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We propose a method for the evaluation of the critical loads for laminated plates with holes. Plates and holes made in these plates may have different geometric shapes and conditions of their fastening. It is assumed that the plate is compressed by static forces in its middle plane. The mathematical statement of the problem is formulated within the framework of the refined first-order theory based on the hypothesis of straight line (Timoshenko-type theory). To solve the problem, we use the Ritz method and the R-functions theory. The solution of the problem of elasticity theory takes into account the inhomogeneous subcritical state of the laminated plate. The reliability of the proposed approach is confirmed by good agreement of the obtained numerical results with the available data. Its efficiency is illustrated by an example of investigation of the problem of stability of laminated plates with one and two quadrangular holes. We analyze the influence of the arrangement of holes, their sizes, and the method of fastening on the critical load and natural frequencies. [ABSTRACT FROM AUTHOR]

We propose a numerical-analytic method aimed at the investigation of free vibrations and stability of functionally graded sandwich-type plates and based on the refined Timoshenko-type theory of the first order. We considered various schemes of arrangement of the layers: (1) the filler is a functionally graded material and the top and bottom layers are made of isotropic materials and (2) vice versa, the filler is made of an isotropic material, whereas the top and bottom layers are made of functionally graded materials. The proposed method is based on the R-functions theory and the Ritz variational method. This method and the developed software take into account the presence of an inhomogeneous subcritical state of the plate. Analytic relations are obtained for the evaluation of the elastic constants and density of the material under the assumption that Poisson's ratios are identical, for the components of functionally graded materials. The numerical results obtained for the eigenfrequencies and the critical load are compared with the available data and their good agreement is demonstrated. To illustrate the possibilities of the proposed approach, we perform the numerical analyses of plates of complex geometric shapes loaded in the middle plane. The influence of various geometric and mechanical parameters on the dynamic behavior of the plate, critical load, and the zones of dynamic instability is investigated. [ABSTRACT FROM AUTHOR]