B-spline Finite Elements for Plane Elasticity Problems PDF Download
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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: 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 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: M. Salmon Publisher: ISBN: Category : Computer programs Languages : en Pages : 60
Book Description
A computer program is presented for the small strain analysis of plane structures in the strain hardening elastic-plastic range. The finite element displacement method is used to perform the linear analyses in the iterative scheme. Bar and constant strain isotropic plane stress triangles are available for use in constructing structural idealizations. The use of ten different sets of material properties, three different material laws, and incremental proportional loading are available as options. Good correlation is shown with available test data and theoretical solutions.
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: Bhavya Aggarwal
Author: Bhavya Aggarwal
Author: Klaus Hollig
Author: Abdelhak Sfendji
Author: Bharat Patel
Author: M. Salmon
Author: Hisham Yousif Salhi
Author: Talal Abdul-Nabi Farhat
Author: Cherif Bouzerira
Author: Brian C. Owens
Author: Faris Ghani Abood