English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we derive a variational formulation for a linear curved beamwhich is natively expressed in global Cartesian coordinates. During derivationthe beam midline is assumed to be implicitly described by a vector distancefunction which eliminates the need for local coordinates. The only geometricalinformation appearing in the final expressions for the governing equations isthe tangential direction, and thus there is no need to introduce normaldirections along the curve. 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 beamtheories are considered.  With the exception of truly three dimensional formulations, models for curvedbeams found in literature are typically derived in the Frenet frame defined bythe geometry of the beam midline. While it is intuitive to formulate curvedbeam models in these local coordinates, the Frenet frame suffers from ambiguityand sudden changes of orientation in straight sections of the beam.  Based on the variational formulation we implement finite element models usingglobal Cartesian degrees of freedom and discuss curvature coupling effects andlocking. Numerical comparisons with classical solutions for both straight andcurved cantilever beams under a tip load are given, as well as numericalexamples illustrating curvature coupling effects.

Variational Formulation of Curved Beams in Global Coordinates