Finite Element Methods With B Splines

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Finite Element Methods With B Splines

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Author : Klaus Hollig
language : en
Publisher: SIAM
Release Date : 2003-01-01

Finite Element Methods With B Splines written by Klaus Hollig and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.

Finite Element Methods with B-Splines describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for B-splines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples.

Finite Element Methods With B Splines

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Author : Klaus Hollig
language : en
Publisher: SIAM
Release Date : 2012-12-13

Finite Element Methods With B Splines written by Klaus Hollig and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-13 with Mathematics categories.

An exploration of the new weighted approximation techniques which result from the combination of the finite element method and B-splines.

Approximation And Modeling With B Splines

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Author : Klaus Hollig
language : en
Publisher: SIAM
Release Date : 2015-07-01

Approximation And Modeling With B Splines written by Klaus Hollig and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-01 with Mathematics categories.

B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.

Implementation Of B Splines In A Conventional Finite Element Framework

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Author : Brian C. Owens
language : en
Publisher:
Release Date : 2010

Implementation Of B Splines In A Conventional Finite Element Framework written by Brian C. Owens and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.

The use of B-spline interpolation functions in the finite element method (FEM) is not a new subject. B-splines have been utilized in finite elements for many reasons. One reason is the higher continuity of derivatives and smoothness of B-splines. Another reason is the possibility of reducing the required number of degrees of freedom compared to a conventional finite element analysis. Furthermore, if B-splines are utilized to represent the geometry of a finite element model, interfacing a finite element analysis program with existing computer aided design programs (which make extensive use of B-splines) is possible. While B-splines have been used in finite element analysis due to the aforementioned goals, it is difficult to find resources that describe the process of implementing B-splines into an existing finite element framework. Therefore, it is necessary to document this methodology. This implementation should conform to the structure of conventional finite elements and only require exceptions in methodology where absolutely necessary. One goal is to implement B-spline interpolation functions in a finite element framework such that it appears very similar to conventional finite elements and is easily understandable by those with a finite element background. The use of B-spline functions in finite element analysis has been studied for advantages and disadvantages. Two-dimensional B-spline and standard FEM have been compared. This comparison has addressed the accuracy as well as the computational efficiency of B-spline FEM. Results show that for a given number of degrees of freedom, B-spline FEM can produce solutions with lower error than standard FEM. Furthermore, for a given solution time and total analysis time B-spline FEM will typically produce solutions with lower error than standard FEM. However, due to a more coupled system of equations and larger elemental stiffness matrix, B-spline FEM will take longer per degree of freedom for solution and assembly times than standard FEM. Three-dimensional B-spline FEM has also been validated by the comparison of a three-dimensional model with plane-strain boundary conditions to an equivalent two-dimensional model using plane strain conditions.

Isogeometric Analysis

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Author : J. Austin Cottrell
language : en
Publisher: John Wiley & Sons
Release Date : 2009-08-11

Isogeometric Analysis written by J. Austin Cottrell 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 2009-08-11 with Technology & Engineering categories.

“The authors are the originators of isogeometric analysis, are excellent scientists and good educators. It is very original. There is no other book on this topic.” —René de Borst, Eindhoven University of Technology Written by leading experts in the field and featuring fully integrated colour throughout, Isogeometric Analysis provides a groundbreaking solution for the integration of CAD and FEA technologies. Tom Hughes and his researchers, Austin Cottrell and Yuri Bazilevs, present their pioneering isogeometric approach, which aims to integrate the two techniques of CAD and FEA using precise NURBS geometry in the FEA application. This technology offers the potential to revolutionise automobile, ship and airplane design and analysis by allowing models to be designed, tested and adjusted in one integrative stage. Providing a systematic approach to the topic, the authors begin with a tutorial introducing the foundations of Isogeometric Analysis, before advancing to a comprehensive coverage of the most recent developments in the technique. The authors offer a clear explanation as to how to add isogeometric capabilities to existing finite element computer programs, demonstrating how to implement and use the technology. Detailed programming examples and datasets are included to impart a thorough knowledge and understanding of the material. Provides examples of different applications, showing the reader how to implement isogeometric models Addresses readers on both sides of the CAD/FEA divide Describes Non-Uniform Rational B-Splines (NURBS) basis functions

Multivariate Splines

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Author : Charles K. Chui
language : en
Publisher: SIAM
Release Date : 1988-01-01

Multivariate Splines written by Charles K. Chui and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.

Subject of multivariate splines presented from an elementary point of view; includes many open problems.

Adaptive Hierarchical Isogeometric Finite Element Methods

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Author : Anh-Vu Vuong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-05-01

Adaptive Hierarchical Isogeometric Finite Element Methods written by Anh-Vu Vuong 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 2012-05-01 with Mathematics categories.

​Isogeometric finite elements combine the numerical solution of partial differential equations and the description of the computational domain given by rational splines from computer aided geometric design. This work gives a well-founded introduction to this topic and then extends isogeometric finite elements by a local refinement technique, which is essential for an efficient adaptive simulation. Thereby a hierarchical approach is adapted to the numerical requirements and the relevant theoretical properties of the basis are ensured. The computational results suggest the increased efficiency and the potential of this local refinement method.

An Introduction To Nurbs

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Author : David F. Rogers
language : en
Publisher: Elsevier
Release Date : 2000-08-22

An Introduction To Nurbs written by David F. Rogers and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-22 with Computers categories.

The latest from a computer graphics pioneer, An Introduction to NURBS is the ideal resource for anyone seeking a theoretical and practical understanding of these very important curves and surfaces. Beginning with Bézier curves, the book develops a lucid explanation of NURBS curves, then does the same for surfaces, consistently stressing important shape design properties and the capabilities of each curve and surface type. Throughout, it relies heavily on illustrations and fully worked examples that will help you grasp key NURBS concepts and deftly apply them in your work. Supplementing the lucid, point-by-point instructions are illuminating accounts of the history of NURBS, written by some of its most prominent figures. Whether you write your own code or simply want deeper insight into how your computer graphics application works, An Introduction to NURBS will enhance and extend your knowledge to a degree unmatched by any other resource. - Presents vital information with applications in many different areas: CAD, scientific visualization, animation, computer games, and more. - Facilitates accessiblity to anyone with a knowledge of first-year undergraduate mathematics. - Details specific NURBS-based techniques, including making cusps with B-spline curves and conic sections with rational B-spline curves. - Presents all important algorithms in easy-to-read pseudocode-useful for both implementing them and understanding how they work. - Includes complete references to additional NURBS resources.

Advanced Finite Element Method In Structural Engineering

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Author : Yu-Qiu Long
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-29

Advanced Finite Element Method In Structural Engineering written by Yu-Qiu Long 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 2009-09-29 with Technology & Engineering categories.

Advanced Finite Element Method in Structural Engineering systematically introduces the research work on the Finite Element Method (FEM), which was completed by Prof. Yu-qiu Long and his research group in the past 25 years. Seven original theoretical achievements - for instance, the Generalized Conforming Element method, to name one - and their applications in the fields of structural engineering and computational mechanics are discussed in detail. The book also shows the new strategies for avoiding five difficulties that exist in traditional FEM (shear-locking problem of thick plate elements; sensitivity problem to mesh distortion; non-convergence problem of non-conforming elements; accuracy loss problem of stress solutions by displacement-based elements; stress singular point problem) by utilizing foregoing achievements.

The Nurbs Book

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Author : Les Piegl
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Nurbs Book written by Les Piegl 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 2012-12-06 with Computers categories.

Until recently B-spline curves and surfaces (NURBS) were principally of interest to the computer aided design community, where they have become the standard for curve and surface description. Today we are seeing expanded use of NURBS in modeling objects for the visual arts, including the film and entertainment industries, art, and sculpture. NURBS are now also being used for modeling scenes for virtual reality applications. These applications are expected to increase. Consequently, it is quite appropriate for The.N'URBS Book to be part of the Monographs in Visual Communication Series. B-spline curves and surfaces have been an enduring element throughout my pro fessional life. The first edition of Mathematical Elements for Computer Graphics, published in 1972, was the first computer aided design/interactive computer graph ics textbook to contain material on B-splines. That material was obtained through the good graces of Bill Gordon and Louie Knapp while they were at Syracuse University. A paper of mine, presented during the Summer of 1977 at a Society of Naval Architects and Marine Engineers meeting on computer aided ship surface design, was arguably the first to examine the use of B-spline curves for ship design. For many, B-splines, rational B-splines, and NURBS have been a bit mysterious.