### Contents of Journal of Mechanical Engineering *53,* 4 (2002)

R. JANCO: Solution of thermo-elastic-plastic problems with consistent
integration of constitutive equations 197
P. LIU, Ch. LU: Indentation of cubic single-crystals with anisotropic
elastic properties 215
J. STEIN: Wind induced vibration of cables of simple overhead
transmission lines (in Slovak) 228
B. BELIK: Differential and difference based changes of position
of the last segment of an open kinematic chain of a robot (in Slovak) 249

# Abstracts

###
Solution of thermo-elastic-plastic problems with consistent integration of
constitutive equations

ROLAND JANCO

In the paper the algorithmically consistent integration of constitutive
equations over the time step (*t*_{n}, t_{n+1}) is
presented by using the one-step backward Euler scheme for solution of
thermo-elastic-plastic problems. Basic equations are derived in the
theoretical part. In that part we can also find the description of the
solution procedure. The solution procedure was implemented in the FE code. The
thermoplastic part of the model utilises the von Mises yield function with the
option of isotropic hardening. Finally, numerical examples for mechanical and
thermal loading condition are presented.

###
Indentation of cubic single-crystals with anisotropic elastic properties

PING LIU, CHUN LU

We have carried out finite element calculations to study the indentation on
the {100}, {110} and {111}
surfaces of cubic single-crystals with anisotropic elastic properties. It is
shown that the indentation orientations significantly affect the stress
distributions and the onset of plastic deformation. The indentation moduli
obtained by the present finite element method through the unloading curves are
consistent with those obtained by a semi-analytical method. In addition,
empirical formulae are proposed to relate indentation moduli with elastic
properties. These formulae allow the estimation of elastic properties with
reasonable accuracy.

###
Wind induced vibrations of cables of simple overhead transmission lines

JURAJ STEIN

Wind induced vibrations (Aeolian vibrations) of simple overhead transmission
lines and resulting conductors fatigue breakages constitute a problem for
utility companies in maintaining uninterrupted supply of electrical energy.
Therefore, there is a need for better understanding of this phenomenon, not
hitherto well described in domestic literature. The contribution describes
briefly the aim of study of Aeolian vibrations of simple conductors of
overhead transmission lines; it explains the excitation mechanism and
vibration synchronization at the so called Strouhal's frequency. Further, a
simplified analysis of the partial differential equation describing these
vibrations is presented using the unifying concept of characteristic length as
a single quantity describing the mechanical properties of the given conductor.
An example is used to illustrate the minute differences between the approach
to the conductor as a taut spring and a taut fixed-fixed beam leading to the
conclusion that in the "free field" the taut string approach is sufficient.
However, the "local effects" in calculating the theoretical value of bending
strain at the clamped end have primary importance.

###
Differential and difference based changes of position of the last segment of
an open kinematic chain of a robot

BARTOLOMEJ BELIK

This paper presents a difference method that allows to control a robot
activity in order to move the gripper point along a given planar or space
trajectory. It is particularly suitable to control gripper position changes of
the open and closed robot mechanism for the compensation of misplacements
caused by various external influences. The control of a robot with the
number of degrees of freedom *i* > 6 cannot be performed exactly. In such
cases
various numerical and variation methods are employed. The most frequently used
methods in the control theory are numerical solutions of difference equations
and the use of Z-Transformation Method which is presented in this paper.