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Exact Solution of Nonlinear Behaviors of Imperfect Bioinspired Helicoidal Composite Beams Resting on Elastic Foundations

Author

Listed:
  • Khalid H. Almitani

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O. Box 80204, Saudi Arabia)

  • Nazira Mohamed

    (Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, Sharkia 44519, Egypt)

  • Mashhour A. Alazwari

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O. Box 80204, Saudi Arabia)

  • Salwa A. Mohamed

    (Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, Sharkia 44519, Egypt)

  • Mohamed A. Eltaher

    (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O. Box 80204, Saudi Arabia
    Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, Sharkia 44519, Egypt)

Abstract

This paper presents exact solutions for the nonlinear bending problem, the buckling loads, and postbuckling configurations of a perfect and an imperfect bioinspired helicoidal composite beam with a linear rotation angle. The beam is embedded on an elastic medium, which is modeled by two elastic foundation parameters. The nonlinear integro-differential governing equation of the system is derived based on the Euler–Bernoulli beam hypothesis, von Kármán nonlinear strain, and initial curvature. The Laplace transform and its inversion are directly applied to solve the nonlinear integro-differential governing equations. The nonlinear bending deflections under point and uniform loads are derived. Closed-form formulas of critical buckling loads, as well as nonlinear postbuckling responses of perfect and imperfect beams are deduced in detail. The proposed model is validated with previous works. In the numerical results section, the effects of the rotation angle, amplitude of initial imperfection, elastic foundation constants, and boundary conditions on the nonlinear bending, critical buckling loads, and postbuckling configurations are discussed. The proposed model can be utilized in the analysis of bio-inspired beam structures that are used in many energy-absorption applications.

Suggested Citation

  • Khalid H. Almitani & Nazira Mohamed & Mashhour A. Alazwari & Salwa A. Mohamed & Mohamed A. Eltaher, 2022. "Exact Solution of Nonlinear Behaviors of Imperfect Bioinspired Helicoidal Composite Beams Resting on Elastic Foundations," Mathematics, MDPI, vol. 10(6), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:887-:d:768447
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    References listed on IDEAS

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    1. Youssef Boutahar & Nadhir Lebaal & David Bassir, 2021. "A Refined Theory for Bending Vibratory Analysis of Thick Functionally Graded Beams," Mathematics, MDPI, vol. 9(12), pages 1-16, June.
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    Cited by:

    1. Nazira Mohamed & Salwa A. Mohamed & Mohamed A. Eltaher, 2022. "Nonlinear Static Stability of Imperfect Bio-Inspired Helicoidal Composite Beams," Mathematics, MDPI, vol. 10(7), pages 1-20, March.
    2. Ammar Melaibari & Salwa A. Mohamed & Amr E. Assie & Rabab A. Shanab & Mohamed A. Eltaher, 2022. "Static Response of 2D FG Porous Plates Resting on Elastic Foundation Using Midplane and Neutral Surfaces with Movable Constraints," Mathematics, MDPI, vol. 10(24), pages 1-25, December.

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