Theoretical Analysis of Buckling for Functionally Graded Thin Plates with Microstructure Resting on an Elastic Foundation

In this paper, the problem of the stability of functionally graded thin plates with a microstructure is presented. To analyse this problem and take into consideration the effect of microstructure, tolerance modelling is used. The tolerance averaging technique allows us to replace the equation with non-continuous, tolerance-periodic, highly oscillating coefficients of the system of differential equations with slowly-varying coefficients, which describes also the effect of the microstructure. As an example, the buckling of a microstructured functionally graded plate band on a foundation is investigated. To obtain results, the tolerance model and the asymptotic model combined together with the Ritz method are used. It is shown that the tolerance model allows us to take into account the effect of microstructure on critical forces.