Acta Scientiarum Polonorum

Abstract: The building structures considered in the paper are plates. Plates are three-dimensional material objects, which are described by two-dimensional models. Plates have some specific qualities. Two-dimensional models, where displacements, deformations and stresses are described by two-variable functions. These functions are determined in a plate’s mid-surface. In case of periodically heterogeneous plates the two-dimensional description is much more difficult due to the fact of a non-linear and oscillating coefficients present in the model equations. The aim of the paper is to provide a brief description of a homogenous modeling method, i.e. the method of averaging those coefficients to make them dependent the diameter of a basic cell only. By the use of that method static and dynamic equations result in constant coefficients. As an example, using this described model, we submitted the precise result for a simply supported plate which is periodically heterogeneous in two dimensions.