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Author: Klaus Hollig Publisher: SIAM ISBN: 0898716993 Category : Mathematics Languages : en Pages : 152
Book Description
An exploration of the new weighted approximation techniques which result from the combination of the finite element method and B-splines.
Author: Klaus Hollig Publisher: SIAM ISBN: 0898716993 Category : Mathematics Languages : en Pages : 152
Book Description
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 :
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: Klaus Hollig Publisher: SIAM ISBN: 1611972949 Category : Mathematics Languages : en Pages : 228
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: Bhavya Aggarwal Publisher: ISBN: Category : Languages : en Pages :
Book Description
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: Klaus Hollig
Author: Klaus Hollig
Author: Brian C. Owens
Author: Martha Sofia Miranda Morales
Author: Klaus Hollig
Author: Bhavya Aggarwal
Author: Jhinwung Kim
Author: Hongrui Wang
Author: Steve Robert Shoaf
Author: Ni Sheng
Author: L. R. T. Gardner