Large deflection of curved elastic beams made of Ludwick type material

doi:10.1007/s10483-017-2213-6

Abstract

Abstract:

The large deflection of an axially extensible curved beam with a rectangular cross-section is investigated. The elastic beam is assumed to satisfy the Euler-Bernoulli postulation and be made of the Ludwick type material. Through reasonably simplified integration, the strain and curvature of the axis of the beam are presented in implicit formulations. The governing equations involving both geometric and material nonlinearities of the curved beam are derived and solved by the shooting method. When the initial curvature of the beam is zero, the curved beam is degenerated into a straight beam, and the predicted results obtained by the present model are consistent with those in the open literature. Numerical examples are further given for curved cantilever and simply supported beams, and the couplings between elongation and bending are found for the curved beams.

Key words: order, flexural-torsional buckling, geometric equation, rotations, curved beam, Ludwick type material, large deflection, nonlinearity

2010 MSC Number:

74B20

Hua LIU, Yi HAN, Jialing YANG. Large deflection of curved elastic beams made of Ludwick type material. Applied Mathematics and Mechanics (English Edition), 2017, 38(7): 909-920.

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