Finite Elements

Theory, Fast Solvers, and Applications in Solid Mechanics

Author: Dietrich Braess

Publisher: Cambridge University Press

ISBN: 9780521011952

Category: Mathematics

Page: 352

View: 5817

This is a thoroughly revised version of the successful first edition. In addition to up-dating the existing text, the author has added new material that will prove useful for research or application of the finite element method. The most important application of finite elements is the numerical solution of elliptic partial differential equations. The author gives a thorough coverage of this subject and includes aspects such as saddle point problems which require a more in-depth mathematical treatment. This is a book for graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

Finite Elements

Theory, Fast Solvers, and Applications in Solid Mechanics

Author: Dietrich Braess

Publisher: Cambridge University Press

ISBN: 113946146X

Category: Mathematics

Page: N.A

View: 3365

This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

Finite Elemente

Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie

Author: Dietrich Braess

Publisher: Springer-Verlag

ISBN: 3662072343

Category: Mathematics

Page: 305

View: 5596


Verfahren, Werkzeuge und Maschinen

Author: Klaus Siegert

Publisher: Springer-Verlag

ISBN: 3540684182

Category: Technology & Engineering

Page: 326

View: 918

Das Lehr- und Fachbuch führt in die Grundlagen der Blechumformung ein und erläutert, wie entsprechende Verfahren in die industrielle Fertigung integriert werden. Ausgewählte Verfahren wie z. B. das Falzen und Feinschneiden werden vergleichend dargestellt. Als weitere Themen behandeln die Experten die „Vorherbestimmbarkeit finaler Produkteigenschaften“, die „Steigerung der Produktivität“ und die „Reduzierung der Fertigungskosten“. Dabei werden Prozesse diskutiert, die bei sich ändernden Produkteingangsparametern für eine konstante Produktgüte sorgen.

Computational Engineering

Theorie und Praxis der Transportmodelle

Author: Jürgen Geiser

Publisher: Springer-Verlag

ISBN: 3658187085

Category: Computers

Page: 291

View: 5000

Das Buch bietet ein ausgewogenes Verhältnis zwischen Theorie und praktischen Anwendungen des berechnenden Ingenieurswesens. Es illustriert sowohl die mathematischen Modelle im Computational Engineering, wie auch die zugehörigen Simulationsmethoden für die verschiedenen Ingenieursanwendungen und benennt geeignete Softwarepakete. Die umfangreichen Beispiele aus der berechnenden Ingenieurswissenschaft, welche Wärme- und Massentransport, Plasmasimulation und hydrodynamische Transportprobleme einschließen, geben dem Leser einen Überblick zu den aktuellen Themen und deren praktische Umsetzung in spätere Simulationsprogramme. Übungsaufgaben und prüfungsrelevante Fragen schließen die einzelnen Kapitel ab.

Structural Analysis with Finite Elements

Author: Friedel Hartmann,Casimir Katz

Publisher: Springer Science & Business Media

ISBN: 3540497021

Category: Technology & Engineering

Page: 598

View: 7235

This book provides a solid introduction to the foundation and the application of the finite element method in structural analysis. It offers new theoretical insight and practical advice. This second edition contains additional sections on sensitivity analysis, on retrofitting structures, on the Generalized FEM (X-FEM) and on model adaptivity. An additional chapter treats the boundary element method, and related software is available at

Robust Algebraic Multilevel Methods and Algorithms

Author: Johannes Kraus,Svetozar Margenov

Publisher: Walter de Gruyter

ISBN: 3110214830

Category: Mathematics

Page: 256

View: 2973

This book deals with algorithms for the solution of linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained after discretization of partial differential equations using finite element methods. Provides a systematic presentation of the recent advances in robust algebraic multilevel methods. Can be used for advanced courses on the topic.

Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

Author: Silvestru Sever Dragomir

Publisher: Springer Science & Business Media

ISBN: 331901448X

Category: Mathematics

Page: 120

View: 827

Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, and quantum computation, to name several. Chapter 1 presents fundamental facts about the numerical range and the numerical radius of bounded linear operators in Hilbert spaces. Chapter 2 illustrates recent results obtained concerning numerical radius and norm inequalities for one operator on a complex Hilbert space, as well as some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse Schwarz inequalities and Grüss type inequalities obtained by the author. Chapter 3 presents recent results regarding the norms and the numerical radii of two bounded linear operators. The techniques shown in this chapter are elementary but elegant and may be accessible to undergraduate students with a working knowledge of operator theory. A number of vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are also employed in this chapter. All the results presented are completely proved and the original references are mentioned.

Advanced Finite Element Methods and Applications

Author: Thomas Apel,Olaf Steinbach

Publisher: Springer Science & Business Media

ISBN: 3642303161

Category: Technology & Engineering

Page: 376

View: 399

This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.

Scientific Computing with MATLAB and Octave

Author: Alfio Quarteroni,Fausto Saleri,Paola Gervasio

Publisher: Springer Science & Business Media

ISBN: 3642124305

Category: Mathematics

Page: 366

View: 3239

Preface to the First Edition This textbook is an introduction to Scienti?c Computing. We will illustrate several numerical methods for the computer solution of c- tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of di?erential equations. With this aim, in Chapter 1 we will illustrate the rules of the game thatcomputersadoptwhenstoringandoperatingwith realandcomplex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will 1 adopt the programming environment MATLAB as a faithful c- panion. We will gradually discover its principal commands, statements and constructs. We will show how to execute all the algorithms that we introduce throughout the book. This will enable us to furnish an - mediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raisedthrough exercises and examples, often stemming from s- ci?c applications.

Nichtlineare Finite-Element-Methoden

Author: Peter Wriggers

Publisher: Springer-Verlag

ISBN: 3642568653

Category: Technology & Engineering

Page: 496

View: 8372

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.

Partielle Differentialgleichungen und numerische Methoden

Author: Stig Larsson,Vidar Thomee

Publisher: Springer-Verlag

ISBN: 3540274227

Category: Mathematics

Page: 272

View: 432

Das Buch ist für Studenten der angewandten Mathematik und der Ingenieurwissenschaften auf Vordiplomniveau geeignet. Der Schwerpunkt liegt auf der Verbindung der Theorie linearer partieller Differentialgleichungen mit der Theorie finiter Differenzenverfahren und der Theorie der Methoden finiter Elemente. Für jede Klasse partieller Differentialgleichungen, d.h. elliptische, parabolische und hyperbolische, enthält der Text jeweils ein Kapitel zur mathematischen Theorie der Differentialgleichung gefolgt von einem Kapitel zu finiten Differenzenverfahren sowie einem zu Methoden der finiten Elemente. Den Kapiteln zu elliptischen Gleichungen geht ein Kapitel zum Zweipunkt-Randwertproblem für gewöhnliche Differentialgleichungen voran. Ebenso ist den Kapiteln zu zeitabhängigen Problemen ein Kapitel zum Anfangswertproblem für gewöhnliche Differentialgleichungen vorangestellt. Zudem gibt es ein Kapitel zum elliptischen Eigenwertproblem und zur Entwicklung nach Eigenfunktionen. Die Darstellung setzt keine tiefer gehenden Kenntnisse in Analysis und Funktionalanalysis voraus. Das erforderliche Grundwissen über lineare Funktionalanalysis und Sobolev-Räume wird im Anhang im Überblick besprochen.

Numerische Behandlung partieller Differentialgleichungen

Author: Christian Großmann,Hans-Görg Roos

Publisher: Springer-Verlag

ISBN: 9783519220893

Category: Mathematics

Page: 572

View: 2845

Mathematiker, Naturwissenschaftler und Ingenieure erhalten mit diesem Lehrbuch eine Einführung in die numerische Behandlung partieller Differentialgleichungen. Diskutiert werden die grundlegenden Verfahren - Finite Differenzen, Finite Volumen und Finite Elemente - für die wesentlichen Typen partieller Differentialgleichungen: elliptische, parabolische und hyperbolische Gleichungen. Einbezogen werden auch moderne Methoden zur Lösung der diskreten Probleme. Hinweise auf aktuelle Software sowie zahlreiche Beispiele und Übungsaufgaben runden diese Einführung ab.


Author: N.A

Publisher: N.A


Category: Mathematics

Page: N.A

View: 7159