A new beam finite element for the analysis of functionally graded materials

Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory

“…It is known that the behaviours of isotropic and FG sandwich beams can be predicted by classical beam theory (CBT) ( [1][2][3][4][5]), first-order shear deformation beam theory (FSBT) ( [6][7][8][9][10][11][12]) and higher-order shear deformation beam theory (HSBT) ( [1,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]) or three-dimensional (3D) elasticity theory ([32-34] and overestimates buckling load and natural frequencies due to ignoring the shear deformation effect.…”

Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories

“…The first-order shear deformation beam theory (FBT) known as Timoshenko beam theory has been proposed to overcome the limitations of the CBT by accounting for the transverse shear deformation effect. Since the FBT violates the zero shear stress conditions on the top and bottom surfaces of the beam, a shear correction factor is required to account for the discrepancy between the actual stress state and the assumed constant stress state [4][5][6][7]. To avoid the use of a shear correction factor and have a better prediction of response of FG beams, higher-order shear deformation theories have been proposed, notable among them are the third-order theory of Reddy [8][9][10][11][12], the sinusoidal theory of Touratier [13], the hyperbolic theory of Soldatos [14], the exponential theory of Karama et al [15], and the unified formulation of Carrera [16][17].…”

Deformation analysis of functionally graded beams by the direct approach

“…Note that in the case of homogeneous materials the general prob lem decouples into the extension torsion problem and the bend ing shear problem, see [21]. The relations of identification (10) and (11), written for straight rods, become…”