Variational Convergences of Dual Energy Functionals for Elastic Materials with a ε-Thin Strong Inclusion

We give a new derivation, based on the complementary energy formulation, of a simplified model for a multi-structure made up of two anisotropic hyper-elastic bodies connected by a thin strong material layer. The model is obtained by identifying the Mosco-limit of the stored complementary energy functional when the thickness is of order ?? and the stiffness of order 1/?? where ?? is a positive real adimensional parameter. In order to prove the existence of the displacement associated with the stress we use a suitable weak version of the Saint-Venant compatibility condition also known as Donati??s theorem.     

On the Flexure of a Saint-Venant Cylinder

The flexure of a Saint-Venant cylinder is defined from a kinematic point of view. A complete solution for the field equations is provided and the gauge choices to define the center of shear and rotation are made consequently. This seems to eliminate some ambiguities present in the literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

A review of the problem of the shear centre(s)

The problem of defining and determinating the shear centre is present in the literature since the first decades of this century. It soon interlaced with the definition of the twist centre and their ways became unextricable in the following decades. A number of researchers dealt with this subject meeting with variable issues, yet in the authors' opinion it seems of some interest to run through it again. In this paper a general survey of the literature is performed and the two definitions of the shear centre (here named kinematic and energetic) are compared. It is remarked how the energetic definition for the shear centre makes it coincide with a suitably chosen twist centre. An example is given to show that the two definitions generally fail to provide the same place even for simple cross sections. It is shown that the two definitions provide the same place, using standard approximate formul?, in the case of thin-walled mono-connected sections with regularly varying thickness and two-connected sections with constant thickness. As a new result, it will be shown that the two definitions of shear centre do not provide the same place for thin-walled sections with connection higher than two even in the trivial case of uniform thickness; an example is given. Received November 25, 1997     

Postcritical Behavior of Cables Undergoing Two Simultaneous Galloping Modes

Abstract. A nonlinear two degree-of-freedom model, describing a flexible elastic suspended cable undergoing galloping oscillations, is analyzed. By using a perturbative approach, the critical conditions occuring for different values of the aerodynamic coefficients are described. Two different type of critical conditions, corresponding to simple or double Hopf bifurcations are found. The nonlinear postcritical behavior of single taut strings in 1:1 primary internal resonance is studied through the multiple scale perturbation method. In the double Hopf bifurcation case the influence of the detuning between the critical eigenvalues on the postcritical behavior is illustrated. It is found that quasi-periodic motions, which are likely to occur in the linear field when the two critical frequencies are incommensurable, are really unstable in the nonlinear range. Therefore, the postcritical behavior of the string consists of stable periodic motions for any detuning values.Sommario. Viene analizzato un modello non lineare a due gradi di libertrappresentativo di un cavo elastico flessibile sospeso alle estremite soggetto ad oscillazioni galoppanti. Utilizzando un approccio perturbativo, vengono descritte le condizioni critiche per differenti valori dei coefficienti aerodinamici. Sono presenti due diversi tipi di condizioni critiche, corrispondenti a biforcazioni di Hopf semplici e doppie. Attraverso il metodo perturbativo delle scale multiple viene studiato il comportamento post-critico non lineare di singole stringhe tese in risonanza interna primaria 1:1. Nel caso di biforcazione doppia di Hopf viene illustrata l'influenza del detuning tra gli autovalori critici sul comportamento post-critico. Si trova che i moti quasi-periodici, presenti in campo lineare quando le due frequenze critiche sono incommensurabili, sono in realtinstabili in campo non lineare. Quindi, il comportamento post-critico della stringa risulta composto da moti periodici stabili per un qualsiasi valore del detuning.     

Analytical study of spherical cloak/anti-cloak interactions

The intriguing concept of “anti-cloaking” has been recently introduced within the framework of transformation optics (TO), first as a “countermeasure” to invisibility-cloaking (i.e., to restore the scattering response of a cloaked target), and more recently in connection with “sensor invisibility” (i.e., to strongly reduce the scattering response while maintaining the field-sensing capabilities). In this paper, we extend our previous studies, which were limited to a two-dimensional cylindrical scenario, to the three-dimensional spherical case. More specifically, via a generalized (coordinate-mapped) Mie-series approach, we derive a general analytical full-wave solution pertaining to plane-wave-excited configurations featuring a spherical object surrounded by a TO-based invisibility cloak coupled via a vacuum layer to an anti-cloak, and explore the various interactions of interest. With a number of selected examples, we illustrate the cloaking and field-restoring capabilities of various configurations, highlighting similarities and differences with respect to the cylindrical case, with special emphasis on sensor-cloaking scenarios and ideas for approximate implementations that require the use of double-positive media only.     

Hydrodynamic Green functions: paradoxes in unsteady Stokes conditions and infinite propagation velocity in incompressible viscous models

Meccanica - We present a simple representation of the hydrodynamic Green functions grounded on the free propagation of a vector field without any constraints (such as incompressibility) coupled...     

A numerical methodology for thermo-fluid dynamic modelling of tyre inner chamber: towards real time applications

Meccanica - The characterization and reproduction of tyre behaviour for vehicle modelling is a topic of particular interest both for real-time driver in the loop simulations and for offline...     

An original perspective on variable-order fractional operators for viscoelastic materials

Meccanica - This work deals with viscoelastic constitutive models involving variable-order fractional operators. There exist two main fractional models in the literature representing the...