Journal of Theoretical and Applied Mechanics

Volume 36, Number 1, 2006



M. Hasan, L. Lilov


Faculty of Mathematics and Informatics, Sofia University “St. Kl. Ohridski”,

5, James Bourchier Blvd, 1164 Sofia, Bulgaria,






Abstract. Compliant mechanisms are widely used in MEMS (Micro-Electro-Mechanical Systems). Their motion is partially or completely generated by the flexibility of some or its entire links, most often considered being large-deflection beams. In this way the task of finding the end-point position of elastic beam (cantilever) is one of the important problems in this field. There are a lot of methods of solving analytically or numerically this problem such as elliptic integrals, finite element methods or by expensive trial and error methods. The known analytical solutions involve simultaneously at least two elliptic functions what make them cumbersome and inconvenient for application. In this paper closed-form solutions using solely one elliptic function are presented.


Key words: flexure (elastic) hinge, compliant mechanism, elastic beam.


G. Peev,


University of Chemical Technology and Metallurgy,

8, St. Kliment Ohridski Blvd, Sofia 1756, Bulgaria,



M. Spasova, R. Mincheva, I. Rashkov


Institute of Polymers, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 103A, Sofia 1113, Bulgaria,

e- mail:




Abstract. A simplified model for predicting the diameter of electrospun fibers is proposed. It accounts for the major forces acting on the straight part of the liquid jet. Its application is based on easily measured characteristics of the spinning process (pump throughput, radius of the straight jet and of the obtained fibers, surface velocity of the jet, needle radius, solution concentration and viscosity, electric field potential, density of polymer and solvent). The model allows evaluating the shear stress and shear rate of the jet flow, as well as the degree of jet elongation in the whipping cone. Five sets of experimental data taken from the literature have been used to assess the model adequacy. The preliminary results are encouraging and evoke specially designed experiments for further model support.


Key words: electrospinning, modelling, predicting the fiber diameter.


Jordan G. Brankov, Nadezhda Zh. Bunzarova


Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str., Bl. 4, Sofia 1113, Bulgaria,





Abstract. The applicability of the theory of Finite-Size Scaling (FSS) to second-order phase transitions far from equilibrium is checked against exact asymptotic results for the 1D Totally Asymmetric Simple-Exclusion Process (TASEP) on chains of L sites with open boundaries. The particles hop to empty sites to the right with probability p, a particle can be injected at the left end with probability  and removed at the right end with probability . It is established that close to the transition point  between the low-density and maximum-current stationary phases the analog of the equilibrium free energy density has a universal FSS form as a function of , where  and , so that . The parameters  and  are different for discrete-time and continuous-time dynamics. A recent interpretation of the normalization factor  for the steady state probability distribution as an equilibrium partition function of weighted lattice paths is used to define a new order parameter, which obeys FSS with a new critical exponent.


Key words: statistical mechanics, stochastic processes, onedimensional models, thermodynamics of phase transitions, nonequilibrium stationary states, finite-size scaling.


M. F. Robbe, C. Strub, P. Galon


Commissariat à l’Energie Atomique de Saclay,

Bât 120, 91191 Gif sur Yvette cedex, France,



B. Dolensky


Forschungszentrum Karlsruhe GmbH, Institut für Reaktorsicherheit,

Postfach 3640, 76021 Karlsruhe, Germany


overview of German and French works relative to slug impact. Part 2: numerical results


Abstract. One of the hypothetical severe accidents studied in nuclear reactors is the upward acceleration of a slug of molten fuel and its impact against the upper head of the reactor vessel. The impact may cause a failure of the head and lead to missiles endangering the reactor containment.

Slug impact is studied by the German and French research centres FZK and CEA-Saclay. FZK tries to quantify the maximum energy that the reactor upper head is able to withstand, by means of the reduced-scale experiments BERDA.

In order to deepen the understanding of the impact process and to extrapolate the experimental results to other combinations of parameters, corresponding theoretical work is performed with the ABAQUS code for the impact of solid structures and the study of the structure response, and the EUROPLEXUS code for the impact of liquid projectiles.


Key words: impact, nuclear reactor, numerical simulation, particle model.