Functionally Graded Materials in Engineering - Structural Interfaces and Attachments in Biology - page 27

In general, the main areas where research on the micromechanics and
homogenization of FGM is needed include:
1. Accounting for local RVE-scale variations in the properties associated with
rapidly varying volume fractions, shapes, and orientation of constituent
materials.
2. Multiscale aspects involving an interaction between local and global scales.
3. Random micromechanical formulations reflecting uncertainties of the distribu-
tion of constituent phases that may be particularly significant at the microscale as
well as uncertainties of constituent material properties.
2.4.2 FGM in Beams, Plates, and Shell Structures
Some of the recent studies of FGM plate structures include analyses of the effect of
grading on the nonlinear forced and free response of thin circular plates [ 26 , 27 ].
Axisymmetric static bending of annular transversely isotropic FGM plates
undergoing uniform pressure was considered in [ 28 ]. Experimental, numerical, and
analytical models of FGM plates subjected to low-velocity impact loading were
reflected in optimization formulation yielding material properties of individual layers
[ 29 ]. A higher-order layer-wise shear-deformation theory for FGM plates was devel-
oped and validated for static and dynamic representative cases [ 30 ]. A geometrically
nonlinear elastic formulation for FGM plates was developed in [ 31 ]. While
the majority of studies referenced above were confined to grading through the
thickness of the structure, elasticity solutions were also developed for FGM
beams with the elastic modulus varying both in the thickness and in the axial
directions [ 32 ].
The bending response of sandwich beams with viscoeleastic FGM facings
resting on an elastic foundation was considered in [ 33 ]. Various aspects of the
response of functionally graded sandwich panels were also considered in recent
studies [ 34 , 35 ].
Dynamic stability of shear-deformable FGMbeams, where the length scales of the
deformation field and the material microstructure are comparable, was investigated
using the couple stress theory [ 36 ]. The problem of dynamic stability of FGM
shear-deformable shells was considered in [ 37 ]. The impact problem of a thick
two-dimensionally graded hollow cylinder subject to an internal pressure was
investigated in [ 38 ] where, predictably, shells with a two-dimensional grading were
found superior to one-dimensional counterparts. Buckling of FGM cylindrical shells
under axial compression was analyzed, accounting for geometric nonlinearity and
initial imperfections [ 39 ]. The effect of through-the-thickness grading on the stress
distribution in hollow spherical shells was shown to be confined mostly to tangential
stresses, while radial stresses remained little affected [ 40 ]. A linear through-the-
thickness distribution of the shear modulus was found to produce a constant hoop or
circumferential stress in elastic FGMhollow cylinders and spheres, respectively [ 41 ].