One-Dimensional Finite Elements

An Introduction to the FE Method
Author: Andreas Oechsner,Markus Merkel
Publisher: Springer Science & Business Media
ISBN: 3642317960
Category: Science
Page: 400
View: 1538

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This textbook presents finite element methods using exclusively one-dimensional elements. The aim is to present 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 easily understands the assumptions and limitations of mechanical modeling as well as the underlying physics without struggling with complex mathematics. But 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 like 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.

Eindimensionale Finite Elemente

Ein Einstieg in die Methode
Author: Markus Merkel,Andreas Öchsner
Publisher: Springer-Verlag
ISBN: 3642049923
Category: Technology & Engineering
Page: 422
View: 2790

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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.

One-Dimensional Finite Elements

An Introduction to the FE Method
Author: Andreas Öchsner,Markus Merkel
Publisher: Springer
ISBN: 331975145X
Category: Science
Page: 418
View: 3166

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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.

Introduction to the Finite Element Method in Electromagnetics


Author: Anastasis C. Polycarpou
Publisher: Morgan & Claypool Publishers
ISBN: 1598290460
Category: Technology & Engineering
Page: 115
View: 7588

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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.

Finite-Elemente-Methoden


Author: Klaus-Jürgen Bathe
Publisher: Springer Verlag
ISBN: 9783540668060
Category: Technology & Engineering
Page: 1253
View: 6396

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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.

An Introduction to the Finite Element Method


Author: Junuthula Narasimha Reddy
Publisher: N.A
ISBN: 9780071244732
Category: Finite element method
Page: 766
View: 4028

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The book retains its strong conceptual approach, clearly examining the mathematical underpinnings of FEM, and providing a general approach of engineering application areas.Known for its detailed, carefully selected example problems and extensive selection of homework problems, the author has comprehensively covered a wide range of engineering areas making the book approriate for all engineering majors, and underscores the wide range of use FEM has in the professional world

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: 8264

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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.

An Introduction to the Finite Element Method


Author: Junuthula Narasimha Reddy
Publisher: McGraw-Hill Science, Engineering & Mathematics
ISBN: 9780070513556
Category: Mathematics
Page: 684
View: 3665

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For final year graduate and postgraduate courses in the finite element method, this book introduces the method as applied to linear, non-linear and one- and two-dimensional problems of engineering and applied sciences. It includes a step-by-step systematic approach to the formulation and analysis of differential and integral equations in variational forms. The book adopts a differential equation approach, avoiding the need for knowledge of the variational principles of solid mechanics in the development of the finite element models. The need for the weighted-integral formulation of differential equations is explained clearly, providing the student with logical reasons for the recasting of differential equations into variational form.

Computational Electromagnetics for RF and Microwave Engineering


Author: David B. Davidson
Publisher: Cambridge University Press
ISBN: 1139492810
Category: Technology & Engineering
Page: N.A
View: 3310

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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.

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: 8312

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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

Finite Element Methods for Computational Fluid Dynamics

A Practical Guide
Author: Dmitri Kuzmin,Jari Hamalainen
Publisher: SIAM
ISBN: 1611973619
Category: Science
Page: 313
View: 8156

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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.

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: 9048

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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.

Introductory Finite Element Method


Author: Chandrakant S. Desai,Tribikram Kundu
Publisher: CRC Press
ISBN: 9780849302435
Category: Technology & Engineering
Page: 520
View: 2295

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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.

An Introduction to Nonlinear Finite Element Analysis

With Applications to Heat Transfer, Fluid Mechanics, and Solid Mechanics
Author: Junuthula Narasimha Reddy,J. N. Reddy
Publisher: Oxford University Press, USA
ISBN: 0199641757
Category: Science
Page: 687
View: 3803

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The second edition of An Introduction to Nonlinear Finite Element Analysis offers an easy-to-understand treatment of nonlinear finite element analysis, which includes element development from mathematical models and numerical evaluation of the underlying physics. Additional explanations, examples, and problems have been added to all chapters. The book may be used as a textbook for an advanced course (after a first course) on the finite element method orthe first course on nonlinear finite element analysis. A solutions manual is available on request from the publisher to instructors who adopt the book as a textbook for a course.

Introduction to the finite element method


Author: Niels Saabye Ottosen,Hans Petersson
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: 410
View: 6325

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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.

Matrix Analysis Framed Structures


Author: William Weaver,James M. Gere
Publisher: Springer Science & Business Media
ISBN: 1468474871
Category: Juvenile Nonfiction
Page: 547
View: 6532

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Matrix analysis of structures is a vital subject to every structural analyst, whether working in aero-astro, civil, or mechanical engineering. It provides a comprehensive approach to the analysis of a wide variety of structural types, and therefore offers a major advantage over traditional metho~ which often differ for each type of structure. The matrix approach also provides an efficient means of describing various steps in the analysis and is easily programmed for digital computers. Use of matrices is natural when performing calculations with a digital computer, because matrices permit large groups of numbers to be manipulated in a simple and effective manner. This book, now in its third edition, was written for both college students and engineers in industry. It serves as a textbook for courses at either the senior or first-year graduate level, and it also provides a permanent reference for practicing engineers. The book explains both the theory and the practical implementation of matrix methods of structural analysis. Emphasis is placed on developing a physical understanding of the theory and the ability to use computer programs for performing structural calculations.

Introduction to Finite Element Vibration Analysis


Author: Maurice Petyt
Publisher: Cambridge University Press
ISBN: 1139490060
Category: Technology & Engineering
Page: N.A
View: 853

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This is an introduction to the mathematical basis of finite element analysis as applied to vibrating systems. Finite element analysis is a technique that is very important in modeling the response of structures to dynamic loads. Although this book assumes no previous knowledge of finite element methods, those who do have knowledge will still find the book to be useful. It can be utilised by aeronautical, civil, mechanical, and structural engineers as well as naval architects. This second edition includes information on the many developments that have taken place over the last twenty years. Existing chapters have been expanded where necessary, and three new chapters have been included that discuss the vibration of shells and multi-layered elements and provide an introduction to the hierarchical finite element method.

Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods


Author: Victor N. Kaliakin
Publisher: CRC Press
ISBN: 9780824706791
Category: Technology & Engineering
Page: 664
View: 6076

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Functions as a self-study guide for engineers and as a textbook for nonengineering students and engineering students, emphasizing generic forms of differential equations, applying approximate solution techniques to examples, and progressing to specific physical problems in modular, self-contained chapters that integrate into the text or can stand alone! This reference/text focuses on classical approximate solution techniques such as the finite difference method, the method of weighted residuals, and variation methods, culminating in an introduction to the finite element method (FEM). Discusses the general notion of approximate solutions and associated errors! With 1500 equations and more than 750 references, drawings, and tables, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods: Describes the approximate solution of ordinary and partial differential equations using the finite difference method Covers the method of weighted residuals, including specific weighting and trial functions Considers variational methods Highlights all aspects associated with the formulation of finite element equations Outlines meshing of the solution domain, nodal specifications, solution of global equations, solution refinement, and assessment of results Containing appendices that present concise overviews of topics and serve as rudimentary tutorials for professionals and students without a background in computational mechanics, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods is a blue-chip reference for civil, mechanical, structural, aerospace, and industrial engineers, and a practical text for upper-level undergraduate and graduate students studying approximate solution techniques and the FEM.