Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures–including high strength, high stiffness, low density and structural perfection–could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young’s modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references. @DOI: 10.1115/1.1490129#

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Mechanics of carbon nanotubes

This review presents the potential that lattice ~or spring network! models hold for micromechanics applications. The models have their origin in the atomistic representations of matter on one hand, and in the truss-type systems in engineering on the other. The paper evolves by first giving a rather detailed presentation of one-dimensional and planar lattice models for classical continua. This is followed by a section on applications in mechanics of composites and key computational aspects. We then return to planar lattice models made of beams, which are a discrete counterpart of non-classical continua. The final two sections of the paper are devoted to issues of connectivity and rigidity of networks, and lattices of disordered ~rather than periodic! topology. Spring network models offer an attractive alternative to finite element analyses of planar systems ranging from metals, composites, ceramics and polymers to functionally graded and granular materials, whereby a fiber network model of paper is treated in considerable detail. This review article contains 81 references. @DOI: 10.1115/1.1432990#

Lattice models in micromechanics

Emerged in the middle of 20th century, composite materials are now one of the hotspot research topics in the modern technology. Their promising characteristics make them suitable for enormous applications in industrial field such as aerospace, automotive, construction, sports, bio-medical and many others. These materials reveal remarkable structural and mechanical properties such as high strength to weight ratio, resistance to chemicals, fire, corrosion and wear; being economical to manufacture. Herein, an overview of composite materials, their characterization, classification and main advantages linked to physical and mechanical properties based on the recent studies are presented. There, were presented the conventional manufacturing techniques of composite and their applications. It was highlighted the tremendous need to discovery new generation of composites that should incorporate the synthetic or natural materials by implementing new efficient manufacturing processes. In the combination of matrix and reinforcement materials, the use of natural materials as constituent are compulsory in order to obtain a complete material degradable as environmentally friendly.

Recent progress of reinforcement materials: a comprehensive overview of composite materials

https://hal.archives-ouvertes.fr/hal-01007419/document

Validity and limitations of linear analytical models for steel wire strands under axial loading, using a 3D FE model

Nonlinear dynamic analysis of a cantilever functionally graded materials (FGM) rectangular plate subjected to the transversal excitation in thermal environment is presented for the first time in this paper. Material properties are assumed to be temperature dependent. The nonlinear governing equations of motion for the FGM plate are derived based on Reddy’s third-order plate theory and Hamilton’s principle. The first two vibration mode functions satisfying the boundary conditions of the cantilever FGM rectangular plates are chosen to be the admissible displacement functions. Galerkin’s method is utilized to convert the governing partial differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms under combined external excitations. The present study focuses on resonance case with 1:1 internal resonance and subharmonic resonance of order 1/2. The asymptotic perturbation method is employed to obtain four nonlinear averaged equations which are then solved by using Runge–Kutta method to find the nonlinear dynamic responses of the plate. It is found that chaotic, periodic and quasi-periodic motions of the plate exist under certain conditions and the forcing excitations can change the form of motions for the FGM rectangular plate.

Nonlinear oscillation of a cantilever FGM rectangular plate based on third-order plate theory and asymptotic perturbation method

Theory of Wire Rope

The Behavior of Sandwich Structures of Isotropic and Composite Materials

Free vibrations of a cantilever beam with a spring-mass system attached to the free end

Transverse vibration of Bernoulli–Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution

In the present paper the Differential Quadrature Method, DQM, and the domain decomposition are used to carry out the free transverse vibration analysis of non-uniform multi-span rotating Timoshenko beams with perfect and not perfect boundary conditions. The cross section could vary in a continuous or discontinuous fashion along the beam length. The material of the beam could be different in each beam span. The influence of elastically clamped boundary conditions at hub end are studied and discussed. The effect of an arbitrary hub radius is considered. The governing differential equations of motion for rotating Timoshenko beams come from the derivation of Hamilton’s principle. The first six natural frequencies of vibration are obtained for many particular situations and for some of them the mode shapes are also available. The examples of applications of the method indicated its effectiveness. The results for particular cases are in excellent agreement with published results and results obtained by means of the finite element method.

Carlos Adolfo Rossit

Papers

Theory of Wire Rope

The Behavior of Sandwich Structures of Isotropic and Composite Materials

Free vibrations of a cantilever beam with a spring-mass system attached to the free end

Transverse vibration of Bernoulli–Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution

Transverse free vibration of non uniform rotating Timoshenko beams with elastically clamped boundary conditions