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Variational formulation of curved beams in global coordinates
Högskolan i Jönköping, Tekniska Högskolan, JTH.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)ORCID iD: 0000-0001-7838-1307
2014 (English)In: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 53, no 4, 611-623 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we derive a variational formulation for the static analysis of a linear curved beam natively expressed in global Cartesian coordinates. Using an implicit description of the beam midline during derivation we eliminate the need for local coordinates. The only geometrical information appearing in the final expressions for the governing equations is the tangential direction. As a consequence, zero or discontinuous curvature, for example at inflection points, pose no difficulty in this formulation. Kinematic assumptions encompassing both Timoshenko and Euler–Bernoulli beam theories are considered. With the exception of truly three-dimensional formulations, models for curved beams found in the literature are typically derived in the local Frenet frame. We implement finite element methods with global degrees of freedom and discuss curvature coupling effects and locking. Numerical comparisons with classical solutions for straight and curved cantilever beams under tip load are given, as well as numerical examples illustrating curvature coupling effects.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2014. Vol. 53, no 4, 611-623 p.
Keyword [en]
Curved beams, Global coordinates, Finite elements, Linear elasticity, Vector distance function
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-80822DOI: 10.1007/s00466-013-0921-0ISI: 000332857000005OAI: oai:DiVA.org:umu-80822DiVA: diva2:651637
Available from: 2013-09-26 Created: 2013-09-26 Last updated: 2017-12-06Bibliographically approved

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Larson, Mats G.Larsson, Karl

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