A three dimensional static and free vibration analysis using RHT-spline formulation

Nhon Nguyen-Thanh, Jacob Muthu, Timon Rabczuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A three dimensional rational splines over hierarchical T-meshes (RHT-spline) for static and vibration analysis are studied in this work. The RHT-spline is a piecewise tricubic rational over a three dimensional hierarchical T-mesh. The idea is based on rational splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support, partition of unity and also achieves C1 continuity. The RHT-splines surfaces inherit all properties of B-spline and NURBS and allows local refinement efficiently. In addition, the RHT-splines can also be considered as a special type of Hermitian interpolation splines over Tmeshes. Several numerical examples are used to demonstrate the reliability of the present method.

Original languageEnglish
Title of host publication8th South African Conference on Computational and Applied Mechanics, SACAM 2012 - Conference Proceedings
PublisherSouth African Association for Theoretical and Applied Mechanics (SAAM)
Pages66-71
Number of pages6
ISBN (Print)9780869707289
Publication statusPublished - 2012
Externally publishedYes
Event8th South African Conference on Computational and Applied Mechanics, SACAM 2012 - Johannesburg, South Africa
Duration: 2012 Sep 32012 Sep 5

Other

Other8th South African Conference on Computational and Applied Mechanics, SACAM 2012
CountrySouth Africa
CityJohannesburg
Period12/9/312/9/5

Fingerprint

Vibration analysis
Splines
Static analysis
Interpolation

Keywords

  • Isogeometric analysis
  • Nurbs
  • Rhtspline
  • T-meshes

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering

Cite this

Nguyen-Thanh, N., Muthu, J., & Rabczuk, T. (2012). A three dimensional static and free vibration analysis using RHT-spline formulation. In 8th South African Conference on Computational and Applied Mechanics, SACAM 2012 - Conference Proceedings (pp. 66-71). South African Association for Theoretical and Applied Mechanics (SAAM).

A three dimensional static and free vibration analysis using RHT-spline formulation. / Nguyen-Thanh, Nhon; Muthu, Jacob; Rabczuk, Timon.

8th South African Conference on Computational and Applied Mechanics, SACAM 2012 - Conference Proceedings. South African Association for Theoretical and Applied Mechanics (SAAM), 2012. p. 66-71.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nguyen-Thanh, N, Muthu, J & Rabczuk, T 2012, A three dimensional static and free vibration analysis using RHT-spline formulation. in 8th South African Conference on Computational and Applied Mechanics, SACAM 2012 - Conference Proceedings. South African Association for Theoretical and Applied Mechanics (SAAM), pp. 66-71, 8th South African Conference on Computational and Applied Mechanics, SACAM 2012, Johannesburg, South Africa, 12/9/3.
Nguyen-Thanh N, Muthu J, Rabczuk T. A three dimensional static and free vibration analysis using RHT-spline formulation. In 8th South African Conference on Computational and Applied Mechanics, SACAM 2012 - Conference Proceedings. South African Association for Theoretical and Applied Mechanics (SAAM). 2012. p. 66-71
Nguyen-Thanh, Nhon ; Muthu, Jacob ; Rabczuk, Timon. / A three dimensional static and free vibration analysis using RHT-spline formulation. 8th South African Conference on Computational and Applied Mechanics, SACAM 2012 - Conference Proceedings. South African Association for Theoretical and Applied Mechanics (SAAM), 2012. pp. 66-71
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