The influence of interpolation errors on finite-element calculations involving stress-curvature proportionalities

Albert Eliot Segall, M. J. Sipics

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The presence of non-linear axial gradients of pressure/temperature in a finite-element model can invoke an often overlooked proportionality between the resulting curvature and bending stresses. Because these stresses can be significant, the use of polynomials and cubic-splines to interpolate any gradients to a finite-element mesh must be carefully weighed against their tendency to undulate through the data. As shown for a test case involving an interpolated pressure-distribution with artificially induced errors, the resulting polynomial oscillation can indeed induce significant variations of both sign and magnitude in the finite-element calculations. In contrast, a constrained B-spline with smoothing provided more reasonable stress predictions.

Original languageEnglish (US)
Pages (from-to)1873-1884
Number of pages12
JournalFinite Elements in Analysis and Design
Volume40
Issue number13-14
DOIs
StatePublished - Aug 1 2004

Fingerprint

Interpolation Error
Interpolation
Curvature
Finite Element
Splines
Polynomials
Gradient
Polynomial Splines
Cubic Spline
Pressure Distribution
B-spline
Pressure distribution
Finite Element Model
Smoothing
Interpolate
Mesh
Oscillation
Polynomial
Prediction
Influence

All Science Journal Classification (ASJC) codes

  • Analysis
  • Engineering(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

Cite this

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The influence of interpolation errors on finite-element calculations involving stress-curvature proportionalities. / Segall, Albert Eliot; Sipics, M. J.

In: Finite Elements in Analysis and Design, Vol. 40, No. 13-14, 01.08.2004, p. 1873-1884.

Research output: Contribution to journalArticle

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AB - The presence of non-linear axial gradients of pressure/temperature in a finite-element model can invoke an often overlooked proportionality between the resulting curvature and bending stresses. Because these stresses can be significant, the use of polynomials and cubic-splines to interpolate any gradients to a finite-element mesh must be carefully weighed against their tendency to undulate through the data. As shown for a test case involving an interpolated pressure-distribution with artificially induced errors, the resulting polynomial oscillation can indeed induce significant variations of both sign and magnitude in the finite-element calculations. In contrast, a constrained B-spline with smoothing provided more reasonable stress predictions.

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