New refined models for curved beams in both linear and nonlinear settings

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)2295-2319
Journal / PublicationMathematics and Mechanics of Solids
Issue number7
Online published8 Feb 2019
Publication statusPublished - 1 Jul 2019


In this paper, we derive a one-dimensional model for curved linear and nonlinear beams with no assumption on either the shape of the cross-section or the prescribed loads on the boundary of the cross-section. This model contains coupled bending, stretching and torsion effects, which is achieved by truncating the potential energy at the seventh order with respect to small transverse dimensions of the cross-section of the beam based on series expansions. In the linear case, we obtain an estimate for the difference between the exact and approximate stress tensors. Nevertheless, we can only show that for the displacement field, the solution of the approximate problem resulting from the truncation of the displacement field at the sixth order only differs from the exact displacement field by a difference of order of magnitude of the seventh order.

Research Area(s)

  • Curved beam theory, error estimation, hyperelasticity, linearized elasticity, truncation of potential energy, variational formulation