## 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

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.