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Pozycja Some remarks on dynamic results for averaged and exact models of thin periodic plates.(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2005) Jędrysiak, Jarosław; Michalak, BohdanThe aim of the paper is to show certain justification of the new non-asymptotic model of thin periodic plates, derived using the tolerance averaging (Wo?niak and Wierzbicki, 2000). The model describes the effect of periodicity cell size on overall plate behaviour, on the contrary to known homogenised models. Results obtained from those models will be compared to solution to and from the "exact" discrete model. It is shown that for long-wave propagation problems, results obtained for a special case of a periodic plate strip (weightless but covered by a periodically distributed system of two concentrated masses) within the non-asymptotic model are close results calculated from the known "exact" solutions based on the method used to analyse longitudinal vibrations of one-dimensional diatomic lattice (Brillouin, 1953). Similar conformity, taking place in special cases of short waves, is also presented.Pozycja Stability of composite plates with non-uniform distribution of constituents.(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2004) Michalak, BohdanThis contribution deals with stability of certain composite plates with a deterministic material structure which is not periodic but can be approximately regarded as periodic in small regions of a plate. The formulation of an approximate mathematical model of these plates, based on a tolerance averaging method, was discussed in Woźniak and Wierzbicki (2000), where the plates under consideration were referred to as heteroperiodic.Pozycja Non-stationary heat transfer in a hollow cylinder with functionally graded material properties.(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2011) Ostrowski, Piotr; Michalak, BohdanThe unidirectional non-stationary heat conduction in a two-phase hollow cylinder is considered. The conductor is made of two-phase stratified composites and has smooth gradation of effective properties in the radial direction. Therefore, we deal here with a special case of functionally graded materials, FGM. The formulation of mathematical model of the conductor is based on a tolerance averaging approach (TAA). Application to the non-stationary heat conduction and a comparison of the tolerance model with the asymptotic one is shown. The effect of geometry and material properties of the conductor on the temperature field is examined.Pozycja Modelling of annular plates stability with functionally granded structure interacting with elastic heterogeneous subsoil.(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2014) Perliński, Wojciech; Gajdzicki, Michał; Michalak, BohdanThis contribution deals with the modelling and analysis of stability problems for thin composite annular plates interacting with elastic heterogeneous subsoil. The object of analysis is an annular plate with a deterministic heterogeneous microstructure and the apparent properties smoothly varying along a radial direction. The aim of contribution is to formulate two macroscopic mathematical models describing stability of this plate. The considerations are based on a tolerance averaging technique. The general results are applied to the analysis of some special stability problems. The obtained results of critical forces with those obtained from finite element method are compared.Pozycja Asymptotic and tolerance 2D-modelling in elastodynamics of certain thin-walled structures(Politechnika Łódzka. Katedra Wytrzymałości Materiałów i Konstrukcji, 2012) Michalak, Bohdan; Woźniak, CzesławPozycja On a modelling of stability of annular plates with functionally graded structure interacting with an elastic heterogeneous subsoil(Politechnika Łódzka. Katedra Wytrzymałości Materiałów i Konstrukcji., 2012) Michalak, Bohdan