Abstract
The paper deals with a closed form solution for the structural behavior of a large family of curved wires in plane. The peculiarity of the approach is to model wires through their radius of curvature, the last expressed by third order polynomials of the slope angle. Castigliano’s theorem application, based on the account of elastic bending and tensile energies, is used to get the flexibility matrix of the curved wires. Shear effects are discarded since wires are considered very slender, but axial energy is computed to get stability in stiffness evaluation, turning critical when wires align with the reference system. The realistic assumption to consider the axial elongation as negligible by respect to bending displacements, suggests the invariance of the wire length. This position is essential in the geometrical fitting of the wire. Eventually, a discrete subdivision in pieces allows to model wires presenting a variegated curvature behavior. Therefore, an optimized fitting having the objective to reduce the number of subdivisions precedes the stiffness identification. The effective geometry of the wire is updated so that non-linear behavior can be faced. Some examples and comparisons with finite element results concerns both linear solutions of complex shapes and non-linear characterization of wires, when severe change of curvature during loading occurs.
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Marotta, E., Salvini, P. (2019). Structural Modelling of Curved Wires. In: Abdel Wahab, M. (eds) Proceedings of the 1st International Conference on Numerical Modelling in Engineering . NME 2018. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-2273-0_20
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DOI: https://doi.org/10.1007/978-981-13-2273-0_20
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