On the equations of an eighth-order theory for nonhomogeneous transversely isotropic plates

2006

Arch Appl Mech

187

The bending problem of a transverse load acting on an isotropic inhomogeneous rectangular plate using both two-dimensional (2-D) trigonometric and three-dimensional (3-D) elasticity solutions is considered. In the present 2-D solution, trigonometric terms are used for the displacements in addition to the initial terms of a power series through the thickness. The effects due to transverse shear and normal deformations are both included. The form of the assumed 2-D displacements is simplified by enforcing traction-free boundary conditions at the faces of the plate. No transverse shear correction factors are needed because a correct representation of the transverse shearing strain is given. The plate material is exponentially graded, meaning that Lamé's coefficients vary exponentially in a given fixed direction (the thickness direction). A wide variety of results for the displacements and stresses of an exponentially graded rectangular plate are presented. The validity of the present 2-D trigonometric solution is demonstrated by comparison with the 3-D elasticity solution. The influence of aspect ratio, side-to-thickness ratio and the exponentially graded parameter on the bending response are investigated.

Section: Introductionmentioning

confidence: 99%

“…The variation of u through the thickness of an EG rectangular plate (k = 0.5, a/ h = 4) As seen from Figs 8,9,15,. and 16, the maximum values of the out-of-plane transverse shear stresses σ 5 and σ 4 do not occur at z = 0.…”

mentioning

confidence: 96%

Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate

2006

Arch Appl Mech

187

“…Even, there are a few studies regarding structural behaviors of inhomogeneous laminated plates [42][43][44]. Different theories of homogeneous composite plates [45] are extended to deal with the corresponding inhomogeneous ones. Fares and Zenkour [46] presented the free vibration and buckling responses of inhomogeneous laminated plates.…”

Section: Introductionmentioning

confidence: 99%

Stresses in inhomogeneous elastic–viscoelastic–elastic sandwich plates via hyperbolic shear deformation theory

J Braz. Soc. Mech. Sci. Eng.

El-Mekawy

2018

A hyperbolic shear deformation theory is proposed to investigate the bending analysis of inhomogeneous elastic/viscoelastic/elastic (EVE) sandwich plates. The sandwich plate is consisting of two elastic material faces and viscoelastic material core. Three kinds of symmetric sandwich plates that are classified depending on thickness of each layer are presented. A fourth type of sandwich plate is considered without viscoelastic core. The equilibrium equations have been solved by using Illyushin's approximation method as well as the effective moduli method. The deflection and stresses of simply supported EVE sandwich plates have been presented due to a hyperbolic theory and compared with those due to other familiar plate theories. The effect of different parameters on bending analysis of sandwich plates is discussed.

“…But, these studies are limited to the response of homogenous, isotropic plates. Even, a few studies accounting for the structural response of inhomogeneous plates deal with special cases of inhomogeneity, anisotropy, and thickness uniformity, and the reported results in open literature are rare [Whitney and Pagano (1970); Bert (1973); Librescu (1975); Reissner (1991Reissner ( , 1994; Fares (1999, 2001); Fares and Zenkour (1999)]. …”

Section: Introductionmentioning

confidence: 99%

Linear Bending Analysis of Inhomogeneous Variable-Thickness Orthotropic Plates Under Various Boundary Conditions

Int. J. Comput. Methods

Allam

Mashat

2007

An exact solution to the bending of variable-thickness orthotropic plates is developed for a variety of boundary conditions. The procedure, based on a Lévy-type solution considered in conjunction with the state-space concept, is applicable to inhomogeneous variable-thickness rectangular plates with two opposite edges simply supported. The remaining ones are subjected to a combination of clamped, simply supported, and free boundary conditions, and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for inhomogeneous variable-thickness plates as for isotropic homogeneous plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Benchmark numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of inhomogeneity, aspect ratio, thickness parameter, and the degree of nonuniformity on the deflections and stresses are investigated.