STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 2: Beams, Plates and Shells Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM).The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume 2 presents a detailed description of the finite element formulation for analysis of slender and thick beams, thin and thick plates, folded plate structures, axisymmetric shells, general curved shells, prismatic structures and three dimensional beams. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems Emphasis is put on the treatment of structures with layered composite materials. The book will be useful for students approaching the finite element analysis of beam, plate and shell structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis.

Author : Maria Augusta Neto,Ana Amaro,Luis Roseiro,José Cirne,Rogério Leal
Publisher : Springer
Page : 314 pages
File Size : 43,5 Mb
Release : 2015-09-29
Category : Technology & Engineering
ISBN : 9783319177106

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Engineering Computation of Structures: The Finite Element Method by Maria Augusta Neto,Ana Amaro,Luis Roseiro,José Cirne,Rogério Leal Pdf

This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It uses straightforward examples to demonstrate a complete and detailed finite element procedure, emphasizing the differences between exact and numerical procedures.

Author : René de Borst,Mike A. Crisfield,Joris J. C. Remmers,Clemens V. Verhoosel
Publisher : John Wiley & Sons
Page : 481 pages
File Size : 54,6 Mb
Release : 2012-07-25
Category : Technology & Engineering
ISBN : 9781118376010

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Nonlinear Finite Element Analysis of Solids and Structures by René de Borst,Mike A. Crisfield,Joris J. C. Remmers,Clemens V. Verhoosel Pdf

Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist René de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature. Key features: Combines the two previous volumes into one heavily revised text with obsolete material removed, an improved layout and updated references and notations Extensive new material on more recent developments in computational mechanics Easily readable, engineering oriented, with no more details in the main text than necessary to understand the concepts. Pseudo-code throughout makes the link between theory and algorithms, and the actual implementation. Accompanied by a website (www.wiley.com/go/deborst) with a Python code, based on the pseudo-code within the book and suitable for solving small-size problems. Non-linear Finite Element Analysis of Solids and Structures, 2nd Edition is an essential reference for practising engineers and researchers that can also be used as a text for undergraduate and graduate students within computational mechanics.

Author : Thomas J. R. Hughes,Ernest Hinton
Publisher : Unknown
Page : 384 pages
File Size : 51,5 Mb
Release : 1986
Category : Mathematics
ISBN : CORNELL:31924005035450

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Finite Element Methods for Plate and Shell Structures: Formulations and algorithms by Thomas J. R. Hughes,Ernest Hinton Pdf

Author : Sudip S. Bhattacharjee
Publisher : CRC Press
Page : 341 pages
File Size : 40,5 Mb
Release : 2021-07-18
Category : Technology & Engineering
ISBN : 9781000412307

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Finite Element Analysis of Solids and Structures by Sudip S. Bhattacharjee Pdf

Finite Element Analysis of Solids and Structures combines the theory of elasticity (advanced analytical treatment of stress analysis problems) and finite element methods (numerical details of finite element formulations) into one academic course derived from the author’s teaching, research, and applied work in automotive product development as well as in civil structural analysis. Features Gives equal weight to the theoretical details and FEA software use for problem solution by using finite element software packages Emphasizes understanding the deformation behavior of finite elements that directly affect the quality of actual analysis results Reduces the focus on hand calculation of property matrices, thus freeing up time to do more software experimentation with different FEA formulations Includes chapters dedicated to showing the use of FEA models in engineering assessment for strength, fatigue, and structural vibration properties Features an easy to follow format for guided learning and practice problems to be solved by using FEA software package, and with hand calculations for model validation This textbook contains 12 discrete chapters that can be covered in a single semester university graduate course on finite element analysis methods. It also serves as a reference for practicing engineers working on design assessment and analysis of solids and structures. Teaching ancillaries include a solutions manual (with data files) and lecture slides for adopting professors.

Author : Theodore H.H. Pian,Chang-Chun Wu
Publisher : CRC Press
Page : 400 pages
File Size : 41,7 Mb
Release : 2005-11-04
Category : Mathematics
ISBN : 9780203487693

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Hybrid and Incompatible Finite Element Methods by Theodore H.H. Pian,Chang-Chun Wu Pdf

While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods.