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

Khalid H. Almitani, Nazira Mohamed, Mashhour A. Alazwari, Salwa A. Mohamed and Mohamed A. Eltaher
Additional contact information
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

Mathematics, 2022, vol. 10, issue 6, 1-20

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.

Keywords: bioinspired imperfect beams; nonlinear bending; buckling and postbuckling; Laplace transform; exact solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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