000013298 001__ 13298
000013298 005__ 20161114160335.0
000013298 04107 $$aeng
000013298 046__ $$k2009-06-22
000013298 100__ $$aRogers K., S.
000013298 24500 $$aModelling a string with varying length using the finite element method

000013298 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013298 260__ $$bNational Technical University of Athens, 2009
000013298 506__ $$arestricted
000013298 520__ $$2eng$$aThis paper presents an investigation into using the finite element method to model a string with a moving constraint at one boundary, causing the string to change in length with time. This simple finite element model using straight elements provides insight into how this may be implemented in more complex models. Two approaches are considered for modelling a constraint which moves along the string. In the first the lengths of all the elements in the finite element model change equally with time, while in the second only the length of the element nearest the end being wound in is varied. When this length becomes small enough, the element is merged with the next element and hence the number of elements in the model decreases with time. This resembles the well understood spaghetti problem, in that essentially one end of a string is being pulled, and this provides a means of validation. Numerical results are compared with those of an analytic model and a perturbation solution and the agreement is very good. The difference in run-time between the two finite element models is also considered. Although run-time is not an issue for the simple string considered here, it may become so when applied to more complex models. Reducing the number of elements with time decreases the run-time, but modifying the system matrices between time steps increases the run-time.

000013298 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013298 653__ $$aFinite Element Method, Variable Length Strings, Axially Moving Strings, Structural Dynamics. Abstract. This paper presents an investigation into using the finite element method to model a string with a moving constraint at one boundary, causing the string to change in length with time. This simple finite element model using straight elements provides insight into how this may be implemented in more complex models. Two approaches are considered for modelling a constraint which moves along the string. In the first the lengths of all the elements in the finite element model change equally with time, while in the second only the length of the element nearest the end being wound in is varied. When this length becomes small enough, the element is merged with the next element and hence the number of elements in the model decreases with time. This resembles the well understood spaghetti problem, in that essentially one end of a string is being pulled, and this provides a means of validation. Numerical results are compared with those of an analytic model and a perturbation solution and the agreement is very good. The difference in run-time between the two finite element models is also considered. Although run-time is not an issue for the simple string considered here, it may become so when applied to more complex models. Reducing the number of elements with time decreases the run-time, but modifying the system matrices between time steps increases the run-time.

000013298 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013298 720__ $$aRogers K., S.$$iFerguson N., S.$$iPerryman A., A.$$iMace B., R.
000013298 8560_ $$ffischerc@itam.cas.cz
000013298 8564_ $$s292043$$uhttps://invenio.itam.cas.cz/record/13298/files/CD443.pdf$$yOriginal version of the author's contribution as presented on CD, section: Fem: modelling and simulation - i.
000013298 962__ $$r13074
000013298 980__ $$aPAPER