Abstract In the present paper, a new fifth-order shear and normal deformation theory (FOSNDT) is developed for the bi-directional bending analysis of laminated composite and sandwich plates subjected to transverse loads. This theory considered the effects of both transverse shear and normal deformations. In-plane displacements use a polynomial shape function expanded up to fifth-order in terms of the thickness coordinate to properly account the effect of transverse shear deformation. Transverse displacement is the function of x, y and z- coordinates to account the effect of transverse normal deformations i.e. thickness stretching. Hence, the present theory involves nine unknowns in the displacement field. The present theory does not require a problem dependent shear correction factor as it satisfies traction free boundary conditions at top and bottom surfaces of the plate. The governing differential equations and associated boundary conditions are obtained using the principle of virtual work. The plate is analysed for simply supported boundary conditions using Navier’s solution technique. To prove the efficiency of the present theory, the non-dimensional displacements and stresses obtained for laminated composite and sandwich plates are compared with existing exact elasticity solutions and other theories. It is observed from the comparision that the displacements and stresses obtained by the present theory are in excellent agreement with the results obtained by exact elasticity solutions compared to other higher-order plate theories available in the literature.

Abstract In the present study, a new fifth-order shear and normal deformation theory (FOSNDT) is developed for the analysis of laminated composite and sandwich plates under cylindrical bending. The theory considered the effects of transverse shear and normal deformations. To account for the effect of transverse shear deformation, in-plane displacement uses polynomial shape function expanded up to fifth-order in-terms of the thickness coordinate. Transverse displacement uses derivative of shape function to account for the effect of transverse normal deformations. Therefore, the present theory involves six independent unknown variables. The theory satisfies traction free boundary conditions at top and bottom surfaces of the plate and does not require the shear correction factor. The principle of virtual work is used to obtain the variationally consistent governing differential equations and associated boundary conditions. Analytical solutions for simply supported boundary conditions are obtained using Navier’s solution technique. Non-dimensional displacements and stresses obtained using the present theory are compared with existing exact elasticity solutions and lower and higher-order theories to prove the efficacy of the present theory. The comparison shows that the displacements and stresses predicted by the present theory are in good agreement with those obtained by using the exact solution.

Abstract A new fifth-order shear and normal deformation theory (FOSNDT) is developed for the static bending and elastic buckling analysis of functionally graded beams. The properties of functionally graded material are assumed to vary through the thickness direction according to power-law distribution (P-FGM). The most important feature of the present theory is that it includes the effects of transverse shear and normal deformations. Axial and transverse displacements involve polynomial shape functions to include the effects of transverse shear and normal deformations. A polynomial shape function expanded up to fifth-order in terms of the thickness coordinate is used to account for the effects of transverse shear and normal deformations. The kinematics of the present theory is based on six independent field variables. The theory satisfies the traction free boundary conditions at top and bottom surfaces of the beam without using problem dependent shear correction factor. The closed-form solutions of simply supported FG beams are obtained using Navier’s solution procedure and non-dimensional results are compared with those obtained by using classical beam theory, first order shear deformation theory and other higher order shear deformation theories. It is concluded that the present theory is accurate and efficient in predicting the bending and buckling responses of functionally graded beams.

In the present paper, an exponential shear deformation theory is used to determine the natural frequencies and critical buckling loads of orthotropic plates. The theory accounts for a parabolic distribution of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The in-plane displacement field uses an exponential function in terms of thickness coordinate to include the effect of shear deformation and rotary inertia. Governing equations and boundary conditions are derived from the dynamic version of principle of virtual work. The Navier type solution is employed for solving the governing equations of simply supported square orthotropic plates. The results obtained using present higher order shear deformation theory are found to be agree well with those obtained by other several existing higher order theories for analyzing the buckling and free vibration behaviour of orthotropic plates.

In the present paper, a variationally consistent exponential shear deformation theory taking into account transverse shear deformation effect is presented for the flexural analysis of thick orthotropic plates. The inplane displacement field uses exponential function in terms of thickness coordinate to include the shear deformation effect. The transverse shear stress can be obtained directly from the constitutive relations satisfying the shear stress free surface conditions on the top and bottom surfaces of the plate, hence the theory does not require shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for static flexure of simply supported orthotropic plates are compared with those of other refined theories and elasticity solution wherever applicable. The results obtained by present theory are in excellent agreement with those of exact results and other higher order theories. Thus the efficacy of the present refined theory is established.

In this paper a trigonometric shear deformation theory is presented for the free vibration of thick orthotropic square and rectangular plates. In this displacement based theory the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The most important feature of the theory is that the transverse shear stress can be obtained directly from the constitutive relations satisfying the shear stress free surface conditions on the top and bottom surfaces of the plate. Hence the theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for frequency of bending mode, shear mode and thickness stretch mode of free vibration of simply supported orthotropic square and rectangular plates are compared with those of other refined theories and exact solution from theory of elasticity wherever applicable.