Variable Kinematic Model for the Analysis of Functionally Graded Material plates

Advanced mixed theories for bending analysis of functionally graded plates

“…The solution of Pan extends that of Pagano [13,14] to FGMs, so it could degenerate in this last if a constant properties material is considered. Two previous authors' works [15,16] have extended the unified formulation (UF) by Carrera [17,18] and the principle of virtual displacements (PVD) to FGM plates; obtained results showed excellent agreement with 3D analysis by Kashtalyan [2] as well as the improvements respect to classical models as that by Zenkour [19]. Extension to thermal case has been provided in [20] where the problem in [5] has been analyzed.…”

A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates

“…q mn sin λx sin µy (26) where q mn =q 0 for sinusoidally distributed load. Assuming that the plate is subjected to in-plane compressive loads of form:…”

“…Large applications of functionally graded (FG) structures have led the development of various plate theories to predict accurately their static, buckling and vibration behaviours. They are generally followed: classical plate theory (CPT) neglecting the transverse shear deformation effects ( [2]- [7]), first-shear deformation theory (FSDT) with linear variation of displacements ( [5], [8]- [14]), higher-order shear deformation theory (HSDT) with higher-order variations of displacements through the plate thickness such as thirdorder shear deformation plate theory (TSDT), sinusoidal shear deformation plate theory (SSDT), hyperbolic shear deformable plate theory (HDT) ( [15]- [25]), quasi-3D theories taking into account normal stretching effect ( [26]- [37]). Moreover, owing to smooth variations of material properties, FG sandwich plates have recently been developed to overcome interface problems between faces and core found in conventional sandwich structures.…”

A layerwise theory for N th-layer functionally graded plates including thickness stretching effects

“…(14) If the plate is subjected to normal sinusoidal load distributed only on the top plate surface , are mode numbers, then, the displacements may be expressed as: 10 where and are arbitrary parameters. Using the constitutive equations , it is possible to get the governing equations in terms of the displacements only, and substitute the expressions into the resulting equations(after dropping the inertia terms); we get an algebraic system of equations in the coefficient and .…”