Large deflections of a beam subject to three-point bending

In this paper, a solution for the equilibrium configuration of an elastic beam subject to three-point bending is given in terms of Jacobi elliptical functions. General equations are derived, and the domain of the solution is established. Several examples that illustrate a use of the solution are dis...

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Bibliographic Details
Published inInternational journal of non-linear mechanics Vol. 69; pp. 84 - 92
Main Author Batista, Milan
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2015
Subjects
Approximation
Beams (structural)
Bending
Cantilever
Deflection
Elastic beams
Elasticity
Large deflections
Mathematical analysis
Mathematical models
Polynomials
Three-point bending test
Elasticity
Large deflections
Three-point bending test
Cantilever
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Summary:In this paper, a solution for the equilibrium configuration of an elastic beam subject to three-point bending is given in terms of Jacobi elliptical functions. General equations are derived, and the domain of the solution is established. Several examples that illustrate a use of the solution are discussed. The obtained numerical results are compared with the results of other authors. An approximation formula by which the beam load is given as a polynomial function of beam deflection is also derived. The range of applicability of the approximation is illustrated by numerical examples. •A new analytical solution of the problem is given in terms of Jacobi elliptical functions and the Jacobi zeta function.•The domain of the solution is established.•Approximation expressions for load factor as a polynomial function of deflection is derived.
Bibliography:ObjectType-Article-1
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content type line 23
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2014.11.024