The Weighted Extended B-splines Finite Element Method PDF Download

Author: Martha Sofia Miranda Morales
Publisher:
ISBN:
Category :
Languages : en
Pages : 57

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Author: Klaus Hollig
Publisher: SIAM
ISBN: 0898716993
Category : Mathematics
Languages : en
Pages : 152

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

Author: Brian C. Owens
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
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.

Author: L. R. T. Gardner
Publisher:
ISBN:
Category :
Languages : en
Pages : 8

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Author: Bhavya Aggarwal
Publisher:
ISBN:
Category :
Languages : en
Pages :

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The finite element method since its development in the 1950's has been used extensively in solving complex problems involving partial differential equations. The conventional finite element methods use piecewise Lagrange interpolation functions for approximating displacements. The aim of this research is to explore finite element analysis using B-spline interpolation. B-splines are piecewise defined polynomial curves which provide higher continuity of derivatives than piecewise Lagrange interpolation functions. This work focuses on the implementation and comparison of the B-spline finite elements in contrast with the conventional finite elements. This thesis observes that the use of B-spline interpolation functions can reduce the computational cost significantly. It is an efficient technique and can be conveniently implemented into the existing finite element programs.

Author: Hongrui Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Author: Steve Robert Shoaf
Publisher:
ISBN:
Category : Finite element method
Languages : en
Pages : 300

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Author: Klaus Hollig
Publisher: SIAM
ISBN: 1611972949
Category : Mathematics
Languages : en
Pages : 228

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Book Description
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.

Author: Arkadiusz Żak
Publisher: Springer Nature
ISBN: 3031568362
Category :
Languages : en
Pages : 332

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Author: Jean-Daniel Boissonnat
Publisher: Springer Science & Business Media
ISBN: 3642274129
Category : Computers
Languages : en
Pages : 758

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Book Description
This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Curves and Surfaces, held in Avignon, in June 2010. The conference had the overall theme: "Representation and Approximation of Curves and Surfaces and Applications". The 39 revised full papers presented together with 9 invited talks were carefully reviewed and selected from 114 talks presented at the conference. The topics addressed by the papers range from mathematical foundations to practical implementation on modern graphics processing units and address a wide area of topics such as computer-aided geometric design, computer graphics and visualisation, computational geometry and topology, geometry processing, image and signal processing, interpolation and smoothing, scattered data processing and learning theory and subdivision, wavelets and multi-resolution methods.