Stability of Composite Plates with a Dense System of Ribs in Two Directions

This paper presents an easy-to-use analytical method for stability analysis of composite plates with dense bidirectional microstructure. The main characteristic feature of such a defined composite is that due to its periodic nature the obtainable governing partial differential equations are characterised by discontinuous, strongly oscillating coefficients. Such cases bring many difficulties during derivation of their solution. In order to simplify calculations, the initial governing equations are transformed with the use of the tolerance averaging technique, so a system of partial differential equations with constant coefficients is obtained. The most important finding of the presented work is that the form of the mentioned equations is similar to the classic equations, which describe the stability issue of the thin homogeneous plate. Consequently, the analytical solution to such issues is easily obtainable. Moreover, when compared to, for example, finite element method (FEM) analysis, it requires substantially less computation resources, which can be perceived as its superior feature. Therefore, the proposed method is convenient for engineering applications. In this paper, a comparative analysis of the results obtained from the proposed analytical models with the results obtained from the FEM has been carried out. The impact of materials and dimensions of microstructure on the values of critical normal and shear forces has also been analysed.