The aim of the paper is to advocate the use of hybrid reasoning systems for computer-assisted analysis of physical systems. The paper starts from a critical assessment of classic numerical techniques, with the problem of sensitivity analysis of fuel rod support spring in a nuclear reactor used as an example. Then, the significance and some basic issues concerning qualitative physics methods of analysis of physical systems are discussed. Using the example of the so-called ``snap-through'' mechanism, the basic principles, advantages and limitations of qualitative simulation technique are shown. Certain future development possibilities are indicated, especially the necessity to formalise the order-of-magnitude reasoning. The recently developing techniques of diagrammatic reasoning are also introduced, with another mechanical example illustrating sources of their advantages for certain kinds of problems. The significant role of logical (expert-system-like) reasoning techniques and constraint-satisfaction systems is shown as well. Finally, the hybrid reasoning system concept is sketched. Such hybrid systems should integrate quantitative (numerical) (numerical) analysis, various methods of qualitative analysis as well as diagrammatic and logical reasoning techniques.

Natural frequencies of a vibrating hollow, elastic sphere are determined using both the 3-D elasticity and Kirchhoff shell theory.

The report is a continuation of the previous one. The closed-form solutions of the scattering problem by the 3-D elasticity and Kirchhoff shell theories are investigated.

The successful numerical analysis of plastic strain localization phenomena in ductile and brittle materials requires the fulfillment of several conditions in accordance with the formulation of the initial boundary value problem (IBVP). Sometimes it is necessary to use the regularization techniques which result in well-posedness of IBVPs. Then, there are several possibilities of introducing an internal length scale. If specific conditions are met, the results obtained in the numerical calculations are free of unexpected mesh sensitivity. In the paper the dynamical boundary values are studied. The rate-dependent regularized models of two materials are presented and used to solve practical engineering problems. The mathematical background which could be used to prove the well-posedness of IBVP as well as the physical arguments are discussed.