Random deformation of a three-layer Hoff plate with stochastic parameters

In the recent years sandwich constructions, most often in the form of plates and shells, have been widely used in many fields of technology. Composite materials, due to their physicalproperties, are often used in agricultural buildings. Howewer the basic resistance parameters of these materials, which greatly influence the deformation of a plate under load, change in a random manner. The objective of the paper was to find a solution for the problem of deformation of a composite object with a regard to a stochastic character of material parameters, loads and boundary conditions. An analisys was made for a composite plate with hardboard facings in which foamed and hardened polyurethane was used as the filler. A variational approach of the finite difference metod was used to develop a numerical model. in order to consider randomness of physical properties of the plates's filler, load and boundary conditions, a numerical random field function generator was built and used, the parameters of which were set experimentally. The obtained results differed considerably from the results obtained by conventional calculations that assume determined values. Therefore, the proposed computing method provides the means for a more precise and complete analysis of the deformation of composite elements in constructions used in agricultural building.

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W pracy omówiono wyniki badań symulacyjnych, dotyczących deformacji płyty trójwarstwowej poddanej losowemu obciążeniu normalnemu, której warstwa rdzenna, ze względu na swoje parametry fizyczne, wykazuje cechy stochastyczne. W szczególności, dokonano oceny wpływu charakteru losowości parametrów wypełniacza płyty, na cechy rozkładu prawdopodobieństwa składowych wektora deformacji ugiętej płyty trójwarstwowej. Ocenie poddano również celowość stosowania proponowanej metody w porównaniu z obliczeniami tradycyjnymi, tj. traktującymi parametry fizyczne rdzenia jako wartości zdeterminowane.