Journal of
Theoretical and Applied Mechanics

Volume
36, Number 1, 2006

**M****.**** H****asan****, L****.**** L****ilov**

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

*5*, *James Bourchier** Blvd** **1164
**Sofia**, **Bulgaria*

*e-mail*:* **ktfpuswe@yahoo.com*;* **lilov@fmi.uni-sofia.bg*

**CLOSED-FORM SOLUTION FOR LARGE-DEFLECTION BEAMS**

**IN COMPLIANT MECHANISMS**

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.

*University** of **Chemical** Technology and Metallurgy*,* *

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

*e-mail*: *g.a.peev@uctu.edu *

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

*e-** mail*: *rashkov@polymer.bas.bg*

**A SIMPLIFIED MODEL FOR PREDICTING THE DIAMETER OF
ELECTROSPUN FIBERS**

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.

*Institute** of **Mechanics** **Bulgarian** **Academy** of Sciences*,

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

e-mail: brankov@imbm.bas.bg, nadezhda@imbm.bas.bg

**F****INITE-SIZE**** ****SCALING**** ****AND**** ****UNIVERSALITY**** ****AT NONEQUILIBRIUM PHASE
TRANSITIONS REVISITET**

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*,

*e-mail*:* **marie-france.robbe@cea.fr*

*Forschungszentrum
Karlsruhe GmbH*, *Institut
für Reaktorsicherheit*,

**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.