Natural shape functions of a compressed Vlasov element

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

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Author(s)

  • A. Y T Leung

Detail(s)

Original languageEnglish
Pages (from-to)431-438
Journal / PublicationThin-Walled Structures
Volume11
Issue number5
Publication statusPublished - 1991
Externally publishedYes

Abstract

To approximate a tube building by thin-walled Vlasov beam, it is unreasonable to neglect the axial force due to dead and live loads. The axial compression makes the lateral displacements (Y, Z) coupled with the torsional displacement (Φ) when warping is concerned. The resulting twelve-order differential equation is customarily solved by finite element method assuming independent cubic shape functions for Y, Z and Φ. It is pointed out here that the displacement functions are not completely independent. Indeed, if one takes the static solutions of the governing ordinary differential equations as shape functions, for the same number of degrees of freedom, one can approximate the Vlasov beam by quintic polynomials plus six hyperbolic-trigonometric functions. For static problems without distributed force, the resulting stiffness equation is exact. For dynamic problems, the resulting finite element converges rapidly. © 1991.

Citation Format(s)

Natural shape functions of a compressed Vlasov element. / Leung, A. Y T.

In: Thin-Walled Structures, Vol. 11, No. 5, 1991, p. 431-438.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review