On the Calculus of Functionally Graded Plates

Abstract

This paper presents some of our results regarding calculus of the functionally graded plates (FGPs). Such plates are made of Functionally Graded Materials (FGMs), which represent a new material class belonging to the composite materials. Our paper presents some material laws in a comparative way. But the main purpose of this paper is to provide calculus concepts and calculus methodologies, based on the means available in scientific research of mechanical engineering field, for the calculation of plates made of FGMs. Thus, the authors use the concepts of multilayer plate and equivalent plate, using both analytical and numerical calculus. The numerical method used are the Finite Element Method (FEM).The calculation aims both to determine the displacements and the stresses of the plates under statical loads, as well as to determine the free vibration frequencies. The research methodology is based on combining analytical calculation, where and when possible, with numerical simulation. The validation of our results is done by comparison with the analytical solution and the comparative analysis of the methods.

Radial Displacements in a Rotating Disc of Uniform Thickness Made of Functionally Graded Material

“…The power coefficient k influence is very important [8], as can be seen in Figures 3 and 4. The qualitative evolution of the relative values of Young's modulus E(r) and Poisson's ratio v(r) versus the value of the relative radius and the power coefficient k can be followed by examining Figures 3 and 4.…”

“…FGMs represent a category of materials that can be called composites but whose elastic and physical properties along one of their dimensions, namely Young's modulus, shear modulus, density, Poisson ratio, thermal or electrical conductivity, etc., are described by material adopted laws (models) [1,4,8]. Usually, one of the materials is a high-resistance material (ceramic) and the other is a common material having low resistance, like aluminum, steel, etc.…”

“…There are many material property laws. The most used one is the power law [1,4,6,8], which can be written as:…”

“…For example, the Poisson ratio variation is often neglected, but the difficulties do not completely disappear [5][6][7]. This study introduces two concepts for approaching the calculation of FGM structures with an acceptable accuracy [8][9][10]: the multilayer structure concept and the concept of equivalent material (structure). This paper displays the calculus results of a rotating disc having a uniform thickness and made of FGMs using these two concepts.…”

The Importance of an Unmanned Surface Vehicle: A Point of View

“…Digital wind tunnel simulation, also known as computational fluid dynamics (CFD) simulation, offers a number of advantages over conventional wind tunnel experiments for the study of a USV. In the study of an ATV in a digital wind tunnel, at least two methods are used: The finite volume method (FVM) and a weighted residual [6] .…”