Intrinsic finite element modeling of curved beams
(English)Manuscript (preprint) (Other academic)
In the mid '90s Delfour and Zolesio [4-6] established elasticity models on surfaces described using the signed distance function, an approach they called intrinsic modeling. For problems in codimension-two, e.g. one-dimensional geometries embedded in R3, an analogous description can be done using a vector distance function. In this paper we investigate the intrinsic approach for the modeling of codimension-two problems by deriving a weak formulation for a linear curved beam expressed in three dimensions from the equilibrium equations of linear elasticity. Based on this formulation we implement a finite element model using global degrees of freedom and discuss upon the effects of curvature and locking. Comparisons with classical solutions for both straight and curved cantilever beams under a tip load are given.
IdentifiersURN: urn:nbn:se:umu:diva-79295OAI: oai:DiVA.org:umu-79295DiVA: diva2:640293