## Contents of the Journal of Mechanical Engineering 50, 1 (1999)


C. HOSCHL: Singularities in the theory of elasticity (in Czech)
(Review paper)                                                             3

S. ADAMCZAK: Errors of the reference methods parameters
in the measurement of roundness deviation of machine elements             15

V. KOMPIS, L. FRASTIA, P. NOVAK, I. BARAN: Hybrid finite element
formulation for computational fluid  mechanics                            24

I. MARKECHOVA: Elastostatic analysis in harmonically non-homogeneous
medium using boundary element method                                      38

A. S. KRAVCHUK: Determination of contact stress for composite sliding
bearings                                                                  52

N. I. IOAKIMIDIS: REDLOG-aided derivation of feasibility conditions
in applied mechanics and engineering problems under simple
inequality constraints                                                    58



## Abstracts

### Singularities in the theory of elasticity

C. HOSCHL

The theory of elasticity gives unique solutions of well posed problems only if some continuity requirements are satisfied. Discontinuities in traction force or in geometry, as well as applied concentrated forces may lead to infinite values of stresses or displacements at some points or lines. In some cases, the stresses are finite but discontinuous and non-unique. The knowledge of such phenomena enables the choice of an appropriate mathematical model with correct interpretation of results of solution when numerical methods are applied. A very important example is the evaluation of stress intensity factors in linear fracture mechanics by numerical methods. In connection with non-unique solutions, the so called Babuska's paradox may be mentioned. Whereas the solution of a bending problem for the thin elastic circular plate is unique, it differs from the case of a plate with polygonal boundary even if the number of sides of the polygon tends to infinity. The solution becomes non-unique in this limit.

### Errors of the reference methods parameters in the measurement of roundness deviation of machine elements

Determination of the real roundness deviation by means of reference methods depends considerably on the defined coefficient of detectability which is a function of method parameters angles \alpha and \beta. The paper analyses the influence of errors resulting from the establishment of these parameters on the error of this coefficient, which in consequence, makes it possible to define the error in the measurement of the real roundness deviation. As the value of this error is known, it is possible to formulate practical conclusions aiming at its minimization.

### Hybrid finite element formulation for computational fluid mechanics

V. KOMPIS, L. FRASTIA, P. NOVAK, I. BARAN

A hybrid FE formulation for the solution of steady fluid flow problems is presented. In the case of linear problems (slow flow and inviscous irrotational flow) we obtain the hybrid-Trefftz formulation, in which the basic equations are satisfied inside the elements in the strong sense. For nonlinear problems the basic equations are satisfied in the discrete least-square sense.

### Elastostatic analysis in harmonically non-homogeneous medium using boundary element method

I. MARKECHOVA

This paper presents a two-dimensional boundary value problem in elastic inhomogeneous medium. It is assumed that the Poisson's ratio is constant and the Young's (or the shear) modulus varies continuously with the position, namely, \mu(x) varies cosinusoidally in the direction of the tension. At first, the fundamental principles of the boundary element method (BEM) analysis of the problem are illustrated. Then, their applications to harmonically non-homogeneous medium are shown. The displacements and stresses are computed using BEM formulation of their boundary integral representations derived in [1] and [2]. It is observed that the results are highly affected by the function describing material inhomogeneity as well as by fineness of discretization meshes used in numerical treatment. A short discussion on suitability of considered meshes is done.

### Determination of contact stress for composite sliding bearings

A. S. KRAVCHUK

The problem of elastic interior contact of a rigid disk and isotropic plate with elastic coating on a cylindrical hole is considered. The presented approach allows to take into account elastic deformations of the layer on the hole and obtain an explicit approximate solution of the contact problem.

### REDLOG-aided derivation of feasibility conditions in applied mechanics and engineering problems under simple inequality constraints

N. I. IOAKIMIDIS

Problems involving symbolic computations and quantified variables in parametric inequality constraints appear quite naturally and frequently in applied mechanics and engineering. In this paper we illustrate the use of REDLOG, a recent logic package of the well-known Reduce computer algebra system, for the solution of several such problems, i.e. for the derivation of simultaneously necessary and sufficient parametric feasibility conditions (free from the quantified variables) so that our parametric inequality constraints can be completely satisfied. The present applications concern some simple problems from the theory of plates, heat transfer, elasticity and strength of materials, whereas an extremely large number of additional related problems appearing in engineering practice can also be solved with the help of REDLOG.