Solution of the Problems of Stability of Laminated Plates with Holes by the Method of R-Functions

Abstract

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.