Natural shape functions of a compressed Vlasov element
Author(s)
Date Issued
1991
Publisher
Elsevier
Journal
Thin-Walled Structures
Volume
11
Issue
5
Start page
431
End page
438
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.
SFU Affiliated Publication
No
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