Finite Element Methods with B-Splines - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Element Methods with B-Splines write by Klaus Hollig. This book was released on 2012-12-13. Finite Element Methods with B-Splines available in PDF, EPUB and Kindle. An exploration of the new weighted approximation techniques which result from the combination of the finite element method and B-splines.
Finite Element Methods with B-splines
Finite Element Methods with B-splines - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Element Methods with B-splines write by Klaus Hollig. This book was released on 2003-01-01. Finite Element Methods with B-splines available in PDF, EPUB and Kindle. 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.
Implementation of B-splines in a Conventional Finite Element Framework
Implementation of B-splines in a Conventional Finite Element Framework - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Implementation of B-splines in a Conventional Finite Element Framework write by Brian C. Owens. This book was released on 2010. Implementation of B-splines in a Conventional Finite Element Framework available in PDF, EPUB and Kindle. 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.
Approximation and Modeling with B-Splines
Approximation and Modeling with B-Splines - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximation and Modeling with B-Splines write by Klaus Hollig. This book was released on 2015-07-01. Approximation and Modeling with B-Splines available in PDF, EPUB and Kindle. 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.
An Introduction to NURBS
An Introduction to NURBS - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to NURBS write by David F. Rogers. This book was released on 2001. An Introduction to NURBS available in PDF, EPUB and Kindle. NURBS (Non-uniform Rational B-Splines) are the computer graphics industry standard for curve and surface description. They are now incorporated into all standard computer-aided design and drafting programs (for instance, Autocad). They are also extensively used in all aspects of computer graphics including much of the modeling used for special effects in film and animation, consumer products, robot control, and automobile and aircraft design. So, the topic is particularly important at this time because NURBS are really at the peak of interest as applied to computer graphics and CAD of all kind.
