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Relevant analyses are presented on the base of the compressible vortex method for simulating the development of two or three co-rotating vortices with different characteristic Mach numbers. The paper aims to discuss this issue.

In addition to having vorticity and dilatation properties, the vortex particles also carry density, enthalpy, and entropy. Taking co-rotating vortices in two-dimensional unsteady compressible flow for an example, truncation of unbounded domains via a nonreflecting boundary condition was considered in order to make the method computationally efficient.

For two identical vortices, the effect of the vortex Mach number on merging process is not evident; if two vortices have the same circulation rather than different radiuses, the vorticity and dilatation fields of the vortex under a vortex Mach number will be absorbed by the vortex under a higher vortex Mach number. For three vortices, if the original arrangement of the vortices is changed, the evolvement of the vorticity and dilatation fields is different.

The paper reveals new mechanism of the three co-rotating vortices by a feasible compressible vortex method.

The purpose of this paper is to present a new device (thermoelastic actuator) for accurate control of position whose principle is based on thermal dilatation of its working unit brought about by induction heating.

The device must satisfy the prescribed operation parameters (mainly the above thermal dilatation). The task to find them is a multiply coupled problem (interaction of electromagnetic field, temperature field and field of thermoelastic displacements) that is solved by the finite element method supplemented with a number of other procedures.

The control of position based on the described thermoelastic effect is very accurate and ranges from 1×10⁻⁶ to 1×10⁻³ m.

The device also contains two self‐locking friction clutches of conical shapes whose purpose is to fix the position of the plunger in the prescribed position. Further attention should be paid to their dynamic behaviour during the process of fixing.

The device can be used in various technical domains such as optics and laser or microscope techniques.

The principal part of the device contains no movable element, which is a substantial advantage in comparison to other systems based on mechanical, hydraulic or pneumatic principles working with movable elements or media.

The paper starts with a review of constitutive equations for rubber‐like materials, formulated in the invariants of the right Cauchy—Green deformation tensor. A general framework for the derivation of the stress tensor and the tangent moduli for invariant‐based models, for both the reference and the current configuration, is presented. The free energy of incompressible rubber‐like materials is extended to a compressible formulation by adding the volumetric part of the free energy. In order to overcome numerical problems encountered with displacement‐based finite element formulations for nearly incompressible materials, three‐dimensional finite elements, based on a penalty‐type formulation, are proposed. They are characterized by applying reduced integration to the volumetric parts of the tangent stiffness matrix and the pressure‐related parts of the internal force vector only. Moreover, hybrid finite elements are proposed. They are based on a three‐field variational principle, characterized by treating the displacements, the dilatation and the hydrostatic pressure as independent variables. Subsequently, this formulation is reduced to a generalized displacement formulation. In the numerical study these formulations are evaluated. The results obtained are compared with numerical results available in the literature. In addition, the proposed formulations are applied to 3D finite element analysis of an automobile tyre. The computed results are compared with experimental data.

The purpose of this paper is to investigate the parameters and operation characteristics of an actuator working on the principle of thermoelasticity whose structure was designed by the authors.

The mathematical model of the system describes the effects of three physical fields (electromagnetic field, temperature field, and field of mechanical strains and stresses due to thermoelasticity). While the electromagnetic field was solved independently, the thermomechanical task in common with the contact problem was solved in the hard‐coupled formulation. The computations were mostly carried out by own codes.

This type of actuator is characterized by extremely high forces acting in its dilatation element.

The parameters of the system may still be improved using a longer field coil and dilatation element. Attention has to be paid, however to the mechanical stability of the system. Another improvement could be achieved by suitably designed cooling of the coil that would allow increasing parameters of the field current (its frequency or amplitude).

The device is promising for various fixing tasks in the industrial environment.

Although the methods of numerical processing of particular fields are known, the paper provides an algorithm for their simultaneous solution while respecting the temperature dependencies of the material properties and continuous change of the contact surfaces.

The transformation of France under De Gaulle from the “sick man of Europe” with governments changing every few months, to one of the world's strongest economies, holds lessons for us all. Of course France's virtual self‐sufficiency in food and fuel always ensured an eventual resurgence under a strong and stable government. We thought of this recently on a trip to Western Provence, the oldest part of France and one off the beaten tourist track. It was one of the earliest provinces of Imperial Rome and in each settlement the Romans tried to reproduce a petite Rome, with arena, theatre, baths and villas, so that many Provencal towns have as many Roman antiquities as Rome itself. In its beauty of line and colour, its architecture, clustered villages on hilltops and the tall Lombardy pines, the countryside looks Italian, but the people seem unlike the Italian, Spanish or French. We thought them descendants of the ancient Gaul, whose tribes settled all over Western Europe, from the shores of the Mediterranean to Galway Bay.

The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set‐distance function in such spaces provides a particular kind of space‐time‐like structure which favors the aggregation of such deformations into fractal forms standing for massive objects. A correlative dilatation of space appears outside the aggregates. At large scale, this dilatation results in an apparent expansion, while at submicroscopic scale the families of fractal deformations give rise to families of particle‐like structure. The theory predicts the existence of classes of spin, charges and magnetic properties, while quantum properties associated with mass have previously been shown to determine the inert mass and the gravitational effects. When applied to our observable space‐time, the model would provide the justifications for the existence of the creation of mass in a specified kind of void, and the fractal properties of the embedding lattice extend the phenomenon to formal justifications of big‐bang‐like events without any need for supply of an extemporaneous energy.

The object of the paper is to illustrate how to obtain the topological derivative as a semidifferential in a general and practical mathematical setting for d-dimensional perturbations of a bounded open domain in the n-dimensional Euclidean space.

The underlying methodology uses mathematical notions and powerful tools with ready to check assumptions and ready to use formulas via theorems on the one-sided derivative of parametrized minima and minimax.

The theory and the examples indicate that the methodology applies to a wide range of problems: (1) compliance and (2) state constrained objective functions where the coupled state/adjoint state equations appear without a posteriori substitution of the adjoint state.

Direct approach that considerably simplifies the analysis and computations.

It was known that the shape derivative was a differential. But the topological derivative is only a semidifferential, that is, a one-sided directional derivative, which is not linear with respect to the direction, and the directions are d-dimensional bounded measures.

Granular flow lubrication is developed in recent years as a new lubrication method which can be used in extreme environments, while the stick-slip mechanisms of granular flow lubrication are an urgent obstacle remains unsolved in fully establishing the granular flow lubrication theory.

A granular flow lubrication research model is constructed by the discrete element method. Using this numerical model, the mesoscopic and macroscopic responses of stick-slip that influenced by the shear velocity, and the influence of the shear velocity and the normal pressure on the vertical displacement are studied.

Research results show that movement states of granular flow lubrication medium gradually transform from the stick-slip state to the sliding state with increased shear velocity, in which these are closely related to the fluctuations of force chains and friction coefficients between granules. The stick-slip phenomenon comes up at lower shear velocity prior to the appearance of granular lift-off between the two friction pair, which comes up at higher shear velocity. Higher normal pressure restrains the dilatation of the granular flow lubrication medium, which in turn causes a decrease in the displacement.

These findings reveal the stick-slip mechanism of granular flow lubrication and can also offer the helpful reference for the design of the new granular lubrication bearing.

Direct copper bonded (DCB) alumina substrates are among sophisticated technical materials suitable for application in electronics, automotive and engineering industries. DCB substrates resist very severe operational conditions and assure high reliability. This technology provides alumina substrates which are very strongly bonded to copper foil, due to the solidified eutectic alloy Cu2O‐Al2O3 or a suitable vitreous solder. Such substrates are ideal for the construction of elements in microelectronics hybrid circuits, power circuits and devices. As the bonding layer of a solidified eutectic or vitreous solder is very thin, the thermal resistivity stays sufficiently low; in addition, the dilatation properties of DCB substrates are close to those of silicon. This enables soldering of large silicon chips without the risk of creating mechanical stress and allows for the production of devices with very high construction effectivity. Examples of such applications are potential‐free modules, bridge circuits, automotive ignition modules and Peltier elements. The vitreous bonding layers are advantageous for certain applications. State‐of‐the‐art DCB bonding technology was developed for DCB aluminium nitride substrates, which have even better thermal qualities.

The non uniform temperature fields in the cross section of the structural elements exposed to fire cause thermal dilatations which induce internal forces. In same time temperature changes cause longitudinal elongations and if these elongations are restricted, additional axial stresses will be induced. In this case the various support conditions can have a significant influence on fire resistance of reinforced concrete elements. In this paper three different support conditions as: pin-pin, pin-fixed and fully fixed were used to model RC beams with various level of axial restraint. The beams were exposed to the ISO-fire curve. The numerically obtained results are presented and based on these results it can be concluded that increasing of axial spring stiffness increases the induced axial forces and the fire resistance of the beams.