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Nonlinear Static Stability of Imperfect Bio-Inspired Helicoidal Composite Beams

Author

Listed:
  • Nazira Mohamed

    (Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, Zagazig P.O. Box 44519, Egypt)

  • Salwa A. Mohamed

    (Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, Zagazig P.O. Box 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, Zagazig P.O. Box 44519, Egypt)

Abstract

The objective of this manuscript is to develop, for the first time, a mathematical model for the prediction of buckling, postbuckling, and nonlinear bending of imperfect bio-inspired helicoidal composite beams with nonlinear rotation angle. The equilibrium nonlinear integrodifferential equations of imperfect (curved) helicoidal composite beams are derived from the Euler–Bernoulli kinematic assumption. The differential integral quadrature method (DIQM) and Newton-iterative method are employed to evaluate the response of imperfect helicoidal composite beams. Following the validation of the proposed model, numerical studies are performed to quantify the effect of rotation angle, imperfection amplitude, and foundation stiffness on postbuckling and bending behaviors of helicoidal composite beams. The perfect beam buckles through a pitchfork bifurcation. However, the imperfect beam snaps through the buckling type. The critical buckling load increases with the increasing value of elastic foundation constants. However, the nonlinear foundation constant has no effect in the case of perfect beams. The present model can be exploited in the analysis of bio-inspired structure, which has a failure similar to a metal and low interlaminar shear stress, and is used extensively in numerous engineering applications.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1084-:d:781221
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    References listed on IDEAS

    as
    1. Eltaher, Mohamed A. & Mohamed, Nazira, 2020. "Nonlinear stability and vibration of imperfect CNTs by Doublet mechanics," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. 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.
    3. Song, Zhiwei & Li, Wei & He, Xiaoqiao & Xie, De, 2021. "Comparisons of matched interface and boundary (MIB) method and its interpolation formulation for free vibration analysis of stepped beams and plates," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    4. 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.
    5. Zhang, Peng & Ma, Jianmin & Duan, Menglan & Yuan, Ye & Wang, Jinjia, 2021. "A high-precision curvature constrained Bernoulli–Euler planar beam element for geometrically nonlinear analysis," Applied Mathematics and Computation, Elsevier, vol. 397(C).
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