Nonlinear bending of polygonal functionally graded plates resting on elastic foundation

Abstract

To investigate nonlinear bending of the functionally graded (FGM) plates with complex shape and resting on elastic foundation a variational-structural method (RFM) is proposed. Mathematical statement of nonlinear boundary value problems of plate bending is carried out in the framework of the classical geometrically nonlinear plate theory. To solve a sequence of linear boundary value problems obtained as a result of the linearization of the original nonlinear system of equations by the method of successive loadings and the Newton method, the method of R-functions was applied. Testing, as well as comparison of the obtained results with the results of other authors, made it possible to establish the reliability and effectiveness of the developed approach and apply it to study the stress-strain state (SSS) of thin plates with complex shape. A computational experiment was carried out for thin hexagonal plates with mixed boundary conditions for various types of external load and elastic foundation characteristics. The relationship between the greatest deflection of the plate and the load is obtained. The results are presented in the form of graphs.