Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

1990 ◽  
Author(s):  
Joanna M. Brown ◽  
Malcolm I. G. Bloor ◽  
M. Susan Bloor ◽  
Michael J. Wilson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spline Approximation ◽  
The Finite Element Method ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Spline Basis ◽  
Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

Analysis of Shell-Like Structures Using Structured Mesh

2010 ◽  
Author(s):  
Ashok V. Kumar ◽  
Prem Dheepak Salem Periyasamy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spline Approximation ◽  
Grid Method ◽  
Complex Surface ◽  
Approximation Schemes ◽  
Shell Elements ◽  
B Spline ◽  
Structured Grid ◽  
Element Method

Shell-like structures are modeled in traditional finite element method using shell elements. The geometry for such structures is modeled using surfaces that represent the mid-plane. A mesh consisting of planar or curved shell elements is then generated for the surface which can be challenging for complex surface geometries and the resultant mesh sometimes poorly approximates the geometry. In order to avoid the problems associated with mesh generation, several meshless methods and structured grid methods have been proposed in the past two decades. In this paper, a structured grid method called Implicit Boundary Finite Element Method (IBFEM) has been used for the analysis of shell-like structures. Three dimensional elements that use uniform B-spline approximation schemes for representing the solution are used to represent the displacement field. The surfaces representing shell passes through these elements and the equations of these surfaces are used to represent the geometry exactly. B-spline approximations can provide higher order solutions that have tangent and curvature continuity. Numerical examples are presented to demonstrate the performance of shell elements using IBFEM and B-spline approximation. The results are compared with traditional shell element solutions.

Finite Element Analysis Using Uniform B-Spline Basis

2008 ◽  
Author(s):  
Ashok V. Kumar ◽  
Ravi K. Burla
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Curve Surface ◽  
Stress And Strain ◽  
Element Analysis ◽  
Element Mesh ◽  
B Spline ◽  
Structured Grids ◽  
Spline Basis ◽  
Element Method

Implicit boundary finite element method uses structured grids for analysis instead of a conforming finite element mesh. The geometry of the structure is represented independently using curve / surface equations. These equations are used to apply boundary conditions even though there may not be nodes available on the boundary. In this paper, this method is applied for analysis using uniform B-spline basis defined over structured grids. Solutions can be constructed that are C1 or C2 continuous throughout the analysis domain using B-spline basis functions. Therefore, the computed stress and strain are continuous in the analysis domain thus eliminating the need for smoothing stress/strain results. Compared to conforming mesh, it is easier to generate structured grids that overlap the geometry and the elements in the grid are regular shaped and undistorted. Numerical examples are presented to demonstrate the performance of these B-spline elements. The results are compared with analytical solutions as well as traditional finite element solutions. Convergence studies for several examples show that B-spline elements provide accurate solutions with fewer elements and nodes as compared to traditional finite element method (FEM).

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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