Comparison Between Bézier Extraction and Associated Bézier Elements in Eigenvalue Problems-Reference-Cited by-同舟云学术

Comparison Between Bézier Extraction and Associated Bézier Elements in Eigenvalue Problems

Published:2022-12-31 Issue: Volume:17 Page:605-615
ISSN:2224-2856
Container-title:WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL
language:en
Short-container-title:

Author:

Provatidis Christopher G.¹

Affiliation:

1. School of Mechanical Engineering, National Technical University of Athens, 9, Iroon Polytechniou str, 15780 Zografou, GREECE

Abstract

This paper shows that the control points which are implicitly encountered in the Bézier extraction during isogeometric analysis can be explicitly used to form Bézier elements of C^0-continuity in several ways, thus eventually leading to a superior accuracy and performance than the C^p-continuity. The study is reduced to the eigenvalue extraction in problems governed by the Helmholtz equation. Analysis is performed in conjunction with piecewise cubic interpolation for three benchmark tests in one and two dimensions. In the latter case a rectangular and a circular acoustical cavity under Neumann boundary conditions are analyzed. Several computational details are also discussed.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

Artificial Intelligence,General Mathematics,Control and Systems Engineering

Reference31 articles.

1. Taig I.C., Structural Analysis by the matrix displacement method, Engl. Electric Aviation Report No. S017, 1961.

2. Irons B.M., Engineering applications of numerical integration in stiffness matrix, J.A.I.A.A., Vol. 4, No. 11, 1966, pp. 2035-2037.

3. Zienkiewicz O.C., The Finite Element Method, McGraw-Hill, 1977.

4. Bathe K.-J., Finite Element Procedures, PrenticeHall, 1996.

5. Gordon W.J., and Hall C.A., Transfinite element methods: Blending-function interpolation over arbitrary curved element domains, Numerische Mathematik, Vol. 21, 1973, pp. 109–112.