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Asymptotic and tolerance 2D-modelling in elastodynamics of certain thin-walled structures
(Politechnika Łódzka. Katedra Wytrzymałości Materiałów i Konstrukcji, 2012) Michalak, Bohdan; Woźniak, Czesław
Free vibrations of an unbounded periodically reinforced elastic layer
(Politechnika Łódzka. Katedra Wytrzymałości Materiałów i Konstrukcji., 2012) Woźniak, Czesław; Wągrowska, M.; Szlachetka, O.; Witkowska-Dobrev, J.
The object of analysis is an unbounded layer made of two isotropic, linear elastic materials and periodically laminated along the Ox1 axis (cf. Fig.1). The layer is resting on the rigid base. It is assumed that the laminas are homogeneous and their number is very large. Hence we deal with a certain microstructured layer. The aim of this contribution is to propose a certain mass discretized model for the analysis of vibrations of the layer. It is shown that there exist two kinds of these vibrations which are independent of x2 and x3 coordinates.
Thermomechanics of microheterogeneous solids and structures : tolerance averaging approach
(Wydawnictwo Politechniki Łódzkiej, 2008) Woźniak, Czesław; Michalak, Bohdan; Jędrysiak, Jarosław; Matysiak, Stanisław; Świtka, Romuald
This book contains a summary of results obtained in Poland during the last decade and oriented towards thermomechanics of functionally graded solids and composite elements with the deterministic microstructure. These results are presented in the form of a textbook for doctor students and research engineers interested in mechanics of microheterogeneous solids and structures. The peculiarity of the presentation is a new "tolerance" approach to the analysis of functionally graded and periodically microheterogeneous media. It progresses from the physical treatment of the tolerance averaging of differential operators to the formation of engineering models for different microstructures and then to the investigation of specific problems in the framework of the derived models. The proposed tolerance models make it possible to investigate more deeply the response of microheterogeneous media then the known homogenization theory. The approach itself is based on physical concepts and heuristic hypotheses rather than on advanced mathematical methods. That is why also the text material should be understood by readers familiar only with foundations of the linear elasticity theory and structural dynamics.