A torsion-free non-linear beam model

• Published in: International journal of non-linear mechanics 2014-01, Vol.58, p.1-10
• Main Authors: Romero, I., Urrecha, M., Cyron, C.J.
• Format: Article
• Language: English
• Subjects: Bending; Continuums; Discretization; Geometrically exact theory; Mathematical analysis; Mathematical models; Non-linear beam; Nonlinearity; Polymer model; Polymers; Structural model; Traction
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2013.08.008

The governing equations of a novel structural model are derived from general balance equations and Lagrangian mechanics. The model represents beam-like slender bodies whose sections can withstand traction and shear forces, plus bending, but no torsional, moments. Although continuum bodies with such a behavior do not exist, multibody systems whose overall response can be described in such a way can be found. In fact, the motivation for this work is the study of certain types of polymers, which can be efficiently modeled as torsion-free rods instead of using long spring–mass chains, for which the proposed continuous model can serve as a basis for efficient finite element discretizations. •The governing equations of a class of beams without torsional stiffness are derived using balance laws and variational methods.•The torsional degrees of freedom are completely eliminated from the model without employing Lagrange multipliers.•The resulting model is the smooth counterpart of beam–spring chains with extensional and bending springs.•The initial boundary value problem obtained opens the door to relatively simple finite element formulations of the thin-beam limit.