This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

https://web.mst.edu/~vbirman/papers/Modeling%20and%20Analysis%20of%20FGM_Review_2007.pdf

Modeling and Analysis of Functionally Graded Materials and Structures

Static analysis of functionally graded beams using higher order shear deformation theory

In this study, problems related to the thermoelastic modeling and behavior of thin-walled beams made of functionally graded materials (FGMs) are addressed. In this context, two structural systems are considered: (i) rotating turbomachinery blades, and (ii) thin-walled beam structures spinning about their longitudinal axis. In all these cases, the structures operate in a high temperature environment. Under the spinning speed, gyroscopic forces are generated. Although conservative in nature, under their influence, as in nonconservative systems, instabilities by flutter and divergence can occur. In this context, the implications on their vibration and instability of conservative and gyroscopic forces considered in conjunction with a temperature field that yields the degradation of elastic properties are investigated. A continuously graded variation in composition of the ceramic and metal phases across the beam wall thickness in terms of a simple power law distribution is implemented. Results highlig...

Thin-Walled Beams Made of Functionally Graded Materials and Operating in a High Temperature Environment: Vibration and Stability

A new one-dimensional high-order theory for orthotropic elastic sandwich beams is formulated. This new theory is an extension of the high-order sandwich panel theory (HSAPT) and includes the in-plane rigidity of the core. In this theory, in which the compressibility of the soft core in the transverse direction is also considered, the displacement field of the core has the same functional structure as in the high-order sandwich panel theory. Hence, the transverse displacement in the core is of second order in the transverse coordinate and the in-plane displacements are of third order in the transverse coordinate. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core and the rotation at the centroid of the core) instead of just one (midpoint transverse displacement) commonly adopted in other available theories. It is proven, by comparison to the elasticity solution, that this approach results in superior accuracy, especially for the cases of stiffer cores, for which cases the other available sandwich computational models cannot predict correctly the stress fields involved. Thus, this theory, referred to as the “extended high-order sandwich panel theory” (EHSAPT), can be used with any combinations of core and face sheets and not only the very “soft” cores that the other theories demand. The theory is derived so that all core=face sheet displacement continuity conditions are fulfilled. The governing equations as well as the boundary conditions are derived via a variational principle. The solution procedure is outlined and numerical results for the simply supported case of transverse distributed loading are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. Furthermore, the results using the classical sandwich model without shear, the first-order shear, and the earlier HSAPT are also presented for completeness. The comparison among these numerical results shows that the solution from the current theory is very close to that of the elasticity in terms of both the displacements and stress or strains, especially the shear stress distributions in the core for a wide range of cores. Finally, it should be noted that the theory is formulated for sandwich panels with a generally asymmetric geometric layout. [DOI: 10.1115/1.4005550]

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Analysis of Sandwich Beams With a Compliant Core and With In-Plane Rigidity—Extended High-Order Sandwich Panel Theory Versus Elasticity

Experiments on curved sandwich panels under blast loading

Dynamic buckling of flat and curved sandwich panels with transversely compressible core

The thermoelastic modeling, vibration and instability of spinning thin-walled beams made of functionally graded ceramic-metal based materials are addressed. In this context, the case of pretwisted beams of non-uniform cross-section along their longitudinal axis and subjected to a temperature field of a prescribed gradient through the blade wall thickness, is considered. A continuously graded variation in composition of the ceramic and metal phases across the beam wall thickness in terms of a simple power law distribution is implemented. Results highlighting the effects of the volume fraction, temperature gradient, cross-section aspect ratio, pretwist, compressive axial load on vibration and instability of spinning beams are presented and pertinent conclusions are outlined.

Spinning thin-walled beams made of functionally graded materials: modeling, vibration and instability

Thin-Walled Rotating Composite Blades Featuring Extension-Twist Elastic Coupling

The present study is concerned with the analysis of the transient response of softcore sandwich structures in the postbuckling range using a higher-order geometrically nonlinear shell model including the transverse core compressibility. The transverse compressibility results in the development of a chaotic vibration with unpredictable wrinkling amplitudes and has significant effects on the eigenfrequency.

Sang Yong Oh

Papers

Dynamic buckling of flat and curved sandwich panels with transversely compressible core

Spinning thin-walled beams made of functionally graded materials: modeling, vibration and instability

Thin-Walled Rotating Composite Blades Featuring Extension-Twist Elastic Coupling

Effect of Transverse Core Compressibility on Dynamic Buckling of Sandwich Structures