A Finite Element Primer For Beginners
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A Finite Element Primer For Beginners
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Author : Tarek I. Zohdi
language : en
Publisher: Springer
Release Date : 2014-08-12
A Finite Element Primer For Beginners written by Tarek I. Zohdi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-12 with Science categories.
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are: (1) Weighted residual methods and Galerkin approximations, (2) A model problem for one-dimensional linear elastostatics, (3) Weak formulations in one dimension, (4) Minimum principles in one dimension, (5) Error estimation in one dimension, (5) Construction of Finite Element basis functions in one dimension, (6) Gaussian Quadrature, (7) Iterative solvers and element by element data structures, (8) A model problem for three-dimensional linear elastostatics, (9) Weak formulations in three dimensions, (10) Basic rules for element construction in three-dimensions, (11) Assembly of the system and solution schemes, (12) Assembly of the system and solution schemes, (13) An introduction to time-dependent problems and (14) A brief introduction to rapid computation based on domain decomposition and basic parallel processing.
A Primer For Finite Elements In Elastic Structures
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Author : W. F. Carroll
language : en
Publisher: John Wiley & Sons
Release Date : 1998-11-05
A Primer For Finite Elements In Elastic Structures written by W. F. Carroll and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-05 with Technology & Engineering categories.
A thorough guide to the fundamentals--and how to use them--of finite element analysis for elastic structures For elastic structures, the finite element method is an invaluable tool which is used most effectively only when one understands completely each of its facets. A Primer for Finite Elements in Elastic Structures disassembles the entire finite element method for civil engineering students and professionals, detailing its supportive theory and its mathematical and structural underpinnings, in the context of elastic structures and the principle of virtual work. The book opens with a discussion of matrix algebra and algebraic equation systems to foster the basic skills required to successfully understand and use the finite element method. Key mathematical concepts outlined here are joined to pertinent concepts from mechanics and structural theory, with the method constructed in terms of one-dimensional truss and framework finite elements. The use of these one-dimensional elements in the early chapters promotes better understanding of the fundamentals. Subsequent chapters describe many two-dimensional structural finite elements in depth, including the geometry, mechanics, transformations, and mapping needed for them. Most chapters end with questions and problems which review the text material. Answers for many of these are at the end of the book. An appendix describes how to use MATLAB(r), a popular matrix-manipulation software platform necessary to perform the many matrix operations required for the finite element method, such as matrix addition, multiplication, inversion, partitioning, rearrangement, and assembly. As an added extra, the m-files discussed can be downloaded from the Wiley FTP server.
A Beginner S Primer Basic Concepts In Mechanics
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Author : Tarek I. Zohdi
language : en
Publisher: Springer Nature
Release Date : 2025-06-23
A Beginner S Primer Basic Concepts In Mechanics written by Tarek I. Zohdi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-23 with Science categories.
As we enter an exciting new era in industrial design, simulation, and manufacturing, a clear understanding of mechanics of solids is needed now more than ever. This primer is a condensed synopsis of basic undergraduate mechanics and is designed to supplement classical textbooks in this area. The focus is on the essentials of mechanics, specifically: • The concept of stress. • Stress-strain relationships. • Failure theory. • Axial loading of a rod. • Transverse (bending) loading of a beam. • Industrial application: modeling of 3D printing. • Transverse shear stresses. • Torsional loading of a rod. • Pressure vessels. • Buckling of columns. • The basics of finite element methods. • A unifying concept: continuum mechanics.
An Explicit Finite Element Primer
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Author : Paul Jacob
language : en
Publisher:
Release Date : 2002
An Explicit Finite Element Primer written by Paul Jacob and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Finite element method categories.
Finite Element Primer
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Author : Bruce Irons
language : en
Publisher:
Release Date : 2000
Finite Element Primer written by Bruce Irons and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Finite element method categories.
The Scaled Boundary Finite Element Method
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Author : John P. Wolf
language : en
Publisher: John Wiley & Sons
Release Date : 2003-03-14
The Scaled Boundary Finite Element Method written by John P. Wolf and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-14 with Technology & Engineering categories.
A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.
Practical Guide To Finite Elements
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Author : Steven Lepi
language : en
Publisher: CRC Press
Release Date : 2020-11-25
Practical Guide To Finite Elements written by Steven Lepi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Technology & Engineering categories.
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.
Finite Element Theory And Its Application With Open Source Codes
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Author : Anthony Pickett
language : en
Publisher: Anthony Pickett
Release Date : 2020-11-10
Finite Element Theory And Its Application With Open Source Codes written by Anthony Pickett and has been published by Anthony Pickett this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-10 with Technology & Engineering categories.
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.
The Finite Element Method Theory Implementation And Applications
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Author : Mats G. Larson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-13
The Finite Element Method Theory Implementation And Applications written by Mats G. Larson 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 2013-01-13 with Computers categories.
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.
Finite Element Model Updating In Structural Dynamics
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Author : Michael Friswell
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Finite Element Model Updating In Structural Dynamics written by Michael Friswell 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 2013-03-09 with Technology & Engineering categories.
Finite element model updating has emerged in the 1990s as a subject of immense importance to the design, construction and maintenance of mechanical systems and civil engineering structures. This book, the first on the subject, sets out to explain the principles of model updating, not only as a research text, but also as a guide for the practising engineer who wants to get acquainted with, or use, updating techniques. It covers all aspects of model preparation and data acquisition that are necessary for updating. The various methods for parameter selection, error localisation, sensitivity and parameter estimation are described in detail and illustrated with examples. The examples can be easily replicated and expanded in order to reinforce understanding. The book is aimed at researchers, postgraduate students and practising engineers.