A Note on Averaging of Stiffnesses of Thin Elastic Periodic Plates - T. Lewiński (Engineering Transactions)
The homogenization problem for a nonhornogeneous plate of doubly periodic structure is discussed. lt has been proved that an effective plate with constant effective homogenized stiffnesses is (in a certain meaning) energy equivalent to the considered heterogeneous plate of Y-periodic stiffnesses. Moreover, the corrector of the homogenized solution is defined and then its elementary derivation is presented, emphasis being put on the physical clearness of the procedure. In the last section a particular case of a plate with the thickness periodic in one (x1) direction is examined. A comparison is made of two sets of formulas for effective stiffnesses proposed by Duvaut and Kączkowski, respectively. lt is noted that the two formulae for D1212 and D2222 do not coincide.