One-Dimensional Finite Elements

An Introduction to the FE Method

Author: Andreas Öchsner,Markus Merkel

Publisher: Springer

ISBN: 331975145X

Category: Science

Page: 418

View: 1664

This textbook presents finite element methods using exclusively one-dimensional elements. It presents the complex methodology in an easily understandable but mathematically correct fashion. The approach of one-dimensional elements enables the reader to focus on the understanding of the principles of basic and advanced mechanical problems. The reader will easily understand the assumptions and limitations of mechanical modeling as well as the underlying physics without struggling with complex mathematics. Although the description is easy, it remains scientifically correct. The approach using only one-dimensional elements covers not only standard problems but allows also for advanced topics such as plasticity or the mechanics of composite materials. Many examples illustrate the concepts and problems at the end of every chapter help to familiarize with the topics. Each chapter also includes a few exercise problems, with short answers provided at the end of the book. The second edition appears with a complete revision of all figures. It also presents a complete new chapter special elements and added the thermal conduction into the analysis of rod elements. The principle of virtual work has also been introduced for the derivation of the finite-element principal equation.
Posted in Science

Eindimensionale Finite Elemente

Ein Einstieg in die Methode

Author: Markus Merkel,Andreas Öchsner

Publisher: Springer-Verlag

ISBN: 3642544827

Category: Science

Page: 428

View: 7235

Die Finite-Elemente-Methode wird in dieser Einführung in ihrer Komplexität auf eindimensionale Elemente heruntergebrochen. Somit bleibt die mathematische Beschreibung weitgehend einfach und überschaubar. Das Augenmerk liegt in jedem Kapitel auf der Erläuterung der Methode und deren Verständnis. Der Leser lernt, die Annahmen und Ableitungen bei verschiedenen physikalischen Problemstellungen in der Strukturmechanik zu verstehen und Möglichkeiten und Grenzen der Methode der Finiten Elemente kritisch zu beurteilen. Diese Herangehensweise ermöglicht das methodische Verständnis wichtiger Themenbereiche, wie z.B. Plastizität oder Verbundwerkstoffe und gewährleistet einen einfachen Einstieg in weiterführende Anwendungsgebiete. Ausführliche durchgerechnete und kommentierte Beispiele und weiterführende Aufgaben mit Kurzlösung im Anhang unterstützen den Lernerfolg. In der zweiten Auflage dieses Lehrbuches wurden alle graphischen Darstellungen überarbeitet, die Wärmeleitung bei den Stabelementen ergänzt und Spezialelemente als neues Kapitel aufgenommen. Auch wurde das Prinzip der virtuellen Arbeiten zur Ableitung der Finite-Elemente-Hauptgleichung eingeführt.
Posted in Science

Eindimensionale Finite Elemente

Ein Einstieg in die Methode

Author: Markus Merkel,Andreas Öchsner

Publisher: Springer-Verlag

ISBN: 3642049923

Category: Technology & Engineering

Page: 422

View: 4231

Die Einführung in die Methode der Finiten Elemente ist so konzipiert, dass sie nur anhand eindimensionaler Elemente erläutert wird. Dadurch bleibt die mathematische Beschreibung überschaubar, dennoch ist die Formulierung stets wissenschaftlich exakt. Das besondere Augenmerk liegt auf der Erläuterung der Methode und deren Verständnis. Leser lernen, die Annahmen und Ableitungen bei verschiedenen physikalischen Problemstellungen in der Strukturmechanik zu verstehen und Möglichkeiten und Grenzen der Methode der Finiten Elemente kritisch zu beurteilen.
Posted in Technology & Engineering

Introduction to the Finite Element Method in Electromagnetics

Author: Anastasis C. Polycarpou

Publisher: Morgan & Claypool Publishers

ISBN: 1598290460

Category: Technology & Engineering

Page: 115

View: 8815

This lecture is written primarily for the non-expert engineer or the undergraduate or graduate student who wants to learn, for the first time, the finite element method with applications to electromagnetics. It is also designed for research engineers who have knowledge of other numerical techniques and want to familiarize themselves with the finite element method.Finite element method is a numerical method used to solve boundary-value problems characterized by a partial differential equation and a set of boundary conditions. Author Anastasis Polycarpou provides the reader with all information necessary to successfully apply the finite element method to one- and two-dimensional boundary-value problems in electromagnetics.The book is accompanied by a number of codes written by the author in Matlab. These are the finite element codes that were used to generate most of the graphs presented in this book. Specifically, there are three Matlab codes for the one-dimensional case (Chapter 1) and two Matlab codes for the two-dimensional case (Chapter 2). The reader may execute these codes, modify certain parameters such as mesh size or object dimensions, and visualize the results. The codes are available on the Morgan & Claypool Web site at http://www.morganclaypool.com.
Posted in Technology & Engineering

Introduction to the Finite Element Method 4E

Author: J. N. Reddy

Publisher: McGraw Hill Professional

ISBN: 1259861910

Category: Technology & Engineering

Page: N.A

View: 9153

A fully updated introduction to the principles and applications of the finite element method This authoritative and thoroughly revised and self-contained classic mechanical engineering textbook offers a broad-based overview and applications of the finite element method. This revision updates and expands the already large number of problems and worked-out examples and brings the technical coverage in line with current practices. You will get details on non-traditional applications in bioengineering, fluid and thermal sciences, and structural mechanics. Written by a world-renowned mechanical engineering researcher and author, An Introduction to the Finite Element Method, Fourth Edition, teaches, step-by-step, how to determine numerical solutions to equilibrium as well as time-dependent problems from fluid and thermal sciences and structural mechanics and a host of applied sciences.. Beginning with the governing differential equations, the book presents a systematic approach to the derivation of weak-forms (integral formulations), interpolation theory, finite element equations, solution of problems from fluid and thermal sciences and structural mechanics, computer implementation. The author provides a solutions manual as well as computer programs that are available for download. •Features updated problems and fully worked-out solutions•Contains downloadable programs that can be applied and extended to real-world situations•Written by a highly-cited mechanical engineering researcher and well-respected author
Posted in Technology & Engineering

Finite-Elemente-Methoden

Author: Klaus-Jürgen Bathe

Publisher: DrMaster Publications

ISBN: 9783540668060

Category: Technology & Engineering

Page: 1253

View: 3995

Dieses Lehr- und Handbuch behandelt sowohl die elementaren Konzepte als auch die fortgeschrittenen und zukunftsweisenden linearen und nichtlinearen FE-Methoden in Statik, Dynamik, Festkörper- und Fluidmechanik. Es wird sowohl der physikalische als auch der mathematische Hintergrund der Prozeduren ausführlich und verständlich beschrieben. Das Werk enthält eine Vielzahl von ausgearbeiteten Beispielen, Rechnerübungen und Programmlisten. Als Übersetzung eines erfolgreichen amerikanischen Lehrbuchs hat es sich in zwei Auflagen auch bei den deutschsprachigen Ingenieuren etabliert. Die umfangreichen Änderungen gegenüber der Vorauflage innerhalb aller Kapitel - vor allem aber der fortgeschrittenen - spiegeln die rasche Entwicklung innerhalb des letzten Jahrzehnts auf diesem Gebiet wieder. TOC:Eine Einführung in den Gebrauch von Finite-Elemente-Verfahren.-Vektoren, Matrizen und Tensoren.-Einige Grundbegriffe ingenieurwissenschaftlicher Berechnungen.-Formulierung der Methode der finiten Elemente.-Formulierung und Berechnung von isoparametrischen Finite-Elemente-Matrizen.-Nichtlineare Finite-Elemente-Berechnungen in der Festkörper- und Strukturmechanik.-Finite-Elemente-Berechnungen von Wärmeübertragungs- und Feldproblemen.-Lösung von Gleichgewichtsbeziehungen in statischen Berechnungen.-Lösung von Bewegungsgleichungen in kinetischen Berechnungen.-Vorbemerkungen zur Lösung von Eigenproblemen.-Lösungsverfahren für Eigenprobleme.-Implementierung der Finite-Elemente-Methode.
Posted in Technology & Engineering

Introductory Finite Element Method

Author: Chandrakant S. Desai,Tribikram Kundu

Publisher: CRC Press

ISBN: 9780849302435

Category: Technology & Engineering

Page: 520

View: 9280

Although there are many books on the finite element method (FEM) on the market, very few present its basic formulation in a simple, unified manner. Furthermore, many of the available texts address either only structure-related problems or only fluid or heat-flow problems, and those that explore both do so at an advanced level. Introductory Finite Element Method examines both structural analysis and flow (heat and fluid) applications in a presentation specifically designed for upper-level undergraduate and beginning graduate students, both within and outside of the engineering disciplines. It includes a chapter on variational calculus, clearly presented to show how the functionals for structural analysis and flow problems are formulated. The authors provide both one- and two-dimensional finite element codes and a wide range of examples and exercises. The exercises include some simpler ones to solve by hand calculation-this allows readers to understand the theory and assimilate the details of the steps in formulating computer implementations of the method. Anyone interested in learning to solve boundary value problems numerically deserves a straightforward and practical introduction to the powerful FEM. Its clear, simplified presentation and attention to both flow and structural problems make Introductory Finite Element Method the ideal gateway to using the FEM in a variety of applications.
Posted in Technology & Engineering

Finite Element Analysis with Error Estimators

An Introduction to the FEM and Adaptive Error Analysis for Engineering Students

Author: J. E. Akin

Publisher: Elsevier

ISBN: 9780080472751

Category: Technology & Engineering

Page: 512

View: 9363

This key text is written for senior undergraduate and graduate engineering students. It delivers a complete introduction to finite element methods and to automatic adaptation (error estimation) that will enable students to understand and use FEA as a true engineering tool. It has been specifically developed to be accessible to non-mathematics students and provides the only complete text for FEA with error estimators for non-mathematicians. Error estimation is taught on nearly half of all FEM courses for engineers at senior undergraduate and postgraduate level; no other existing textbook for this market covers this topic. The only introductory FEA text with error estimation for students of engineering, scientific computing and applied mathematics Includes source code for creating and proving FEA error estimators
Posted in Technology & Engineering

An Introduction to Linear and Nonlinear Finite Element Analysis

A Computational Approach

Author: Prem Kythe,Dongming Wei

Publisher: Springer Science & Business Media

ISBN: 0817681604

Category: Mathematics

Page: 445

View: 1558

Modern finite element analysis has grown into a basic mathematical tool for almost every field of engineering and the applied sciences. This introductory textbook fills a gap in the literature, offering a concise, integrated presentation of methods, applications, software tools, and hands-on projects. Included are numerous exercises, problems, and Mathematica/Matlab-based programming projects. The emphasis is on interdisciplinary applications to serve a broad audience of advanced undergraduate/graduate students with different backgrounds in applied mathematics, engineering, physics/geophysics. The work may also serve as a self-study reference for researchers and practitioners seeking a quick introduction to the subject for their research.
Posted in Mathematics

Introduction to the finite element method

Author: Niels Saabye Ottosen,Hans Petersson

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 410

View: 2084

Providing a systematic approach and simple introduction ot the finite element method, this self-contained book will enable the reader to obtain a clear understanding of the concepts involved in this traditionally complicated methodology.
Posted in Mathematics

TEXTBOOK OF FINITE ELEMENT ANALYSIS

Author: P. SESHU

Publisher: PHI Learning Pvt. Ltd.

ISBN: 8120323157

Category: Mathematics

Page: 340

View: 5775

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.
Posted in Mathematics

The Scaled Boundary Finite Element Method

Author: John P. Wolf

Publisher: John Wiley & Sons

ISBN: 9780471486824

Category: Technology & Engineering

Page: 378

View: 4246

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.
Posted in Technology & Engineering

Computational Electromagnetics for RF and Microwave Engineering

Author: David B. Davidson

Publisher: Cambridge University Press

ISBN: 1139492810

Category: Technology & Engineering

Page: N.A

View: 5766

This hands-on introduction to computational electromagnetics (CEM) links theoretical coverage of the three key methods - the FDTD, MoM and FEM - to open source MATLAB codes (freely available online) in 1D, 2D and 3D, together with many practical hints and tips gleaned from the author's 25 years of experience in the field. Updated and extensively revised, this second edition includes a new chapter on 1D FEM analysis, and extended 3D treatments of the FDTD, MoM and FEM, with entirely new 3D MATLAB codes. Coverage of higher-order finite elements in 1D, 2D and 3D is also provided, with supporting code, in addition to a detailed 1D example of the FDTD from a FEM perspective. With running examples through the book and end-of-chapter problems to aid understanding, this is ideal for professional engineers and senior undergraduate/graduate students who need to master CEM and avoid common pitfalls in writing code and using existing software.
Posted in Technology & Engineering

First Course in the Finite Element Method

Author: Daryl L. Logan

Publisher: Cengage Learning

ISBN: 0534552986

Category: Mathematics

Page: 752

View: 7387

A First Course in the Finite Element Analysis provides a simple, basic approach to the finite element method that can be understood by both undergraduate and graduate students. It does not have the usual prerequisites (such as structural analysis) require
Posted in Mathematics

Finite Element Methods for Computational Fluid Dynamics

A Practical Guide

Author: Dmitri Kuzmin,Jari Hamalainen

Publisher: SIAM

ISBN: 1611973619

Category: Science

Page: 313

View: 1443

This informal introduction to computational fluid dynamics and practical guide to numerical simulation of transport phenomena covers the derivation of the governing equations, construction of finite element approximations, and qualitative properties of numerical solutions, among other topics. To make the book accessible to readers with diverse interests and backgrounds, the authors begin at a basic level and advance to numerical tools for increasingly difficult flow problems, emphasizing practical implementation rather than mathematical theory. Finite Element Methods for Computational Fluid Dynamics: A Practical Guide explains the basics of the finite element method (FEM) in the context of simple model problems, illustrated by numerical examples. It comprehensively reviews stabilization techniques for convection-dominated transport problems, introducing the reader to streamline diffusion methods, Petrov?Galerkin approximations, Taylor?Galerkin schemes, flux-corrected transport algorithms, and other nonlinear high-resolution schemes, and covers Petrov?Galerkin stabilization, classical projection schemes, Schur complement solvers, and the implementation of the k-epsilon turbulence model in its presentation of the FEM for incompressible flow problem. The book also describes the open-source finite element library ELMER, which is recommended as a software development kit for advanced applications in an online component.
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Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics

Author: Shen R. Wu,Lei Gu

Publisher: John Wiley & Sons

ISBN: 1118382072

Category: Mathematics

Page: 352

View: 8926

A systematic introduction to the theories and formulations ofthe explicit finite element method As numerical technology continues to grow and evolve withindustrial applications, understanding the explicit finite elementmethod has become increasingly important, particularly in the areasof crashworthiness, metal forming, and impact engineering.Introduction to the Explicit Finite Element Method forNonlinear Transient Dynamics is the first book to addressspecifically what is now accepted as the most successful numericaltool for nonlinear transient dynamics. The book aids readers inmastering the explicit finite element method and programming codewithout requiring extensive background knowledge of the generalfinite element. The authors present topics relating to the variationalprinciple, numerical procedure, mechanical formulation, andfundamental achievements of the convergence theory. In addition,key topics and techniques are provided in four clearly organizedsections: • Fundamentals explores a framework of the explicitfinite element method for nonlinear transient dynamics andhighlights achievements related to the convergence theory • Element Technology discusses four-node,three-node, eight-node, and two-node element theories • Material Models outlines models of plasticity andother nonlinear materials as well as the mechanics model of ductiledamage • Contact and Constraint Conditions covers subjectsrelated to three-dimensional surface contact, with examples solvedanalytically, as well as discussions on kinematic constraintconditions Throughout the book, vivid figures illustrate the ideas and keyfeatures of the explicit finite element method. Examples clearlypresent results, featuring both theoretical assessments andindustrial applications. Introduction to the Explicit Finite Element Method forNonlinear Transient Dynamics is an ideal book for bothengineers who require more theoretical discussions and fortheoreticians searching for interesting and challenging researchtopics. The book also serves as an excellent resource for courseson applied mathematics, applied mechanics, and numerical methods atthe graduate level.
Posted in Mathematics

Resonant MEMS

Fundamentals, Implementation, and Application

Author: Oliver Brand,Isabelle Dufour,Stephen Heinrich,Fabien Josse

Publisher: John Wiley & Sons

ISBN: 3527676368

Category: Technology & Engineering

Page: 512

View: 8045

Part of the AMN book series, this book covers the principles, modeling and implementation as well as applications of resonant MEMS from a unified viewpoint. It starts out with the fundamental equations and phenomena that govern the behavior of resonant MEMS and then gives a detailed overview of their implementation in capacitive, piezoelectric, thermal and organic devices, complemented by chapters addressing the packaging of the devices and their stability. The last part of the book is devoted to the cutting-edge applications of resonant MEMS such as inertial, chemical and biosensors, fluid properties sensors, timing devices and energy harvesting systems.
Posted in Technology & Engineering

A Primer for Finite Elements in Elastic Structures

Author: W. F. Carroll,William F. Carroll

Publisher: John Wiley & Sons

ISBN: 9780471283454

Category: Science

Page: 494

View: 4682

A thorough guide to the fundamentals--and how to use them--offinite element analysis for elastic structures For elastic structures, the finite element method is an invaluabletool which is used most effectively only when one understandscompletely each of its facets. A Primer for Finite Elements inElastic Structures disassembles the entire finite element methodfor civil engineering students and professionals, detailing itssupportive theory and its mathematical and structuralunderpinnings, in the context of elastic structures and theprinciple of virtual work. The book opens with a discussion of matrix algebra and algebraicequation systems to foster the basic skills required tosuccessfully understand and use the finite element method. Keymathematical concepts outlined here are joined to pertinentconcepts from mechanics and structural theory, with the methodconstructed in terms of one-dimensional truss and framework finiteelements. The use of these one-dimensional elements in the earlychapters promotes better understanding of the fundamentals.Subsequent chapters describe many two-dimensional structural finiteelements in depth, including the geometry, mechanics,transformations, and mapping needed for them. Most chapters end with questions and problems which review the textmaterial. Answers for many of these are at the end of the book. Anappendix describes how to use MATLAB(r), a popularmatrix-manipulation software platform necessary to perform the manymatrix operations required for the finite element method, such asmatrix addition, multiplication, inversion, partitioning,rearrangement, and assembly. As an added extra, the m-filesdiscussed can be downloaded from the Wiley FTP server.
Posted in Science

An Introduction to Boundary Element Methods

Author: Prem K. Kythe

Publisher: CRC Press

ISBN: 9780849373770

Category: Mathematics

Page: 384

View: 8643

The finite element and the boundary element methods are the two most important developments in numerical mathematics to occur in this century. Many engineering and mathematics graduate curricula now include a course in boundary element methods. Such a course must cover numerical methods, basic methodology to real problems, and interactive computer usage. Both theory and applications, necessary for applied courses, are available in this new textbook. An Introduction to Boundary Element Methods is logically organized and easy to read. The topics are carefully selected and meticulously presented. Applications are described for use in identifying potential problems and for heat transfer, diffusion equations, linear elasticity, water waves, ocean acoustics, acoustic scattering, aerodynamics, porous media, and simple laminar flows. More than 20 computer subroutines help develop and explain the computational aspect of the subject. Hundreds of figures, exercises, and solved examples supplement text and help clarify important information. The computer programs have been tested on some benchmark problems. Even in single precision the results are more accurate and better than those obtained from available Fortran programs.
Posted in Mathematics