The work is devoted to the practical application of dual grids in the boundary element method (BEM). Definitions of dual grids on the plane are given and algorithm constructing dual grid for a given triangulation is described. The problem of utilizing two numerical solutions of one problem defined on the couple of dual grids is considered and the results of this technique are demonstrated. The examples from geomechanics modelling the contact interaction of shallow foundations and elastic bases are presented.

T.W. Chiu. Object oriented programming and applications of boundary element method in ground vehicle aerodynamics. CAMES 2000 (7)

The phenomenal development and popularisation of Object Oriented Programming (OOP) in recent years has created a new dimension in the innovation and implementation of powerful panel method techniques.
Although many scientists and engineers are already employing OOP languages such as C++, some of them are still using the languages in a procedural and non-hierarchical manner, leaving a large proportion of these languages' capability unexplored. This paper presents the idea and implementation of OOP in the panel method, which is widely used in ground vehicle aerodynamics. Program examples will show that OOP enables the writing of highly modularised, reusable, readable and debuggable panel method programs.
*Keywords:* object oriented programming, panel method, BEM, ground vehicle aerodynamics.

W. Cichorski and A. Stolarski. Sensitivity of the numerical solution to finite element mesh for reinforced concrete deep beams. CAMES 2000 (7)

An analysis of the influence of the manner of dividing the structure on the numerical solution of the static problems of the concrete and of the reinforced concrete deep beams, using a constitutive model of the concrete that demonstrates the material softening, is given. Detailed results of the numerical solutions are presented in the paper. The results indicate that taking into account the scale parameters makes it possible to increase the objectivity of the numerical results of modelling of the behaviour of concrete and reinforced concrete structures when the material softening is considered. The numerical analysis for the reinforced concrete deep beams indicates the differentiation of the obtained results according to the fracture energy values.

J. Kunes and Z. Veselư. Numerical solution of the thermomechanical processes in the thin layer structure of thermal barrier. CAMES 2000 (7)

High demands for dynamic thermal insulating protection of machine parts lead to the development of thermal barriers. The mathematical and simulation model has been developed to simulate thermomechanical processes during thermal shock on the surface of different thermal barrier structures. The finite element method has been applied to the heterogeneous thin layer structure of the thermal barrier. Temperature, temperature gradient, heat flux, thermally induced stress and strain have been chosen as the characteristics describing the dynamic behaviour of the thermal barrier during the thermal shock. Results of the simulation for several alternatives of thermal barrier are discussed to summarize the effect of characteristic parameters of the thermal barrier to its dynamic behaviour.
*Keywords:* computer simulation, FEM, thermomechanical processes, thermal barrier, special industrial application.

P. Ladeveze and L. Arnaud. A new computational method for structural vibrations in the medium-frequency range. CAMES 2000 (7)

In the paper a new approach for the computation of slightly damped elastic structural vibrations over the medium frequency range is proposed. The effective quantities (deformation energy, vibrational intensity, etc...) are evaluated after resolution of a small system of equations that does not in any way result from a fine ``finite element'' discretisation of the structure.

M. Lupu and E. Scheiber. Optimal airfoil in an inverse problem of jet aerodynamics. CAMES 2000 (7)

The paper deals with a special inverse boundary problem, when the boundary of the domain is completely unknown and a singular integral equation for the velocity angle is obtained. For the model of free plane symmetric incompressible jet forked by an airfoil, the boundary equations and airfoil shape are ``a posteriori'' determined, while the velocity along them is ``a priori'' prescribed. With the aim to obtain minimum drag, in the present paper there is solved the optimization problem for airfoils, using the penalty method and the golden section method. In the case of optimum, numerical computations are performed and the airfoil design together with the drag coefficient are obtained.
*Keywords:* inviscid jets, inverse problems, singular integral equation, optimum airfoil, optimization.

N. Vrankovic;, M. Stegic and N. Kranjcevic. Shakedown of elastic-thermo-plastic structures. CAMES 2000 (7)

Recently formulated shakedown theorems for materials with temperature-dependent yield stress [1] are applied to evaluation of the elastic shakedown boundary. In order to simulate actual shakedown behavior of elastic-thermo-plastic structures resulting from experimental investigations, the material model of the German mild steel St 37 is considered. It is found that the obtained elastic shakedown boundaries are within the corresponding boundaries based on the classical shakedown theory. Two examples are compared with the well-known solutions obtained for the neglected yield stress dependence on temperature.