Nonlinear finite elements for continua and structures

Author: Ted Belytschko,Wing Kam Liu,Brian Moran

Publisher: John Wiley & Sons Inc

ISBN: N.A

Category: Mathematics

Page: 650

View: 7986

Nonlinear Finite Elements for Continua and Structures Ted Belytschko, Wing Kam Liu, Brian Moran Northwestern University, Evanston, Illinois This book provides a comprehensive description of the major methodologies of nonlinear finite element analysis for solid mechanics, as applied to continua and structures. Treatment of the subject is integrated in such a way that the reader can gain an understanding of the fundamental methods, a feeling for the comparative usefulness of different approaches and an appreciation of the difficulties inherent in nonlinear analysis. In-depth coverage of the following is given: * Lagrangian and arbitrary Lagrangian Eulerian treatments of continua * many of the material laws used in today's software and research * solution methods, including explicit and implicit time integration methods and methods for equilibrium problems * basic concepts such as stability and smoothness, and techniques such as linearization and regularization * methods for shells and structures * contact-impact problems * element technology, including multi-field elements Ideal for self-study, no other book provides such a comprehensive description of nonlinear finite element analysis for solid mechanics. This is an invaluable reference not only for final year undergraduates, postgraduates, academics and engineers working on sophisticated finite element software and in the field of solid mechanics, but also for all users of nonlinear finite element programs.
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Nonlinear Finite Elements for Continua and Structures

Author: Ted Belytschko,Wing Kam Liu,Brian Moran,Khalil Elkhodary

Publisher: John Wiley & Sons

ISBN: 1118700082

Category: Science

Page: 832

View: 6635

This updated and expanded edition of the bestselling textbookprovides a comprehensive introduction to the methods and theory ofnonlinear finite element analysis. New material provides a conciseintroduction to some of the cutting-edge methods that have evolvedin 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, SecondEdition focuses on the formulation and solution of discreteequations for various classes of problems that are of principalinterest in applications to solid and structural mechanics. Topicscovered include the discretization by finite elements of continuain one dimension and in multi-dimensions; the formulation ofconstitutive equations for nonlinear materials and largedeformations; procedures for the solution of the discreteequations, including considerations of both numerical andmultiscale physical instabilities; and the treatment of structuraland contact-impact problems. Key features: Presents a detailed and rigorous treatment of nonlinear solidmechanics and how it can be implemented in finite elementanalysis Covers many of the material laws used in today's software andresearch Introduces advanced topics in nonlinear finite elementmodelling of continua Introduction of multiresolution continuum theory and XFEM Accompanied by a website hosting a solution manual andMATLAB® and FORTRAN code Nonlinear Finite Elements for Continua and Structures, SecondEdition is a must have textbook for graduate students inmechanical engineering, civil engineering, applied mathematics,engineering mechanics, and materials science, and is also anexcellent source of information for researchers and practitionersin industry.
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Nichtlineare Finite-Element-Methoden

Author: Peter Wriggers

Publisher: Springer-Verlag

ISBN: 3642568653

Category: Technology & Engineering

Page: 496

View: 9000

Die Anwendung der Finite-Element-Methode auf nichtlineare technische Probleme hat in den letzten Jahren - auch wegen der stark angestiegenen Rechnerleistung - erheblich zugenommen. Bei nichtlinearen numerischen Simulationen sind verschiedene Aspekte zu berücksichtigen, die das Wissen und Verstehen der theoretischen Grundlagen, der zugehörigen Elementformulierungen sowie der Algorithmen zur Lösung der nichtlinearen Gleichungen voraussetzen. Hierzu soll dieses Buch beitragen, wobei die Bandbreite nichtlinearer Finite-Element-Analysen im Bereich der Festkörpermechanik abgedeckt wird. Das Buch wendet sich an Studierende des Ingenieurwesens im Hauptstudium, an Doktoranden aber auch an praktisch tätige Ingenieure, die Hintergrundwissen im Bereich der Finite-Element-Methode erlangen möchten.
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Tragwerke

Author: Anton Pech

Publisher: Birkhäuser

ISBN: 3035615160

Category: Architecture

Page: 168

View: 6079

Der überarbeitete Einführungsband zeigt und erläutert das Zusammenwirken aller Konstruktionsteile im Bauwerk zur Abtragung horizontaler und vertikaler Einwirkungen in den Baugrund. Typische Tragwerkselemente, insbesondere die im Hochbau eingesetzten Flächentragwerke, die für die Modellierung komplexer Strukturen verwendete Fachwerksanalogie sowie die Gebäudesicherheitsklassen werden eingehend dargestellt. Enthalten ist auch ein Überblick zur aktuellen Bauweise im Massiv- und Skelettbau. Die Risikoanalyse für Bestandsgebäude sowie Konstruktionsbeispiele wurden neu aufgenommen, die Normen auf europäische Regelungen umgestellt.
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Finite-Elemente-Methoden

Author: Klaus-Jürgen Bathe

Publisher: Springer Verlag

ISBN: 9783540668060

Category: Technology & Engineering

Page: 1253

View: 2803

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.
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Eindimensionale Finite Elemente

Ein Einstieg in die Methode

Author: Markus Merkel,Andreas Öchsner

Publisher: Springer-Verlag

ISBN: 3642049923

Category: Technology & Engineering

Page: 422

View: 3144

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.
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Nichtlineare Finite-Elemente-Berechnungen

Kontakt, Kinematik, Material

Author: Wilhelm Rust

Publisher: Springer-Verlag

ISBN: 3658133783

Category: Technology & Engineering

Page: 341

View: 648

Dieses Lehrbuch beschreibt die numerische Berechnung von Nichtlinearitäten in der Strukturmechanik, d. h. große Drehungen, große Dehnungen (geometrische Nichtlinearitäten), nichtlineares Materialverhalten, besonders Plastizität und zeitabhängiges Verhalten, und Kontakt. Darauf aufbauend werden Stabilitätsprobleme und Traglastberechnungen behandelt. Dabei wird am Beispiel einfacher Systeme die Problematik erläutert, formelmäßig erfasst, in den Kontext der Finiten Elemente eingebunden und bis zum Dreidimensionalen verallgemeinert. Die einzelnen Schritte werden detailliert bis hin zu Zahlenbeispielen. Die vorliegende Auflage wurde vollständig überarbeitet und im Bereich der mathematischen Methoden, der kontinuumsmechanischen Darstellung, im Vergleich der verschiedenen Konzepte für große Verformungen, bei Stabilität und dem Bogenlängenverfahren erweitert. Das Kontaktkapitel wurde um Mortar-Kontakt und um Beispielrechnungen, die auch die Lösung der nichtlinearen Gleichungen erläutern, ergänzt.
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FEM-Formelsammlung Statik und Dynamik

Hintergrundinformationen, Tipps und Tricks

Author: Lutz Nasdala

Publisher: Springer-Verlag

ISBN: 365806630X

Category: Technology & Engineering

Page: 274

View: 1480

Die vorliegende Formelsammlung richtet sich an die Anwender kommerzieller Finite Elemente Programme, die bereits die im Rahmen einer typischen FEM-Einführungsvorlesung erworbenen Grundkenntnisse mitbringen und sich einen Überblick über die Möglichkeiten dieser sehr leistungsstarken Programmpakete verschaffen m öchten. Denn nur wer die Unterschiede zwischen den verschiedenen Analysearten, Elementen oder Kontaktalgorithmen kennt, kann diese auch effizient einsetzen. Der Autor zeigt anhand der wichtigsten Formeln, erläuternder Skizzen und anschaulicher Beispiele das gesamte Anwendungsspektrum der FEM für statische und dynamische Problemstellungen. Damit schließt das Buch die Lücke zwischen einer FEM-Grundvorlesung und den Möglichkeiten eines kommerziellen FE-Programms.
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Nonlinear Finite Element Methods

Author: Peter Wriggers

Publisher: Springer Science & Business Media

ISBN: 3540710000

Category: Mathematics

Page: 560

View: 4400

Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations. This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.
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A First Course in Finite Elements

Author: Jacob Fish,Ted Belytschko

Publisher: Wiley

ISBN: 9780470035801

Category: Mathematics

Page: 336

View: 4839

Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations. Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements: Adopts a generic approach to the subject, and is not application specific In conjunction with a web-based chapter, it integrates code development, theory, and application in one book Provides an accompanying Web site that includes ABAQUS Student Edition, Matlab data and programs, and instructor resources Contains a comprehensive set of homework problems at the end of each chapter Produces a practical, meaningful course for both lecturers, planning a finite element module, and for students using the text in private study. Accompanied by a book companion website housing supplementary material that can be found at http://www.wileyeurope.com/college/Fish A First Course in Finite Elements is the ideal practical introductory course for junior and senior undergraduate students from a variety of science and engineering disciplines. The accompanying advanced topics at the end of each chapter also make it suitable for courses at graduate level, as well as for practitioners who need to attain or refresh their knowledge of finite elements through private study.
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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: 870

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.
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Eindimensionale Finite Elemente

Ein Einstieg in die Methode

Author: Markus Merkel,Andreas Öchsner

Publisher: Springer-Verlag

ISBN: 3642544827

Category: Science

Page: 428

View: 3851

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.
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Programming the Finite Element Method

Author: I. M. Smith,D. V. Griffiths,L. Margetts

Publisher: John Wiley & Sons

ISBN: 1118535928

Category: Technology & Engineering

Page: 688

View: 2102

Many students, engineers, scientists and researchers havebenefited from the practical, programming-oriented style of theprevious editions of Programming the Finite Element Method,learning how to develop computer programs to solve specificengineering problems using the finite element method. This new fifth edition offers timely revisions that includeprograms and subroutine libraries fully updated to Fortran 2003,which are freely available online, and provides updated material onadvances in parallel computing, thermal stress analysis, plasticityreturn algorithms, convection boundary conditions, and interfacesto third party tools such as ParaView, METIS and ARPACK. Asin the previous editions, a wide variety of problem solvingcapabilities are presented including structural analysis,elasticity and plasticity, construction processes in geomechanics,uncoupled and coupled steady and transient fluid flow and linearand nonlinear solid dynamics. Key features: • Updated to take into account advances in parallelcomputing as well as new material on thermal stressanalysis • Programs use an updated version of Fortran 2003 • Includes exercises for students • Accompanied by website hosting software Programming the FiniteElement Method, Fifth Edition is an ideal textbook forundergraduate and postgraduate students in civil and mechanicalengineering, applied mathematics and numerical analysis, and isalso a comprehensive reference for researchers and practitionersemstyle="mso-bidi-font-style: normal;"./em Further information and source codes described in this text canbe accessed at the following web sites: • ahref="http://www.inside.mines.edu/~vgriffit"www.inside.mines.edu/~vgriffit/a/PFEM5 for the serial programs from Chapters 4-11 • www.parafem.org.ukfor the parallel programs from Chapter 12
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Computational Methods for Reinforced Concrete Structures

Author: Ulrich Häußler-Combe

Publisher: John Wiley & Sons

ISBN: 3433603634

Category: Technology & Engineering

Page: 354

View: 6789

The book covers the application of numerical methods to reinforced concrete structures. To analyze reinforced concrete structures linear elastic theories are inadequate because of cracking, bond and the nonlinear and time dependent behavior of both concrete and reinforcement. These effects have to be considered for a realistic assessment of the behavior of reinforced concrete structures with respect to ultimate limit states and serviceability limit states. The book gives a compact review of finite element and other numerical methods. The key to these methods is through a proper description of material behavior. Thus, the book summarizes the essential material properties of concrete and reinforcement and their interaction through bond. These basics are applied to different structural types such as bars, beams, strut and tie models, plates, slabs and shells. This includes prestressing of structures, cracking, nonlinear stressstrain relations, creeping, shrinkage and temperature changes. Appropriate methods are developed for each structural type. Large displacement and dynamic problems are treated as well as short-term quasi-static problems and long-term transient problems like creep and shrinkage. Most problems are illustrated by examples which are solved by the program package ConFem, based on the freely available Python programming language. The ConFem source code together with the problem data is available under open source rules at concrete-fem.com. The author aims to demonstrate the potential and the limitations of numerical methods for simulation of reinforced concrete structures, addressing students, teachers, researchers and designing and checking engineers.
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Extended Finite Element Method

Tsinghua University Press Computational Mechanics Series

Author: Zhuo Zhuang,Zhanli Liu,Binbin Cheng,Jianhui Liao

Publisher: Academic Press

ISBN: 0124078567

Category: Technology & Engineering

Page: 286

View: 5813

Extended Finite Element Method provides an introduction to the extended finite element method (XFEM), a novel computational method which has been proposed to solve complex crack propagation problems. The book helps readers understand the method and make effective use of the XFEM code and software plugins now available to model and simulate these complex problems. The book explores the governing equation behind XFEM, including level set method and enrichment shape function. The authors outline a new XFEM algorithm based on the continuum-based shell and consider numerous practical problems, including planar discontinuities, arbitrary crack propagation in shells and dynamic response in 3D composite materials. Authored by an expert team from one of China's leading academic and research institutions Offers complete coverage of XFEM, from fundamentals to applications, with numerous examples Provides the understanding needed to effectively use the latest XFEM code and software tools to model and simulate dynamic crack problems
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Finite Elemente

Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie

Author: Dietrich Braess

Publisher: Springer-Verlag

ISBN: 3662072343

Category: Mathematics

Page: 305

View: 4289

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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: 9498

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.
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Shock Wave Science and Technology Reference Library, Vol. 2

Solids I

Author: Y. Horie

Publisher: Springer Science & Business Media

ISBN: 3540684085

Category: Science

Page: 369

View: 1197

This book is the first of several volumes on solids in the Shock Wave Science and Technology Reference Library. This is a unique collection, and the library as a whole sets out to comprehensively and authoritatively cover and review at research level the subject matter with all its ramifications. All the chapters are self-contained and can be read independently of each other, though they are of course thematically interrelated.
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