Wave theory of the laminated plates with approximate consideration of the transverse shear

Composite materials are widely used in the production of aircraft for various purposes. Having several unique properties, composites, due to their heterogeneous structure, are poorly resistant to shock loads. Impulse action spreads inside the material in the form of stress waves, which are reflected on internal inhomogeneities, can overlap, and create very significant bursts of stress. This often leads to the well-known types of failure – spalling and delamination. Practice shows that these fractures occur almost immediately after the loading impulse. To verify the spalling strength, it is necessary to consider the initial unsteady phase of the response to the external impulse. There are sufficiently reliable theories to verify this strength; usually, they do not take transverse shear into account, otherwise the solution becomes unnecessarily cumbersome and poorly observable. Nevertheless, attempts are often made to refine the calculations by approximate consideration of transverse shear. This article presents the wave theory of laminated plates with approximate consideration of transverse shear. The possibility of specifying the calculation of impulse-loaded plates is considered. The inconsistency of the resulting model is proved.

Buckling and Vibration Performance of a Composite Laminated Plate with Elastic Boundaries Subjected to Local Thermal Loading

In this paper, a model is established for the calculation of the vibrations of a composite laminated plate with elastic boundary conditions subjected to local thermal loading. The model is based on first-order shear deformation theory using the finite element method. The influence of boundary conditions, heating area, and heating location on buckling and vibrations of a composite laminated plate was investigated, and there were two stages in which the critical temperature increased sharply during the transition from free boundary to simply supported and rigid fixed boundaries. The thermal buckling of locally heated laminated plates is generally not checked in practical applications unless the heated area exceeds approximately 10% of the total area of the plates. The stronger the boundary constraint is, the greater the influence of the heated area is on the vibrational frequencies of the composite laminated plate.