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Statics of thin‐walled pretwisted beams
Author(s) -
Krenk S.,
Gunneskov O.
Publication year - 1981
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620170909
Subject(s) - torsion (gastropod) , image warping , statically indeterminate , mathematics , mathematical analysis , statics , boundary value problem , discretization , bending moment , strain energy , potential energy , classical mechanics , physics , finite element method , medicine , surgery , artificial intelligence , computer science , thermodynamics
The displacement and strain fields of thin‐walled pretwisted beams are prescribed in terms of generalized displacements for extension, bending, torsion and warping. Differential equations and boundary conditions are obtained from the elastic potential energy functional without assuming coincidence of the beam axis with any of the structural axes. This procedure gives a unique consistent definition of sectional moments and generalized forces. Some simple explicit formulae are derived for homogeneous tension–torsion. For the general case a computer code is developed on the basis of discretized generalized displacements and a modified energy functional, devised to obtain consistent lengthwise variation of the stresses and a unique decomposition of the torsional moment. Examples show agreement with analytical results for cylindrical beams and illustrate the various coupling effects for beams with pretwist. They also demonstrate the usefulness of the explicit formulae for homogeneous tension–torsion.