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Thermomechanical Analysis of Large Deflection of Shear Deformable FG-CNT Reinforced Composite Beams Using Perturbation Technique
  • Hadi Babaei,
  • Yaser Kiani,
  • M.R. Eslami
Hadi Babaei
Islamic Azad University South Tehran Branch
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Yaser Kiani
Amirkabir university of Technology
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M.R. Eslami
Amirkabir University of Technology
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Abstract

Present investigation deals with the geometrically non-linear bending response of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams. It is assumed that beam is resting on a three parameter elastic foundation . Uniform thermal field is also included into the formulation and properties are considered as temperature dependent. Distribution of CNTs in the beam may be uniform or functionally graded according to linear distribution of volume fraction of CNTs across the thickness. The equivalent properties of the composite media are obtained with the aid of the refined rule of mixtures approach which is calibrated with the available data based on the molecular dynamics simulations. The governing equations of the beam are obtained based on first order, third order and sinusoidal theories. To capture the large deformations, the von K\’arm\’an type of kinematic assumptions are included. Two types of boundary conditions are included which are immovable pinned and immovable clamped. The established equations are reformulated and transferred into dimensionless presentation. After that, using the powerful two step perturbation technique, closed form expressions are provided to trace the non-linear load-deflection paths of the beam. Results of this study are compared with the available data in the open literature. After that novel results are provided to discuss the effects of boundary conditions, temperature change, foundation stiffness, slenderness ratio, CNT volume fraction and distribution profiles. It is shown that graded pattern of CNTs and volume fraction of CNT are two important factors on the geometrically nonlinear response of the CNTRC beam.

Peer review status:Published

28 Aug 2020Submitted to Mathematical Methods in the Applied Sciences
01 Sep 2020Submission Checks Completed
01 Sep 2020Assigned to Editor
04 Sep 2020Reviewer(s) Assigned
08 Oct 2020Review(s) Completed, Editorial Evaluation Pending
08 Oct 2020Editorial Decision: Revise Major
27 Nov 20201st Revision Received
27 Nov 2020Submission Checks Completed
27 Nov 2020Assigned to Editor
27 Nov 2020Reviewer(s) Assigned
27 Nov 2020Review(s) Completed, Editorial Evaluation Pending
30 Nov 2020Editorial Decision: Accept
28 Feb 2021Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.7120