A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates - Mahi, Amale; Adda Bedia, El Abbas; Tounsi, Abdelouahed (Applied mathematical modelling, 2015)
A new hyperbolic shear deformation theory applicable to bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates is presented. This new theory has five degrees of freedom, provides parabolic transverse shear strains across the thickness direction and hence, it does not need shear correction factor. Moreover, zero-traction boundary conditions on the top and bottom surfaces of the plate are satisfied rigorously. The energy functional of the system is obtained using Hamilton’s principle. Analytical solutions of deflection and stresses are obtained using Navier-type procedure. Free vibration frequencies are then accurately calculated using a set of boundary characteristic orthogonal polynomials associated with Ritz method. Numerical comparisons are conducted to verify and to demonstrate the accuracy and efficiency of the present theory. Excellent agreement with the known results in the literature has been obtained.