### Contents of Journal of Mechanical Engineering *54,* 5-6 (2003)

KOMPIS, V., DEKYS, V.: Analysis of local stress and displacement
fields in contact of 3D bodies with curved surfaces 253
MAUNDER, E. A. W., RAMSAY, A. C. A.: A basis for an axisymmetric
hybrid-stress element 263
von ESTORFF, O., HAGEN, CH.: Dynamic response of blocks on
a half-space including nonlinear effects 277
ALEXANDROV, S.: Solution behaviour and fracture near frictional
interfaces in metal forming processes 293
MALENOVSKY, E., POCHYLY, F., KLAS, R.: Contribution to
the theoretical, computational and experimental analysis
of Taylor vortices in thin fluid film 307
NAKASHIMA, M.: Unconditionally stable explicit difference schemes
for a two-dimensional parabolic differential equation with variable
coefficients (V) 327

# Abstracts

###
Analysis of local stress and displacement fields in contact of 3D bodies with
curved surfaces

VLADIMIR KOMPIS, VLADIMIR DEKYS

The paper describes a computational model for displacement and stress fields
of elastic bodies with spherical surfaces in contact. It is assumed that the
bodies are thin walled, so that the contact area is determined by the
penetration of the rigid surfaces in accordance to Hertz theory. The
displacement and stress fields are described by the gradients of the first and
second order of weak singular integrals. All the integration and
differentiation are performed numerically with very good accuracy for all the
most important points on and near the surface.

###
A basis for an axisymmetric hybrid-stress element

EDWARD A. W. MAUNDER, ANGUS C. A. RAMSAY

Recent developments of hybrid-stress elements are presented suitable for
modelling axisymmetric problems when a strong form of equilibrium is required.
Potential instability problems due to spurious kinematic modes are shown to be
avoided by appropriate selection of statically admissible stress fields and
edge displacements, and by the use of the macro-element concept. This paper is
restricted to elements for problems where a hole occurs along the axis of
symmetry; simple numerical examples are included to illustrate element
characteristics, to verify the associated software, and to compare with
conventional conforming displacement models. Suggestions are included for
future work to develop axisymmetric hybrid models further.

###
Dynamic response of blocks on a half-space including nonlinear effects

OTTO VON ESTORFF, CHRISTIAN HAGEN

In the present contribution, a three-dimensional approach for the direct
coupling of FEM and BEM in the time domain is outlined, which allows to take
into account physical and geometrical non-linearities, unbounded subdomains,
as well as incident wave fields. Employing this approach, the dynamic
behaviour of building-like structures, namely blocks and walls, resting on
half-spaces, is investigated. The response of these systems to impulse loads
and to incident waves is studied, and the influence of soil properties like
stiffness and yield strength on the overall dynamic behaviour of the
soil-structure systems is analysed. From the numerical examples it becomes
obvious that the presented approach works very well. The three-dimensional
formulation allows the investigation of rather realistic problems in dynamic
soil-structure interaction and earthquake engineering.

###
Solution behaviour and fracture near frictional interfaces in metal forming
processes

SERGEI ALEXANDROV

Assuming a rigid plastic, hardening material model with a damage evolution
equation, it is shown that the velocity fields must in general satisfy
sticking boundary conditions at maximum friction surfaces. Exceptions to this
rule are also derived in terms of a special velocity distribution and friction
surface geometry. Applying sticking friction boundary conditions, a closed
form solution for a simple problem is obtained. It is shown that no solution
may exist if a conventional fracture criterion is applied. To achieve the
existence, a new fracture criterion is proposed.

###
Contribution to the theoretical, computational and experimental analysis of
Taylor vortices in thin fluid film

EDUARD MALENOVSKY, FRANTISEK POCHYLY, ROMAN KLAS

This contribution mainly deals with computational modelling of flow with
Taylor vortices between two cylinders. The liquid is assumed to be
incompressible and the flow laminar. The theoretical analysis is based on the
application of Navier-Stokes and continuity equations. Velocities and pressure
fields are solved in perpendicular co-ordinates but for the description of
geometrical configuration, curvilinear co-ordinates are used. Using special
transformation relations, it is possible to separate the liquid and rigid body
motions from each other. This new approach allows to analyze liquid motion
based on the solution of eigenvalue problem. Though stationary motion is
analyzed, the eigenvalue problem is solved for nonstationary motion as a
response to Dirac's pulse. The Bezier body is used for describing the liquid
volume and also for approximating the solution (velocities and pressures) by
numerical analysis, which is a totally new approach. Many different boundary
conditions on the plane, which is perpendicular to the axis of rotation, can
be used. The dependence of the eigenvalues on angular velocity is presented,
length is analyzed on the model sample, and some results were compared with
the experiment. Some analyses of the model sample were also made in
Computational Fluid Dynamic (CFD) FLUENT. Generally, a totally new approach is
presented, which allows a more precise analysis of liquid motion.

###
Unconditionally stable explicit difference schemes for a two-dimensional
parabolic differential equation with variable coefficients (V)

MASAHARU NAKASHIMA

The computational aspects of heat transfer in engineering structures and
materials are important since non-uniform heat flows may have a significant
effect on the performance character. Its application area is in the
development of advanced structural materials, component behavior and
structural design. Several different techniques for numerical analysis of heat
transient problems exist. Discretizing the space, time integration methods are
often used. However, for a system where, e.g. the thermal diffusion is rapid
and variable in time, the numerical integration runs in difficulties when
choosing the optimum time step. In the past, implicit methods were used to
analyze such systems. Unlike the past efforts in this area, the present paper
describes an explicit unconditionally stable method, and the optimum time step
problems are overcome. A numerical test model is presented to justify our
method.