Journal of
Theoretical and Applied Mechanics
Volume
34, Number 3, 2004
G.
Lebon
17
Allée du 6 Aout, Sart Tilman B5, B 4000 Liège, Belgique,
e-mail:
g.lebon@ulg.ac.be
Acad.
G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria,
e-mail:
baltov@eagle.cu.bas.bg
M. Grmela
University
of Montreal, Ecole Polytechnique, Génie Chimique,
e-mail: miroslav.grmela@
polymtl.ca
EXTENDED THERMODYNAMICS OF THERMO-ELASTICITY,
VISCO-ELASTICITY AND VISCO-PLASTICITY
Abstract. The objective of this paper is to propose an original description of thermo-elasticity, visco-elasticity and visco-plasticity based on Extended Irreversible Thermodynamics. Although the latter has been widely used as a support of fluid mechanics, this work is a first attempt to apply this thermodynamic formalism to deformable solids. After a short recall of the bases and tenets of Extended Irreversible Thermodynamics, we consider as a first application the problem of thermo-elasticity, i.e. the simplest coupling between heat transport and deformation. The most original result is that the classical Fourier law is substituted by a Cattaneo equation allowing for the effects of inertia. In a second part, one examines the more complex behaviour of visco-elastic bodies before dealing, in a further section, with the problem of visco-plasticity. The originality of the present description compared to more classical treatments is emphasised. It is shown that Extended Irreversible Thermodynamics opens the way to a simple and attractive approach of these important aspects of continuum mechanics and that, contrarily to some criticisms, it accommodates the case of deformable solids.
Key words: thermodynamics, thermo-elasticity, visco-elasticity, visco-plasticity.
Democritus University of Thrace, Dept. Civil Engineering & Dept. of Environment Engineering, GR-67100 Xanthi, Greece,
e-mail:
liolios@civil.duth.gr
S.
Radev, T. Angelov
Institute of Mechanics,
Bulgarian Academy of Sciences,
Acad. G. Bonchev Str., Bl.
4, 1113 Sofia, Bulgaria,
e-mail: stradev@imbm.bas.bg, taa@imbm.bas.bg
NONCONVEX
NUMERICAL APPROACH TO THE SEISMIC SOIL-PIPELINE INTERACTION UNDER INSTABILIZING
ENVIRONMENTAL EFFECTS
Abstract. A numerical
approach is presented for an hemivariational inequality problem arising in
structural engineering. This problem concerns the dynamic soil-pipeline
interaction under soil degradation caused by environmental effects. Unilateral
contact conditions due to tensionless and elastoplastic softening-fracturing
behaviour of the soil as well as due to gapping are taken into account. The
numerical approach is based on a double discretization, in space by FEM and /or
BEM and in time, and on nonconvex optimization. So the number of the problem
unknowns is significantly reduced and a nonconvex linear complementarity
problem is solved in each time-step.
Key words: soil-pipeline interaction, hemivariational inequality problem, numerical approach.
Institute of Mechanics,
Bulgarian Academy of Sciences,
Acad. G. Bonchev Str., Bl.
4, 1113 Sofia, Bulgaria,
e-mail: Lusy@imbm.bas.bg
FEM
MODELLING OF THERMO-MECHANICAL BEHAVIOUR OF TWO-PHASE LAMINATED PLATES
Abstract. The FEM is used
to study the thermoelastic behaviour of a two-phase functionally graded plate
at high temperature loading. The layers are distributed exponentially through
the plate thickness. The ceramic phase is brittle elastic with different
tensile and compression strength limits. The metallic phase is elastic-plastic.
The thermal and mechanical properties of both materials strongly depend on
temperature. Several failure criteria at different boundary conditions are
applied to predict the stable state of the structures of interest. The optimal
design is based on two cost functions, comparing stress-strain fields and
temperature variations corresponding to different layer distributions or volume
concentrations.
Key
words:
functionally graded laminated plates, thermal loading, optimal design.
Institute of Mechanics,
Bulgarian Academy of Sciences,
Acad. G. Bonchev Str., Bl.
4, 1113 Sofia, Bulgaria,
e-mail: iankovr@yahoo.com,
datcheva@imbm.bas.bg
Acad. G. Bonchev Str., Bl.
8, 1113 Sofia, Bulgaria,
e-mail: epopova@iph.bio.bas.bg
Coudraystrasse 11C, D-99423
Weimar, Duetschland,
e-mail: tom.schanz@bauing.uni-weimar.de
Numerical modelling of consolidation with uncertainty
in soil properties
Abstract. A coupled
hydro-mechanical problem with an uncertain parameter is presented. Application
of interval methods of obtaining of sharp safety regions for the response
variables under a worst case scenario and for a sensitivity analysis of the
mechanical system is demonstrated. A boundary value problem for one-dimensional
consolidation under a constant load where the elastic modulus of the solid
skeleton is assumed to be uncertain and varying within prescribed bounds is
solved. Deterministic and interval solutions are obtained and analysed.
Key words: soil, consolidation,
interval arithmetic.
V.
Petrov, E. Nikolova
Institute
of Mechanics, Bulgarian Academy of Sciences,
Acad.
G. Bonchev Str., Bl.4, 1113 Sofia, Bulgaria,
e-mail:
valko@imbm.bas.bg
J.
Timmer
Centre
for Data Analysis and Modelling, University of Freiburg,
Eckerstr.
1, 79104 Freiburg, Germany,
e-mail:
jeti@fdm.uni-freiburg.de
Dynamical
analysis of cell function models.
A Review
Abstract. The system
analysis of cell functions and especially mitosis (growth and division) in
eukaryotes is so complex that it defies understanding by verbal arguments only.
The insight into details of biochemical kinetics of cell functions requires
mathematical modeling of the type practiced in the classical dynamics, i. e. by
differential equations. In this paper we review dynamical modeling of cell
signal pathways and more in detail - division in eukaryotes. The recent
development of dynamical synthesis and analysis of cell function models is
described in general terms, and molecular mechanisms of mitosis control are
presented verbally. The transition from verbal to mathematical description of
Novak-Tyson model of mitosis control is considered, in order to illustrate “in
action” the application of dynamical modelling to the cell cycle process.
Moreover, a subtle dilemma of bistable or self-oscillatory character of cell
cycle is discussed in terms of the theory of dynamical systems.
Key words: dynamical system,
signal transduction, function control.
V. Kavardzhikov, N. Kounov, K. Prodanov
Institute of Mechanics, Bulgarian
Academy of Sciences,
Acad. G. Bonchev Str., Bl.4, 1113 Sofia, Bulgaria,
e-mail: kavarj@lmbm.bas.bg
A
SCANNING LASER PHOTOMETRIC TECHNIQUE FOR INVESTIGATION OF ERYTHROCYTE
SEDIMENTATION
Abstract. A scanning
laser densitometer is elaborated, which is designed for an effective
investigation of blood samples with hematocrit values layng in the interval 30%-65%. The
densitometer is used for obtaining of blood samples sedimentation pictures after a
precise adjustment and callibration. One of these pictures is demonstrated as
an example. Density fluctuations of sedimenting erythrocyte substantion, having
relatively high spatial frequences, are clearly visualized and monitored for a
first time.They reveal a structure formation in the sediment during the first
two hours of sedimentation process. A numerical processing and
parametrisation of the sedimentation pictures utilizing
unitary Karhunen-Loeve transformation is carried out.
Key
words: laser scanning densitometer, erythrocyte sedimentation picture, Karhunen-Loéve tranformation.