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Equilibrium Finite Element Formulations
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Book Synopsis Equilibrium Finite Element Formulations by : J. P. Moitinho de Almeida
Download or read book Equilibrium Finite Element Formulations written by J. P. Moitinho de Almeida and published by John Wiley & Sons. This book was released on 2017-03-20 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Equilibrium Finite Element Formulations by : J. P. Moitinho de Almeida
Download or read book Equilibrium Finite Element Formulations written by J. P. Moitinho de Almeida and published by Wiley. This book was released on 2017-02-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite Element Formulation for Inelastic Equilibrium by : Turhan Kasar
Download or read book Finite Element Formulation for Inelastic Equilibrium written by Turhan Kasar and published by . This book was released on 1975 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Procedures by : Klaus-Jürgen Bathe
Download or read book Finite Element Procedures written by Klaus-Jürgen Bathe and published by Klaus-Jurgen Bathe. This book was released on 2006 with total page 1056 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Analysis by : M Moatamedi
Download or read book Finite Element Analysis written by M Moatamedi and published by CRC Press. This book was released on 2018-07-20 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Finite Element Method Set by : O. C. Zienkiewicz
Download or read book The Finite Element Method Set written by O. C. Zienkiewicz and published by Elsevier. This book was released on 2005-11-25 with total page 1863 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Written by the leading professors in their fields, the three books cover the basis of the method, its application to solid mechanics and to fluid dynamics. * This is THE classic finite element method set, by two the subject's leading authors * FEM is a constantly developing subject, and any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in these books * Fully up-to-date; ideal for teaching and reference
Book Synopsis Structural Analysis with the Finite Element Method. Linear Statics by : Eugenio Oñate
Download or read book Structural Analysis with the Finite Element Method. Linear Statics written by Eugenio Oñate and published by Springer Science & Business Media. This book was released on 2010-02-25 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Finite Element Analysis by : Barna Szabó
Download or read book Introduction to Finite Element Analysis written by Barna Szabó and published by John Wiley & Sons. This book was released on 2011-03-21 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)
Book Synopsis Finite Element Analysis of Solids and Structures by : Sudip S. Bhattacharjee
Download or read book Finite Element Analysis of Solids and Structures written by Sudip S. Bhattacharjee and published by CRC Press. This book was released on 2021-07-18 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Engineering Computation of Structures: The Finite Element Method by : Maria Augusta Neto
Download or read book Engineering Computation of Structures: The Finite Element Method written by Maria Augusta Neto and published by Springer. This book was released on 2015-09-29 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite Element Analysis of Structures through Unified Formulation by : Erasmo Carrera
Download or read book Finite Element Analysis of Structures through Unified Formulation written by Erasmo Carrera and published by John Wiley & Sons. This book was released on 2014-07-29 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Formulations and Computational Algorithms in Finite Element Analysis by : Klaus-Jürgen Bathe
Download or read book Formulations and Computational Algorithms in Finite Element Analysis written by Klaus-Jürgen Bathe and published by MIT Press (MA). This book was released on 1977 with total page 1120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Analysis in Engineering Design by : Rajasekaran S.
Download or read book Finite Element Analysis in Engineering Design written by Rajasekaran S. and published by S. Chand Publishing. This book was released on 2008 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Finite Element Methods by : Dieter Dinkler
Download or read book Introduction to Finite Element Methods written by Dieter Dinkler and published by Springer Nature. This book was released on 2023-09-28 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: The textbook at hand offers an introduction to Finite Element Methods from an engineering point of view comprising the basic principles of virtual work, derivations of displacement-based, mixed and hybrid element formulations for 1-D and 2-D membrane as well as bending structures and heat conduction. Different element geometries, including triangular elements and the isoparametric concept, and related numerical integration schemes, are presented. The element matrices and load vectors are derived in detail, the assembly at the system level is discussed with respect to fulfillment of boundary conditions and numerical efficiency. Evaluation of errors and investigations concerning the quality of the elements complete the work flow.
Book Synopsis The Finite Element Method in Thermomechanics by : Tai-Ran Hsu
Download or read book The Finite Element Method in Thermomechanics written by Tai-Ran Hsu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapid advances in the nuclear and aerospace technologies in the past two decades compounded with the increasing demands for high performance, energy-efficient power plant components and engines have made reliable thermal stress analysis a critical factor in the design and operation of such equipment. Recently, and as experienced by the author, the need for sophis ticated analyses has been extended to the energy resource industry such as in-situ coal gasification and in-situ oil recovery from oil sands and shales. The analyses in the above applications are of a multidisciplinary nature, and some involve the additional complexity of multiphase and phase change phenomena. These extremely complicated factors preclude the use of classical methods, and numerical techniques such as the finite element method appear to be the most viable alternative solution. The development of this technique so far appears to have concentrated in two extremes; one being overly concerned with the accuracy of results and tending to place all effort in the implementation of special purpose element concepts and computational algorithms, the other being for commercial purposes with the ability of solving a wide range of engineering problems. However, to be versatile, users require substantial training and experience in order to use these codes effectively. Above all, no provision for any modifi cation of these codes by users is possible, as all these codes are proprietary and access to the code is limited only to the owners.
Book Synopsis Nonlinear Finite Elements for Continua and Structures by : Ted Belytschko
Download or read book Nonlinear Finite Elements for Continua and Structures written by Ted Belytschko and published by John Wiley & Sons. This book was released on 2014-01-07 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis TEXTBOOK OF FINITE ELEMENT ANALYSIS by : P. SESHU
Download or read book TEXTBOOK OF FINITE ELEMENT ANALYSIS written by P. SESHU and published by PHI Learning Pvt. Ltd.. This book was released on 2003-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and a review of mathematical preliminaries, the book gives a detailed discussion on FEM as a technique for solving differential equations and variational formulation of FEM. This is followed by a lucid presentation of one-dimensional and two-dimensional finite elements and finite element formulation for dynamics. The book concludes with some case studies that focus on industrial problems and Appendices that include mini-project topics based on near-real-life problems. Postgraduate/Senior undergraduate students of civil, mechanical and aeronautical engineering will find this text extremely useful; it will also appeal to the practising engineers and the teaching community.
