Available Online: http://www.ejpau.media.pl/volume5/issue2/civil/abs-01.html
NONASYMPTOTIC MODELLING OF THIN PLATES
Wiesław Nagórko, Czesław Woźniak
The subject of considerations is a thin elastic plate reinforced by a large number of periodically spaced elastic stiffeners.
The purpose of this contribution is to propose a certain new averaged 2D – model of the periodic structure under consideration. This purpose could be also attained by applying the known asymptotic homogenization approach i. e. by taking into account the results given in . However, the homogenized 2D – model derived in , represented by the Kirchhoff’s plate equations with constant (effective) coefficients, cannot be applied to the analysis of problems in which the effect of a period length on the dynamic plate behaviour plays an important role. In the present contribution in order to remove this drawback we apply an alternative nonasymptotic approach to the modelling of periodic structures which is based on the tolerance averaging technique. All details concerning this technique as well as the full list of references can be found in ; nevertheless to make this paper self consistent, we outline in Section 3 fundamental concepts of the tolerance averaging.
It is assumed that the plate under consideration is thin and can be described in the framework of the Kirchhoff’s plate theory.
At the same time we assume that the torsional rigidity of stiffeners can be neglected and that their deflection is governed by the Euler – Bernoulli beam theory equation. For the sake of simplicity we shall also neglect the rotational inertia effect on a dynamic structure behaviour.
Key words: plates, nonasymptotic modelling, composite structures, periodic structures.