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Keywords = bioinspired imperfect beams

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20 pages, 6640 KiB  
Article
Nonlinear Static Stability of Imperfect Bio-Inspired Helicoidal Composite Beams
by Nazira Mohamed, Salwa A. Mohamed and Mohamed A. Eltaher
Mathematics 2022, 10(7), 1084; https://doi.org/10.3390/math10071084 - 28 Mar 2022
Cited by 29 | Viewed by 2091
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 [...] Read more.
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. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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20 pages, 12700 KiB  
Article
Exact Solution of Nonlinear Behaviors of Imperfect Bioinspired Helicoidal Composite Beams Resting on Elastic Foundations
by Khalid H. Almitani, Nazira Mohamed, Mashhour A. Alazwari, Salwa A. Mohamed and Mohamed A. Eltaher
Mathematics 2022, 10(6), 887; https://doi.org/10.3390/math10060887 - 10 Mar 2022
Cited by 27 | Viewed by 2916
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 [...] Read more.
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. Full article
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