Numerical Solution of Static and Dynamic Problems of Functionally Graded Structural Members

Abstract

The concept of Functionally Graded Materials (FGMs) was first enunciated in 1984 by a group of material scientists in Japan during a space plane project in the form of thermal barrier material which can withstand a huge temperature fluctuation across a very thin
cross-section (Loy et al., 1999). Since then, FGMs have taken major attention as heat-shielding advanced structural materials in various engineering applications and in manufacturing industries viz. aerospace, nuclear reactor, automobile, aircrafts, space vehicles, biomedical and steel industries. These materials are generally ceramic-metal composites in which material
properties vary continuously in thickness direction from one interface to another in a specific mathematical pattern. The ceramic constituent provides high-temperature resistance due to its low thermal conductivity, whereas the ductile metal constituent prevents fracture caused by stresses due to high temperature gradient in a very short span of time.
In this regard, static and dynamic characteristics of FG structural members are of considerable importance in both research and industrial sectors. On the other hand, these
problems are governed by higher-order Partial Dierential Equations (PDEs). However it is
not always possible to find the analytical solutions for such problems. Accordingly numerical
methods may be applied to solve such PDEs. Although there exists various numerical methods to handle these PDEs, but sometimes these are problem dependent and may not handle all sets of boundary conditions along with complicating eects with ease. So it is a challenging task to develop numerical methods which may be general to undertake the investigation. Present problems have been investigated based on computationally ecient numerical
procedures viz. Rayleigh-Ritz and Generalized Dierential Quadrature (GDQ). At first, static problem related to thin FG rectangular plates subjected to various sets of possible classical boundary conditions under external mechanical loads is carried out using Rayleigh-Ritz
method. Next, this method is also implemented to vibration problems of uniform FG beams based on dierent existing and newly proposed shear deformation beam theories, whereas GDQ to vibration of Euler-Bernoulli non-uniform FG beam. In addition, free vibration of thin
FG plates under various possible classical boundary supports have been studied with dierent geometries viz. rectangular, elliptic and triangular. Then study on vibration of isotropic thick rectangular plates based on newly proposed shear deformation plate theories has been done. Lastly vibration of FG rectangular plates under dierent complicating eects is also studied. The plate vibration problems along with complicating environments have been solved here by means of Rayleigh-Ritz method. In each of these investigations, FG material properties
vary gradually in thickness direction either in power-law or exponential law forms. Numerical solution of titled problems are systematically found and corresponding results are reported after the test of convergence and comparison with available results.