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New shape functions for non-uniform curved Timoshenko beams with arbitrarily varying curvature using basic displacement functions

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Abstract

Basic Displacement Functions (BDFs) are introduced and derived using the basic principles of structural mechanics. BDFs are then utilized to obtain new shape functions for arbitrarily curved non-uniform beams, including the effects of shear deformation and extensibility of neutral axis. The main virtue of the proposed shape functions is their susceptibility to the variations in cross-sectional area, moment of inertia, and curvature along the axis of the beam element. Competence of the present method in static and free vibration analyses, as well as its applicability to the special case of straight Timoshenko beam has been verified through several numerical examples.

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Authors and Affiliations

  1. School of Civil Engineering, University College of Engineering, University of Tehran, Tehran, P.O. Box 11365-4563, Iran

    A. Shahba, R. Attarnejad, S. Jandaghi Semnani & H. Honarvar Gheitanbaf

  2. Centre of Numerical Methods in Engineering, University of Tehran, Tehran, Iran

    A. Shahba & R. Attarnejad

  3. Centre of Excellence for Engineering and Management of Infrastructures, School of Civil Engineering, University of Tehran, Tehran, Iran

    R. Attarnejad

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  1. A. Shahba
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  2. R. Attarnejad
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  3. S. Jandaghi Semnani
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  4. H. Honarvar Gheitanbaf
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Correspondence to A. Shahba.

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Shahba, A., Attarnejad, R., Jandaghi Semnani, S. et al. New shape functions for non-uniform curved Timoshenko beams with arbitrarily varying curvature using basic displacement functions. Meccanica 48, 159–174 (2013). https://doi.org/10.1007/s11012-012-9591-9

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