Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes

2020 ◽  
Vol 41 (8) ◽  
pp. 1227-1250 ◽  
Author(s):  
S. Zghal ◽  
A. Frikha ◽  
F. Dammak
Keyword(s):  
Carbon Nanotubes ◽  
Large Deflection ◽  
Geometrical Nonlinearity ◽  
Nanocomposite Structures

scholarly journals A Seminalytical Approach to Large Deflections in Compliant Beams under Point Load

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
N. Tolou ◽  
J. L. Herder
Keyword(s):  
Cantilever Beam ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometrical Nonlinearity ◽  
Adomian Decomposition Method ◽  
Analytical Form ◽  
Point Load ◽  
Large Deflections ◽  
Adomian Decomposition

The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large deflection of members continues to be an interesting problem in mechanical systems. This paper deals with an analytical investigation of large deflections in compliant mechanisms. The main objective is to propose a convenient method of solution for the large deflection problem in CMs in order to overcome the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of linear elastic material under vertical end point load. This can further be used as a building block in more complex compliant mechanisms. First, the governing equation has been obtained for the cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that affect the characteristics of the deflection have been examined. The results reveal that the proposed procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied to a large class of practical problems for the purpose of analysis and optimization.

Design of Planar Large-Deflection Compliant Mechanisms With Decoupled Multi-Input-Output Using Topology Optimization

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Benliang Zhu ◽  
Qi Chen ◽  
Hai Li ◽  
Hongchuan Zhang ◽  
Xianmin Zhang
Keyword(s):  
Topology Optimization ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Geometrical Nonlinearity ◽  
Method Comparison ◽  
Output Coupling ◽  
Large Displacements ◽  
Interpolation Scheme ◽  
Input Output ◽  
Output Behavior

This paper presents a method for topology optimization of large-deflection compliant mechanisms with multiple inputs and outputs by considering the coupling issue. First, the objectives of the design problem are posed by modeling the output loads using several springs to enable control of the input–output behavior. Second, a scheme is proposed to obtain a completely decoupled mechanism. Both input coupling and output coupling are considered. Third, with the implementation of an energy interpolation scheme to stabilize the numerical simulations, the geometrical nonlinearity is considered to appropriately capture the large displacements of compliant mechanisms. Finally, several numerical examples are presented to demonstrate the validity of the proposed method. Comparison studies with the obtained results without considering the coupling issues are also presented.

On the effective elastic moduli of carbon nanotubes for nanocomposite structures

2004 ◽  
Vol 35 (2) ◽  
pp. 95-101 ◽  
Author(s):  
Kin-Tak Lau ◽  
Mircea Chipara ◽  
Hang-Yin Ling ◽  
David Hui
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Moduli ◽  
Effective Elastic Moduli ◽  
Nanocomposite Structures

Analytical investigation on nonlinear dynamic behavior and free vibration analysis of laminated nanocomposite plates

2019 ◽  
Vol 233 (19-20) ◽  
pp. 6866-6878 ◽  
Author(s):  
Nguyen Dinh Khoa ◽  
Pham Dinh Nguyen
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Analytical Investigation ◽  
Functionally Graded ◽  
Geometrical Parameters

This work presents the results of the dynamic behavior and natural frequencies of laminated polymer plates that are reinforced by carbon nanotubes. The laminated nanocomposite plates have two components: carbon nanotubes reinforced in different polymer matrices. The nonlinear equations are obtained by Reddy's third-order laminated plate theory with von Kármán's geometrical nonlinearity and solved by both Runge–Kutta and Galerkin methods. Detailed studies for the influences of carbon nanotubes' different types of reinforcements and weight fractions, geometrical parameters, Winkler and Pasternak foundations on the deflection–time curves, and natural frequencies of laminated functionally graded carbon nanotube-reinforced composite plates are examined.

scholarly journals A Pseudo-Rigid-Body Model for Large Deflections of Fixed-Clamped Carbon Nanotubes

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Larry L. Howell ◽  
Christopher M. DiBiasio ◽  
Michael A. Cullinan ◽  
Robert M. Panas ◽  
Martin L. Culpepper
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Molecular Simulations ◽  
Design Parameters ◽  
Body Model ◽  
Initial Design ◽  
Rigid Body Model

Carbon nanotubes (CNTs) may be used to create nanoscale compliant mechanisms that possess large ranges of motion relative to their device size. Many macroscale compliant mechanisms contain compliant elements that are subjected to fixed-clamped boundary conditions, indicating that they may be of value in nanoscale design. The combination of boundary conditions and large strains yield deformations at the tube ends and strain stiffening along the length of the tube, which are not observed in macroscale analogs. The large-deflection behavior of a fixed-clamped CNT is not well-predicted by macroscale large-deflection beam bending models or truss models. Herein, we show that a pseudo-rigid-body model may be adapted to capture the strain stiffening behavior and, thereby, predict a CNT’s fixed-clamped behavior with less than 3% error from molecular simulations. The resulting pseudo-rigid-body model may be used to set initial design parameters for CNT-based compliant mechanisms. This removes the need for iterative, time-intensive molecular simulations during initial design phases.

An analytical approach on nonlinear mechanical and thermal post-buckling of nanocomposite double-curved shallow shells reinforced by carbon nanotubes

2018 ◽  
Vol 233 (11) ◽  
pp. 3888-3903 ◽  
Author(s):  
Nguyen Dinh Duc ◽  
Pham Dinh Nguyen ◽  
Nguyen Huy Cuong ◽  
Nguyen Van Sy ◽  
Nguyen Dinh Khoa
Keyword(s):  
Carbon Nanotubes ◽  
Amorphous Polymer ◽  
Geometrical Nonlinearity ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Shallow Shells ◽  
Elastic Foundations ◽  
Nonlinear Mechanical ◽  
Post Buckling ◽  
The Galerkin Method

This work presents the nonlinear mechanical and thermal post-buckling of nanocomposite double-curved shallow shells reinforced by single-walled carbon nanotubes resting on elastic foundations based on the higher order shear deformation theory with geometrical nonlinearity in von Karman–Donnell sense. The composite shells are made of various amorphous polymer matrices: poly(methyl methacrylate) (PMMA) and poly{(m-phenylenevinylene)-co-[(2,5-dioctoxy-p-phenylene) vinylene]} (PmPV). The governing equations are solved by the Galerkin method and Airy's stress function to achieve mechanical and thermal post-buckling behaviors of nanocomposite double-curved shallow shells. Various types of distributions of carbon nanotubes, both uniform distributions, and functionally graded distributions are examined. The material properties of nanocomposite double-curved shallow shells are assumed to be temperature dependent. Detailed parametric studies are carried out on the effect of various types of distribution and volume fractions of carbon nanotubes, temperature increments, elastic foundations, edge to radius and edge to thickness ratios on the nonlinear mechanical and thermal post-buckling of nanocomposite double-curved shallow shells reinforced by CNTs.

scholarly journals Large Deflection of Prismatic Cantilever Beam Exposed to Combination of End Inclined Force and Tip Moment

2017 ◽  
Vol 12 (1) ◽  
pp. 98 ◽  
Author(s):  
Ibrahim Abu-Alshaikh ◽  
Hashem S. Alkhaldi ◽  
Nabil Beithou
Keyword(s):  
Numerical Solution ◽  
Cantilever Beam ◽  
Large Deflection ◽  
Elliptic Integral ◽  
Geometrical Nonlinearity ◽  
Closed Form Solution ◽  
Form Solution ◽  
Integration Constant ◽  
Computational Time ◽  
Special Cases

The large deflection of a prismatic Euler-Bernoulli cantilever beam under a combination of end-concentrated coplanar inclined force and tip-concentrated moment is investigated. The angle of inclination of the applied force with respect to the horizontal axis remains unchanged during deformation. The cantilever beam is assumed to be naturally straight, slender, inextensible and elastic. The large deflection of the cantilever beam induces geometrical nonlinearity; hence, the nonlinear theory of bending and the exact expression of curvature are used. Based on an elliptic integral formulation, an accurate numerical solution is obtained in terms of an integration constant that should satisfy the boundary conditions associated with the cantilever beam. For some special cases this integration constant is exactly found, which leads to closed form solution. The numerical solution obtained is quite simple, accurate and involves less computational time compared with other techniques available in literature. The details of elastica and its corresponding orientation curves are presented and analyzed for extremely large load combinations. A comparative study with pre-obtained results has been made to verify the accuracy of the presented solution; an excellent agreement has been obtained.

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