Studies of Refinement and Continuity in Isogeometric Structural Analysis (Preprint)

Abstract

We investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework. We consider two simple one-dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate NURBS solids. We also develop a local refinement strategy that we utilize in one of the shell analyses. We find that increased smoothness, that is, the "k-method," leads to a significant increase in accuracy for the problems of structural vibrations over the classical C^0-continuous "p-method," whereas a judicious insertion of C^0-continuous surfaces about singularities in a mesh otherwise generated by the k-method, usually outperforms a mesh in which all basis functions attain their maximum level of smoothness. We conclude that the potential for the k-method is high, but smoothness is an issue that is not well understood due to the historical dominance of C^0-continuous finite elements and therefore further studies are warranted.

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Document Details

Document Type
Technical Report
Publication Date
Jan 26, 2007
Accession Number
ADA464045

Entities

People

  • A. Reali
  • J. A. Cottrell
  • Thomas J.R. Hughes

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Computer-Aided Design
  • Continuity
  • Engineering
  • Equations
  • Finite Element Analysis
  • Frequency
  • Geometry
  • Hemispherical Shells
  • Potential Energy
  • Resonant Frequency
  • Structural Analysis
  • Vibration
  • Weighting Functions

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design