The Using of the Multilayer Plate Concept in the Calculus of Functionally Graded Plates

Abstract

In the calculus of functionally graded plates, the concept of multilayer plate is often used. For the use of this concept in this calculus, the continuous variation of the respective properties is replaced with a step variation. The first problem that arises in front of the user is related to the number of layers, which must be a finite and reasonably large number, to be accessible to the current calculus and to ensure the necessary accuracy of the results (under 5%). Another problem, generally poorly substantiated, is the one related to the assumption of a constant value of the Poisson’s ratio (usually 0.30 for the considered materials) over the entire plate thickness. The paper also contains a quantitative study of the influence of the Poisson ratio (4,…,10%), whose variation can be neglected, but only in certain circumstances. The presentation and substantiation of how to use the multilayer plate concept through models, methods and methodologies, along with the substantiation of the choice of the number of layers and the influence of the Poisson’s ratio, represent the main evidence of the originality of this work. The proposed numerical models are based on the use of common 3D finite elements. The software Ansys is used, which offers a multilayer finite element, which is taken into account in the comparative analysis of the results. The validation of the results is carried out by comparison with the analytical solution. The objective and purpose of this paper, that of completing the palette of achievements regarding the calculus of functionally graded plates, without modification of the stiffness matrices of the finite elements and using existing software products, are fulfilled.