In this paper the steady flow of a viscous incompressible fluid in a slightly asymmetrical channel is considered. The flow is considered for channel with a small aspect ratio. The solution is expanded into a Taylor series with respect to the Reynolds number. Using the D-T method (Drazin and Tourigny), a bifurcation study is performed. Parameter ranges for the Reynolds number, where no, one or two solutions of the given type exist, are computed.

G. Popper. Solving systems of polynomial equations using Gröbner basis calculations with applications to mechanics. CAMES 1997 (4)

Solving systems of algebraic equations is presented using the Gröbner Basis Package of the computer algebra system MAPLE V. The Gröbner basis computations allow exact conclusions on the solutions of sets of polynomial equations, such as to decide if the given set is solvable, if the set has (at most) finitely many solutions, to determine the exact number of solutions in case there are finitely many, and their actual computation with arbitrary precision. The Gröbner basis computations are illustrated by two examples: computing the global equilibrium paths of a propped cantilever and of a simple arch.

D. Tejszerska. Computer analysis of vibrations of hoisting system. CAMES 1997 (4)

Model of longitudinal vibrations of mine hoist, treated as a discrete-continuous system is formulated. The model includes phenomena connected with variations of the load, carried by each rope and with sliding of the rope contacting with pulley. The effects of changes of length of both branches of rope, variations of their stiffness, internal damping, friction and diversification of parameters of individual ropes in multirope system are taken into account. General model equations, relations describing movement of elementary segments of ropes and of the whole system, and the method of solving the obtained equations are presented in the paper. Nonlinear system of partial and ordinary differential equations is solved numerically. Example results of numerical simulation, showing the possibilities of the formulated model and the program - are presented.

T. Sokól and M. Witkowski. Some experiences in the equilibrium path determination. CAMES 1997 (4)

The paper presents numerical techniques useful in nonlinear analysis of structures. The main attention is focused on procedures for the determination of equilibrium paths and examination of critical points. Most of them are connected with the arc length method and can be treated as additional tools, that improve the effectiveness and reliability of computations. It was confirmed in a number of test examples, presented in authors' earlier papers. In this paper only one, but the most representative example including different types of critical points has been chosen. The conclusions are that even highly nonlinear problems can effectively be solved using relatively simple algorithms.

P. Kowalczyk and M. Kleiber. Parameter sensitivity for large deformation inelastic problems. CAMES 1997 (4)

The algorithm for parametric sensitivity assessment for both materially and geometrically nonlinear static problems is presented. Similarly to its geometrically linear version presented elsewhere, the sensitivity analysis is shown to reduce to a linear problem with the same operator matrix that has been used in just completed equilibrium iteration, which makes the computations very efficient. Both total and updated Lagrangian approaches are analysed, including design differentiation of the configuration update transformation. Sensitivity with respect to constitutive parameters is discussed in detail. Possible extensions towards cross-sectional geometry or general shape parameters are pointed out.

S. Tokarzewski, A. Galka and I. Andrianov. Bounds on the effective transport coefficients of two-phase media from discrete theoretical and experimental data. CAMES 1997 (4)

By applying Padé approximants and continued fractions technique we investigate a composite material of the effective modulus consisting of two components of real moduli. Our estimations generalize the previous bounds reported in previous papers. The inequalities achieved are applied for the evaluation of the upper and lower bounds from the given experimental measurements.

T. Chi and E. Dembicki. Optimization of the block foundations. CAMES 1997 (4)

Optimization of shape and size of foundation should consider the type of loading, numerous geotechnical and geological parameters as well as various safety and economic criteria. Dimensioning depends on various, often controversial, conditions and involves many uncertainties. Therefore we search compromise solutions using nondeterministic analysis based on mathematical logic. In our solution we use computer simulations and results of reliability theory.

P. Kolakowski and J. Holnicki-Szulc. Optimal remodelling of truss structures (simulation by virtual distortions). CAMES 1997 (4)

Optimal remodelling for least-weight trusses under single as well as multi-load state and limits imposed on local strains is considered. The so called Virtual Distortion Method is applied to simulate process of structural remodelling through fictitious "virtual distortions". In effect, applying knowledge of strains induced by virtual distortions modelling material redistribution, analytical formulas for sensitivity analysis and remodelling simulation process can be obtained. Various algorithms for the VDM-based structural remodelling have been proposed and tested on examples of elastic and elasto-plastic trusses.