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Pozycja Modelling of annular plates stability with functionally graded structure interacting with elastic heterogeneous subsoil(Polish Society of Theoretical and Applied Mechanics, 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 On a certain nonlinear model of thin periodic plates(Wydawnictwo Politechniki Łódzkiej, 2012) Domagalski, Łukasz; Gajdzicki, Michał; Jędrysiak, JarosławThe object under consideration are thin plates, which structure is periodic in planes parallel to the midplane. Plates of this kind consist of many small, repetitive elements, called periodicity cells, that can be treated as thin plates. The microstructure size is characterized by the diameter of the cell, which is called the microstructure parameter l. It is assumed that mechanical properties (bending and membrane stiffness tensors' components) of such plates are periodic, highly-oscillating, non-continuous functions. The main aim is to propose a mathematical model describing moderately large static deflections problem of considered plates, which is based on the tolerance modelling technique. A calculational example for a specific problem is included. The results are compared with results obtained within the linear model and with Finite Element Method.