Nonorthogonal solution for thin-walled members - a finite element formulation

Natl Research Council Canada
Publication Type:
Journal Article
Canadian Journal Of Civil Engineering, 2006, 33 (4), pp. 421 - 439
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Conventional solutions for the equations of equilibrium based on the well-known Vlasov thin-walled beam theory uncouple the equations by adopting orthogonal coordinate systems. Although this technique considerably simplifies the resulting field equations, it introduces several modelling complications and limitations. As a result, in the analysis of problems where eccentric supports or abrupt cross-sectional changes exist (in elements with rectangular holes, coped flanges, or longitudinal stiffened members, etc.), the Vlasov theory has been avoided in favour of a shell finite element that offer modelling flexibility at higher computational cost. In this paper, a general solution of the Vlasov thin-walled beam theory based on a nonorthogonal coordinate system is developed. The field equations are then exactly solved and the resulting displacement field expressions are used to formulate a finite element. Two additional finite elements are subsequently derived to cover the special cases where (a) the St.Venant torsional stiffness is negligible and (b) the warping torsional stiffness is negligible
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