Duality and Unified Analysis of Discrete Approximations in Structural Dynamics and Wave Propagation: Comparison of rho-method Finite Elements with kappa-method NURBS (Preprint)

Abstract

We study the discretization behavior of classical finite element and NURBS approximations on problems of structural vibrations and wave propagation. We find that, on the basis of equal numbers of degrees-of-freedom and bandwidth, NURBS have superior approximation properties. In fact, we observe that the high mode behavior of classical finite elements is divergent with the order of approximation, a surprisingly negative result. On the other hand, NURBS offer almost spectral approximation properties, and all modes converge with increasing order of approximation.

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Document Details

Document Type
Technical Report
Publication Date
Oct 10, 2007
Accession Number
ADA478678

Entities

People

  • A. Reali
  • Giancarlo Sangalli
  • Thomas J.R. Hughes

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Computer-Aided Design
  • Difference Equations
  • Differential Equations
  • Dynamics
  • Eigenvalues
  • Equations
  • Evanescent Waves
  • Finite Element Analysis
  • Frequency
  • Frequency Response
  • Helmholtz Equations
  • Resonant Frequency
  • Two Dimensional
  • Vibration
  • Wave Propagation
  • Waves

Fields of Study

  • Physics

Readers

  • Neurotoxicology
  • Operations Research
  • Wave Propagation and Nonlinear Chaotic Dynamics.