Functionally Graded Materials in Engineering - Structural Interfaces and Attachments in Biology - page 28

The through-the-thickness grading has a significant effect on buckling of truncated
conical FGM shells undergoing hydrostatic pressure [ 42 ]. An example of a finite
element free vibration analysis of doubly curved shear-deformable shells with
through-the-thickness grading is found in [ 43 ]. A graded finite element was devel-
oped for FGM geometrically nonlinear shells accounting for shear deformability
through the first-order theory in [ 44 ]. Although thermal problems are avoided in our
chapter, it is worth mentioning here the work analyzing thermomechanical behavior
of FGM cylindrical shells with flowing fluid; this analysis may relate to problems of
blood vessels that are also graded through their thickness [ 45 ].
The response of FGM structures with damage has received relatively little
attention. Vibrations of FGM beams with cracks of various orientation were
analyzed in [ 46 ].
Among potential applications of FGM structures wings and thin-walled blades
were considered in [ 47 , 48 ]. In particular the torsional stability of the wing was
enhanced using spanwise grading of material properties, rather than through-
the-thickness grading. Nonlinear supersonic flutter of FGM plates graded in the
thickness direction was considered in [ 49 ]. Temperature is often present in aero-
space structures; accordingly, we cite here papers accounting for thermal effects that
are avoided in the rest of this survey. Among other applications, numerous studies
have been conducted on functionally graded coatings; referenced here is paper [ 50 ].
A comprehensive review of earlier applications of FGM can be found in [ 3 ].
It is emphasized that the study of static and dynamic response of FGM structures
should be comprehensive, including a local strength analysis. The latter is particu-
larly important in FGM since their strength is a function of location, varying with
the volume fraction, orientation, and shape of inclusions. In addition, fracture
toughness of FGM is a function of coordinates and material architecture. These
observations further emphasize the necessity of the analysis and design addressing
all aspects of

the problem, i.e., micromechanics, stiffness, strength, and

macromechancial response.

2.4.3 FGM in Smart Structures

Research of smart FGM has mostly been confined to piezoelectrics. Panda and Ray
analyzed the effectiveness of a 1-3 piezoelectric composite employed as a
constraining layer to control nonlinear vibrations of a functionally graded plate,
including an optimum location of a damping patch [ 51 ]. The sliding frictional
contact problem of a graded piezoelectric half-plane in the state of plane strain
was considered by Ke et al. [ 52 ]. The displacements and electric potential in a
radially graded piezoelectric hollow shaft were found in [ 53 ]. Transient dynamic
problems in inhomogeneous piezoelectric solids were analyzed by a meshless
Petrov-Galerkin method concentrating on the unit step function loading [ 54 ]. Free
vibrations and static response of doubly curved magneto-electro-elastic FGM shells
with grading in the thickness direction were investigated in [ 55 , 56 ], respectively.