The Equivalent Material Concept in Functionally Graded Plates Calculus

Functional graded materials are composed of two extremely dissimilar materials whose properties vary continuously, in accordance with a material law, with respect to their thickness (beam or plate). The concept of equivalent material involves the replacement of the given material of the plate, with an homogeneous and isotropic material, with the same geometric characteristics (shape and dimensions), with the same load, which leads to the same behavior of the given plate. This chapter aims to provide a way to solve a complex problem (mathematical and structural), as in the case of FGM plates, with available means, starting with the analytical calculus, but especially with the numerical one, with known professional numerical programs, with common finite elements, with any others numerical methods (e.g. Element Free Galerkin Method), without intervention in the structure of the program, in the finite element matrices, in other words without dedicated calculation programs. more than that, the concept of equivalent material has a high degree of generality, being able to be used both in the calculation of slabs, but also of other structures (beams, tubes with thick walls, disks in rotational motion, etc.). This concept - equivalent material - can be successfully used both in static and dynamic analysis of structures. Thus, the use of the concept of equivalent material is exemplified by the calculus regarding the transverse displacement and the modal analysis of a functionally graded plate. The concept of the calculus approach (equivalent material), the models and the methodology are valid for any type of load, different geometries of the plate and materials that are the basis for the realization of the functionally graded material. The finite element approach is used in this chapter with the Ansys program and one of the most well-known finite elements, the 3D Solid185 element, in both the common (structural) and multilayer finite element versions.