The paper presents a survey of the kinematical hypotheses and the governing equations of the refined theories of plates. By carrying out a comparative analysis of various, apparently different, kinematical hypotheses proposed by various authors, it is shown that the kinematical hypothesis by Vlasov (1957) is a pattern for all of them.

A solenoidal part of displacement field appearing in a plate made of material with constraints has been determined. The semi-inverse method has been applied to description. The results being obtained together with the already known biharmonic representation (Jemielita, 1992) might be useful in a new micropolar plate theory formulation.

An experimental analysis was performed to model transverse impact of free-free and free supported square duralumin beams loaded at different locations along their length. The applied impact load was obtained from tests carried out on a single Hopkinson pressure bar equipped with a high speed camera. The experimental set-up consisted of an Hopkinson measuring bar that is brought in contact with the beam. In this one-point impact experiment, a cylindrical striker, fired by the air gun, impacts the Hopkinson bar and generates stress waves that travel along the bar and impinge upon the aluminum beam. The stress waves are recorded by strain gages mounted on the Hopkinson measuring bar. These are used to calculate the applied load on the beam. Dynamical displacements of the impact zone of tested beam were recorded by the high speed camera. The dynamic experiments show that the plastic deformation, adjacent to the impact location, is due to combined dominant bending and stretching modes. Most of the plastic deformation is confined to the impact zone of tested beams. The plastic strain magnitude and distribution near the impact zone is similar for all tested impact locations, but higher for the more symmetrical impacts. The conversion of impact energy into kinetic, elastic strain energy and plastic dissipation work is characterized for various impact locations along the specimen of beam.

In this paper, the present exact solutions in the plate theory using the cylindrical deflection method and represented by the Fourier series corresponding to the oblique or Cartesian coordinates are given for a hingely supported triangular plate subject to a distributed load in form of a hexagonal pyramid and for a rectangular hingely supported plate subject to loading in form of a truncated octagonal pyramid. In the case of the rectangular hingely supported plate under the truncated octagonal pyramid load, a series of parametric solutions has been obtained. The solutions depend on the parameter ε. For various values of the parameter ε, various load cases are found.

The paper presents a certain way which determines the critical buckling force for a micro-heterogeneous FGM plate band. A stiffness matrix of an individual cell of such band, different for various cells, has been determined.The obtained matrix can also be treated as a variable stiffness matrix of a "superelement" in the Finite Element