A Gaussian sinc-collocation approach for whipping cantilever with a follower shear force at the tip

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2 Citations (Scopus)

Abstract

A spatial discretization scheme, based on a set of Gaussian sine functions, is proposed for the temporal projection of a set of partial differential equations (PDEs), describing the non-linear dynamics of an elastic-plastic hardening-softening (EPHS) cantilever, subjected to a follower shear force at its tip. The dynamics so described correspond to planar whipping of a pipe conveying fluid, ruptured near a right-angled bend. The constitutive EPHS moment curvature relationship used here follows the earlier work of Reid et al. (Proceedings of the Royal Society of London, Series A 1998; 454:997-1029). Compared to the more classical Lagrangian polynomial-based collocation functions, the Gaussian sine functions have better localization properties. Moreover, for a relatively large number of collocation points, use of such functions does not lead to numerical overflow or underflow problems, often associated with the use of higher order polynomial collocation functions. The spatial discretization leads to a set of non-linear ordinary differential equations (ODEs) in time, which are in turn integrated via a fourth order adaptive Runge-Kutta scheme. Some numerical results for a cantilever whipping in a plane are presented to further illustrate the present approach. The method is a step forward towards the development of a mesh-free non-linear beam element, suitable for dynamic analyses of pipe networks and pipe-on-pipe impact problems. Copyright (C) 2003 John Wiley Sons, Ltd.

Original languageEnglish
Pages (from-to)869-892
Number of pages23
JournalInternational Journal for Numerical Methods in Engineering
Volume58
DOIs
Publication statusPublished - 2003

Keywords

  • Gaussian sinc functions
  • collocation
  • elastic-plastic hardening-softening model
  • pipe whip
  • FINITE-ELEMENT ANALYSIS
  • LARGE DEFLECTIONS
  • BEAM THEORY
  • FORMULATION
  • EQUATION
  • SYSTEMS

Cite this

@article{3affd2936a894762bd12c6ed5c60e467,
title = "A Gaussian sinc-collocation approach for whipping cantilever with a follower shear force at the tip",
abstract = "A spatial discretization scheme, based on a set of Gaussian sine functions, is proposed for the temporal projection of a set of partial differential equations (PDEs), describing the non-linear dynamics of an elastic-plastic hardening-softening (EPHS) cantilever, subjected to a follower shear force at its tip. The dynamics so described correspond to planar whipping of a pipe conveying fluid, ruptured near a right-angled bend. The constitutive EPHS moment curvature relationship used here follows the earlier work of Reid et al. (Proceedings of the Royal Society of London, Series A 1998; 454:997-1029). Compared to the more classical Lagrangian polynomial-based collocation functions, the Gaussian sine functions have better localization properties. Moreover, for a relatively large number of collocation points, use of such functions does not lead to numerical overflow or underflow problems, often associated with the use of higher order polynomial collocation functions. The spatial discretization leads to a set of non-linear ordinary differential equations (ODEs) in time, which are in turn integrated via a fourth order adaptive Runge-Kutta scheme. Some numerical results for a cantilever whipping in a plane are presented to further illustrate the present approach. The method is a step forward towards the development of a mesh-free non-linear beam element, suitable for dynamic analyses of pipe networks and pipe-on-pipe impact problems. Copyright (C) 2003 John Wiley Sons, Ltd.",
keywords = "Gaussian sinc functions, collocation, elastic-plastic hardening-softening model, pipe whip, FINITE-ELEMENT ANALYSIS, LARGE DEFLECTIONS, BEAM THEORY, FORMULATION, EQUATION, SYSTEMS",
author = "Reid, {Stephen R} and D. Roy",
year = "2003",
doi = "10.1002/NME.805",
language = "English",
volume = "58",
pages = "869--892",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",

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TY - JOUR

T1 - A Gaussian sinc-collocation approach for whipping cantilever with a follower shear force at the tip

AU - Reid, Stephen R

AU - Roy, D.

PY - 2003

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N2 - A spatial discretization scheme, based on a set of Gaussian sine functions, is proposed for the temporal projection of a set of partial differential equations (PDEs), describing the non-linear dynamics of an elastic-plastic hardening-softening (EPHS) cantilever, subjected to a follower shear force at its tip. The dynamics so described correspond to planar whipping of a pipe conveying fluid, ruptured near a right-angled bend. The constitutive EPHS moment curvature relationship used here follows the earlier work of Reid et al. (Proceedings of the Royal Society of London, Series A 1998; 454:997-1029). Compared to the more classical Lagrangian polynomial-based collocation functions, the Gaussian sine functions have better localization properties. Moreover, for a relatively large number of collocation points, use of such functions does not lead to numerical overflow or underflow problems, often associated with the use of higher order polynomial collocation functions. The spatial discretization leads to a set of non-linear ordinary differential equations (ODEs) in time, which are in turn integrated via a fourth order adaptive Runge-Kutta scheme. Some numerical results for a cantilever whipping in a plane are presented to further illustrate the present approach. The method is a step forward towards the development of a mesh-free non-linear beam element, suitable for dynamic analyses of pipe networks and pipe-on-pipe impact problems. Copyright (C) 2003 John Wiley Sons, Ltd.

AB - A spatial discretization scheme, based on a set of Gaussian sine functions, is proposed for the temporal projection of a set of partial differential equations (PDEs), describing the non-linear dynamics of an elastic-plastic hardening-softening (EPHS) cantilever, subjected to a follower shear force at its tip. The dynamics so described correspond to planar whipping of a pipe conveying fluid, ruptured near a right-angled bend. The constitutive EPHS moment curvature relationship used here follows the earlier work of Reid et al. (Proceedings of the Royal Society of London, Series A 1998; 454:997-1029). Compared to the more classical Lagrangian polynomial-based collocation functions, the Gaussian sine functions have better localization properties. Moreover, for a relatively large number of collocation points, use of such functions does not lead to numerical overflow or underflow problems, often associated with the use of higher order polynomial collocation functions. The spatial discretization leads to a set of non-linear ordinary differential equations (ODEs) in time, which are in turn integrated via a fourth order adaptive Runge-Kutta scheme. Some numerical results for a cantilever whipping in a plane are presented to further illustrate the present approach. The method is a step forward towards the development of a mesh-free non-linear beam element, suitable for dynamic analyses of pipe networks and pipe-on-pipe impact problems. Copyright (C) 2003 John Wiley Sons, Ltd.

KW - Gaussian sinc functions

KW - collocation

KW - elastic-plastic hardening-softening model

KW - pipe whip

KW - FINITE-ELEMENT ANALYSIS

KW - LARGE DEFLECTIONS

KW - BEAM THEORY

KW - FORMULATION

KW - EQUATION

KW - SYSTEMS

U2 - 10.1002/NME.805

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JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

ER -