Journal of Theoretical and Applied Mechanics
Volume 39, Number 2, 2009
Ivanka Stamova
Department
of Mathematics, Bourgas
Free University,
8000
e-mail: stamova@bfu.bg
Lyapunov
method for boundedness of the solutions of impulsive functional differential
equations with respect to sets
Abstract. In the present paper problems
related to the boundedness of the solutions of impulsive functional
differential equations with respect to sets of sufficiently general type are
considered. The investigations are carried out by means of piecewise continuous
functions, which are analogues to the classical Lyapunov functions coupled with
the Razumikhin technique.
Key words: impulsive functional
differential equations, boundedness of the solutions, Lyapunov method,
Razumikhim technique.
Stanimir Iliev, Nina
Pesheva
Acad.
e-mails: stani@imbm.bas.bg, nina@imbm.bas.bg
Dimitar Iliev
Department of Mathematics and
Informatics,
5,
e-mail: diliev@fmi.uni–sofia.bg
On the quasi-
Abstract.
The quasi-static motion of straight contact lines is considered in the
context of the “Wilhelmy plate” geometry: a vertical homogeneous solid plate is
withdrawn at constant velocity from a bath of liquid. We apply a model, which
takes into account explicitly the dissipation due to the moving contact line.
Asymptotic solutions are derived of the differential equations describing the
capillary rise height of the contact line and the contact angle relaxation. We
find that the time relaxation of the height and the cosine of the contact angle
are given by sums of exponential functions. The asymptotic solutions are
compared with experimental results and with numerically obtained solutions
which are based on lubrication theory with a correction factor for finite
contact angles.
Key words: relaxation, dissipative system
dynamics, dynamic contact angles.
L. Hadj-Taïeb, E. Hadj-Taïeb
Unité de
Recherche: Mécanique des
Fluides Appliquée et Modélisation,
ENIS, B.P.
W 3038
e-mails: lamjed@quebecemail.com;
Ezed.Hadj@enis.run.tn
EFFECT OF PIPE-WALL VISCOELASTIC
Abstract. A mathematical model has been
developed to calculate transient flows in viscoelastic pipes with vapour
cavitation. This model takes into account both the viscoelastic behaviour of
the pipe wall and the vapour cavitation phenomenon. When the liquid pressure
falls below the vapour pressure, a bubbly cavitating flow of homogeneous
liquid-vapour mixture occurs in some part of the pipeline. The mixture density
is expressed by means of a non linear expression of
the liquid volume fraction. The pipe wall behaviour is simulated based
on the mechanical principle by introducing additional viscoelastic term into
the mass balance fluid equation. The
application of mass and momentum conservation laws yields to a system of
hyperbolic partial differential equations. The later is resolved by the finite
differences scheme of Lax-Wendroff. The proposed
model is tested for transient flows with and without vapour cavitation. The
obtained numerical results are discussed and compared with experimental data.
Key words: transient flow, vapour cavitation,
viscoelastic pipe, finite differences, fluid-structure interaction.
M. Derras,
D. Tréheux
LTDS, UMR
36 av. Guy
de Collongue, 69134
e-mail:
Der_mok@hotmail.fr, Daniel.Treheux@ec-lyon.fr
B. Serier
LECM, Département de Génie
Mécanique, Université Djillali Liabes,
BP 89 Cité Larbi Ben M’hidi, Sidi
Bel Abbés 22000, Algérie,
e-mail:
boualems@yahoo.fr
Finite element analysis of
thermal residual stresses and fracture of metal/ceramic bonds
Abstract. In this study, a
finite element analysis was used to investigate the residual stress in a
nickel-alumina bimaterial. The rate-dependent inelastic behaviour of metal at
high temperature has been taken into consideration. The high value of these
residual stresses occurs on the ceramic side near to the interface, which may
result in failure by cracking away from the bond during the cooling stage of
the joining process. In order to understand the fracture behaviour of near
interface crack during the cycle of cooling, stress intensity factor and energy
release rate under thermal loading condition were evaluated.
Key words: bimaterial, alumina-nickel, bonding, creep, residual stress, crack.
M.
Elmeguenni, B. Bachir Bouiadjra, M. Benguediab, A. Mankour, A. Benhamena
Department of Mechanical Engineering,
BP 89, Cité Ben M’hidi, Sidi Bel Abbes, 22000,
e-mail: elmeguennimohamed@yahoo.fr
Finite element analysis of elastic–plastic interaction
effect of the microdefects near the
crack tip in confined plasticity
Abstract. In this study
the finite element method is used to analyse the effect of microdefect presence
near a main crack on the shape and the size variation of the plastic zone ahead
the main crack for small scale plasticity in Aluminium alloy 2024 T3. The
effects of the
horizontal and the vertical distance between the crack tip-microdefect on the plastic
zone are analysed. The obtained results show that the plastic zone
shape and size ahead the crack tip are very influenced by the microdefect
presence. Furthermore, the shape and size of the plastic zone ahead the crack
tip are very influenced by the presence of the inclusion. The reduction rate of
the plastic zone size can exceed 75% in the close vicinity of the crack tip.
The presence of the
microcavity affects in very significant way the shape and the size of the crack
plastic zone. Moreover, the relative distance between the crack tip and the
microcavity has a very important effect on the size of the confined plastic
zone.
The microcrack presence can provoke the
division of the plastic zone ahead of the main crack in two parts. It is also
shown that the effect of the microcrack disappears when the relative distance
between the two cracks exceeds 10%.
Key words: main crack, inclusion,
micro-cavity, micro-crack, plastic zone, Finite Element Method (FEM).
Junhua Zhao
Institute of Nano Science, Nanjing University of
Aeronautics and Astronautics, 210016 Nanjing,
China,
Department of Structural Engineering,
Norwegian
e-mails: junhua.zhao@ntnu,no;
jhzhao@nuaa.edu.cn
Role
of elasticity and an analogy solution for three-dimensional
elastic–plastic crack-tip fields
Abstract. A three-parameter analogy solution
for mode-I Three-Dimensional (3D) crack tip fields (stress, strain and energy
fields) at whole plastic zone in power hardening materials is presented under
small scale yielding condition by introducing the elastic-plastic Poisson's
ratio ve and out-of-plane
stress constraint factor Tz.
The influence of elastic deformation and energy on the near tip constraint for
each layer is investigated along the thickness. It is interesting to find that
the effect of elastic deformation in this sensitive region of the forward
sector ahead of a crack tip is considerable and should be mainly taken into
account. The elastic strain energy is always higher than the plastic strain
energy and is the dominant term in this sensitive sector. The T-stress has great effect on the elastic
and plastic strain energy. It can be found that all the values of ve decrease with the increase
of Tz for a given T-stress and increase with increasing
absolute value of T/σ0 at a same Tz for different n on the ligament. Finally, the 3D
elastic-plastic finite element analysis is carried out to validate the analogy
solution.
Key words: elastic-plastic crack-tip fields, out-of-plane stress constraint factor Tz, elastic-plastic Poisson's
ratio ve, T-stress, three-dimensional crack.