On the Modelling of Carbon Nano Tubes as Generalized Continua

Aminpour, Hossein; Rizzi, Nicola Luigi

doi:10.1007/978-3-319-31721-2_2

Cited by 18 publications

(4 citation statements)

References 18 publications

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“…he generalizations consists in introducing some extra kinematical descriptors to include in the picture the effects of such changes. The principle of virtual work plays a relevant role also in the deduction of evolution equations for reduced‐order one‐dimensional continuum models: the reader is referred for instance to the papers and references cited therein for some examples of the application of such deduction processes.…”

Section: Annotated Translation Of No 3 (Pp 611–622)mentioning

confidence: 99%

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”^** by E. Hellinger

Eugster

Dell’Isola

2016

Z Angew Math Mech

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The fundamental review article DIE ALLGEMEINEN ANSÄTZE DER MECHANIK DER KONTINUA in the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. IV‐4, Hft. 5 (1913) by Ernst Hellinger has not been translated into English so far. We believe that such a circumstance is really deprecative, as the insight reached by Hellinger in the mathematical structure of continuum mechanics seems, in some aspects, unsurpassed even nowadays. Hellinger's scientific manuscripts do not fill more than one and half boxes in library storage , but their impact on mathematics and mechanical sciences is profound. Indeed, the Hellinger‐Reissner variational principle is still a fundamental tool in theoretical and numerical mechanics. The intent of this paper is threefold: i) to allow to those who cannot understand German to enjoy the reading of a crystal‐clear and still topical article whose content has some enlightening parts, ii) to show that only one century ago the principle of virtual work (or virtual velocities) was regarded as the central principle in continuum mechanics and that Hellinger did forecast already then the main lines of its development, iii) to discuss some technical and conceptual aspects of the variational principles in continuum mechanics which some authors consider still controversial.

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Section: Annotated Translation Of No 3 (Pp 611–622)mentioning

confidence: 99%

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”^** by E. Hellinger

Eugster

Dell’Isola

2016

Z Angew Math Mech

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“…In the study of micro-structured materials, some problems of buckling can arise for the complexity of the micro-structure. Some methods to address these issues can be found in, for example, [36,37]. Numerical methods have been developed to analyze particular classes of lattices: one can refer to [38–44] for some basic ideas that can be also used to improve simulations of systems similar to the one investigated in this work.…”

Section: Discussionmentioning

confidence: 99%

Shear horizontal waves in composite materials: Behavior under rotation and initial stress

Abd-alla

Othman

Hasbullah

2017

Mathematics and Mechanics of Solids

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The main scope of this paper is to present in a simple and concise way a mathematical model of composite materials able to describe the propagation of shear horizontal waves in the case where composite is rotating and subjected to an initial stress. This work is aimed at the relevant possibility to apply the obtained results for the establishment of highachievement applications of piezoelectric and semiconductor composites and surface acoustic waves devices. We conclude by analyzing numerical computations in which the influence of the rotation, initial stress and electromagnetic boundary conditions are graphically observed.

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“…The present paper investigates the dynamics of a 1D continuum which is intended as the homogenized limit of a discrete mechanical system consisting of masses connected by nonlinear springs and a pantographic microstructure. The study of different kinds of microstructures, which are today much easier to obtain thanks to the possibility of driving the manufacturing process by means of computers [1], has led to the development of new models in continuum mechanics (apart from classical works such as [2,3], the reader can find interesting results in [4][5][6][7][8][9][10][11]). The pantographic microstructure (for a detailed description see [12,13]) is particularly interesting because it is at the same time very simple in principle but still leads to homogenized continua that are beyond the scope of classical continuum models (see [14,15] for convergence theorems involving structures of this type).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of 1D nonlinear pantographic continua

2016

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In this paper a mechanical system consisting of a chain of masses connected by nonlinear springs and a pantographic microstructure is studied. A homogenized form of the energy is justified through a standard passage from finite differences involving the characteristic length to partial derivatives. The corresponding continuous motion equation, which is a nonlinear fourth-order PDE, is investigated. Traveling wave solutions are imposed and quasi-soliton solutions are found and numerically compared with the motion of the system resulting from a generic perturbation.

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On the Modelling of Carbon Nano Tubes as Generalized Continua

Cited by 18 publications

References 18 publications

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”^** by E. Hellinger

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”^** by E. Hellinger

Shear horizontal waves in composite materials: Behavior under rotation and initial stress

Dynamics of 1D nonlinear pantographic continua

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On the Modelling of Carbon Nano Tubes as Generalized Continua

Cited by 18 publications

References 18 publications

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger

Shear horizontal waves in composite materials: Behavior under rotation and initial stress

Dynamics of 1D nonlinear pantographic continua

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Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”^** by E. Hellinger

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”^** by E. Hellinger