Main results are cleary seen from the scientific papers in that period. The process of rotational symmetric tube bulging with inside pressure and axial compression enables the standard tubes to be formed into different rotational symmetric hollow parts in such a way that their central part is expanded into a desired shape while the ends remain unchanged. The superposition of axial compression contributes to a more favorable forming stress state, which reflects in larger forming limits and smaller wall thinning in the widened area. A physical and mathematical model were built for computer evaluation of new developement mechanism of the residual current circuit breaker with over current protection. The circuit-breaking time is approximatly one third shorter than these ones which were produced in the factory before. A physical and mathematical model were built for solving an optimization problem of the thickness of a circular annulus plate at buckling process. The plate is loaded with uniform axially symmetric in-plane loads on the inner and on the outer edges. The variable thickness of the plate is approximated by the function of radial coordinates and design variables. An optimisation problem is defined to find optimal sets of design variables which maximize buckling loads at constant weight/ volume of the plate. The required buckling loads are determined according to the standard buckling equations and the material is modelled by the small strain J2 flow and deformation theories of plasticity where an elastic linear hardening rheological model is considered. The methods of the next cases were developed: the identification of nonlinearity of complex nonlinear dynamic systems in the phase space, the identification of quadratic type nonlinearities in vibroisolation elements and at cutting process using bispectral analysis, fault diagnosis at mass-production using the continuous wavelet transform, the estimation of structural damping by using the Gabor wavelet function at short signals and the prediction of magnetic noise at DC electric motors. Solution to a time dependent inverse boundary value problem in solid mechanics by means of numerical methods. Combined with an experimental registration of the thermo-mechanical response the research allows for time and temperature dependent material characterization of theological and thermal properties. The main objective followed in the research was to simplify and to reduce the number of experiments needed for a reliable material characterization of complex relationships, thus obtaining credible input material data for a numerical analysis of the direct boundary value problem. Numerical solution of time dependent inverse boundary value problems. Sensitivity analysis of elasto-plastic problems. Improvement of computational efficiency.