## Contents of the Journal of Mechanical Engineering *48,* 1 (1997)

SLADEK, J., SLADEK, V.: The state of art in boundary element methods
for fracture mechanics 1

BALLO, I.: The influence of transverse crack on flexural vibrations
of slender continuous shaft (in Slovak) 25

MAJERCAK, P., KRAL, S., GOLDFARB, V. I.: Meshing characteristics of the
spiroid gearings (in Slovak) 37

HLAVNA, V., JURSA, P., MERKISZ, J.: Low temperature of a combustion engine
and its emissions (in Slovak) 47

# Abstracts

### Review paper

The state of art in boundary
element methods for fracture mechanics

J. SLADEK and V. SLADEK

In this paper a review of various boundary
element formulations for fracture mechanics problems is presented. The
topics include the modelling strategies, boundary integral equations, and
advanced contour integral formulations for evaluation of fracture parameters
(stress intensity factors or *J*-integral and *T*-stresses) that
have been
developed in elastostatics, elastodynamics, thermoelasticity and inelastic
fracture problems. The boundary element method formulation of general crack
problems in terms of displacement discontinuities appears to be the most
effective among all existing formulations. The overall accuracy is dependent
on the precision of the evaluation of boundary integrals. Therefore a great
attention is devoted to find nonsingular boundary integral formulations.

###
The influence of transverse crack on flexural vibrations of slender
continuous shaft

I. BALLO

In the paper the mathematical model of the above-mentioned
problem is derived by means of the large finite element method. The crack
is modelled by a spatial joint combined with two orthogonal springs. The
springs exert unequal bending moments in the
*z\chi* and *z*\eta planes
on both parts of the shaft with nonlinear term in the *z\chi* plane. The
linear part of the stiffness of both springs was calculated according to
[1]. The mathematical model of the shaft could be solved by means of the
small parameter theory. In the first part of the paper the zero-approximation
of the shaft transverse deflection is established. It is the so-called
one-frequency solution of the linearised part of the problem. The condition
for the ``breathing'' of the crack is formulated, too. The solution of
the full nonlinear problem is made according to the average theory. By
means of this theory the amplitudes and phases of the second and third
harmonics of the rotational frequency are calculated and depicted in figures
2, 3, 4.

###
Meshing characteristics of the spiroid gearings

P. MAJERCAK, S. KRAL, V. I. GOLDFARB

Basic expressions
accounting for the meshing portions of the spiroid gearing: equation of
the worm surface and its normal, expression for the relative speed of surfaces
and contact lines in the meshing place, which is described by the meshing
equation, are presented in the paper.

###
Low temperature of a combustion engine and
its emissions

V. HLAVNA, P. JURSA, J. MERKISZ

A thermal condition of an engine during its operation is
one of the decisive factors which influence harmful emissions in exhaust
gases. The paper deals with an influence of low temperature on formation
of air-fuel mixture in a combustion engine and consequences of this fact
on the content of harmful emissions in exhaust gases. The experiment itself
illustrates the concentration dependence of the harmful emissions on the
thermal condition of the engine within the period of its start until its
thermal stabilization.