Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory

Sayyad, Atteshamuddin S.,Ghugal, Yuwaraj M. Techno-Press 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.51 No.5

An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is presented for static flexure of cross-ply laminated composite and sandwich plates. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the transverse shear deformation effect. The cosine function in thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term (involving thickness coordinate z) is expanded in power series, the kinematics of higher order theories (which are usually obtained by power series in thickness coordinate z) are implicitly taken into account to good deal of extent. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The closed-form solutions of simply supported cross-ply laminated composite and sandwich plates have been obtained. The results of present theory are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory.

An inverse hyperbolic theory for FG beams resting on Winkler-Pasternak elastic foundation

Sayyad, Atteshamuddin S.,Ghugal, Yuwaraj M. Techno-Press 2018 Advances in aircraft and spacecraft science Vol.5 No.6

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

Thermoelastic bending analysis of laminated plates subjected to linear and nonlinear thermal loads

Swami, Sandhya K.,Ghugal, Yuwaraj M. Techno-Press 2021 Advances in aircraft and spacecraft science Vol.8 No.3

The paper presents the analytical solutions for thick orthotropic laminated plates using trignometric shear deformation theory. The effects transverse shear and transverse normal strains are included with linear and nonlinear thermal loads. The displacement field of the theory includes the trigonometric functions in thickness coordinate of plate to account for these effects. The displacement field enforces to give the realistic variation of shear stresses across the thickness of plate and thus obviates the need of shear correction factor. The main novelty of the present study is the inclusion of thickness stretching effect in the theory. Another novelty is the application of nonlinear thermal profile consistent with the displacement field of the theory. The principle of virtual work is used to obtain the governing equations and boundary conditions. Simply supported laminated square plates are considered for numerical study to evaluate thermoelastic response. The results obtained by present theory with thickness stretching effect are compared with other refined theories disregarding this effect. It is observed that the results of present theory deviate significantly from the results of other higher order shear deformation theories for antisymmetric crossply laminated plates. The results of symmetric cross-ply laminated plates subjected to linear sinusoidal thermal load are in close agreement with those of exact theory, which validates the accuracy of present shear and normal deformation theory.

Cylindrical bending of multilayered composite laminates and sandwiches

Sayyad, Atteshamuddin S.,Ghugal, Yuwaraj M. Techno-Press 2016 Advances in aircraft and spacecraft science Vol.3 No.2

In a whole variety of higher order plate theories existing in the literature no consideration is given to the transverse normal strain / deformation effects on flexural response when these higher order theories are applied to shear flexible composite plates in view of minimizing the number of unknown variables. The objective of this study is to carry out cylindrical bending of simply supported laminated composite and sandwich plates using sinusoidal shear and normal deformation plate theory. The most important feature of the present theory is that it includes the effects of transverse normal strain/deformation. The displacement field of the presented theory is built upon classical plate theory and uses sine and cosine functions in terms of thickness coordinate to include the effects of shear deformation and transverse normal strain. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the shear stress free conditions at the top and bottom surfaces of the plate without using the problem dependent shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of minimum potential energy. The accuracy of the proposed theory is examined for several configurations of laminates under various static loadings. Some problems are presented for the first time in this paper which can become the base for future research. For the comparison purpose, the numerical results are also generated by using higher order shear deformation theory of Reddy, first-order shear deformation plate theory of Mindlin and classical plate theory. The numerical results show that the present theory provides displacements and stresses very accurately as compared to those obtained by using other theories.

Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory

Atteshamuddin S. Sayyad,Yuwaraj M. Ghugal 국제구조공학회 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.51 No.5

An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is presented for static flexure of cross-ply laminated composite and sandwich plates. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the transverse shear deformation effect. The cosine function in thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term (involving thickness coordinate z) is expanded in power series, the kinematics of higher order theories (which are usually obtained by power series in thickness coordinate z) are implicitly taken into account to good deal of extent. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The closed-form solutions of simply supported cross-ply laminated composite and sandwich plates have been obtained. The results of present theory are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory.

Bending analysis of exponentially varied FG plates using trigonometric shear and normal deformation theory

Sunil S. Yadav,Keshav K. Sangle,Mandar U. Kokane,Sandeep S. Pendhari,Yuwaraj M. Ghugal Techno-Press 2023 Advances in aircraft and spacecraft science Vol.10 No.3

In this paper, bending analysis of exponentially varying functionally graded (FG) plate is presented using trigonometric shear deformation theory (TSDT) considering both transverse shear and normal deformation effects. The in-plane displacement field consists of sinusoidal functions in thickness direction to include transverse shear strains and transverse displacement include the effect of transverse normal strain using the cosine function in thickness coordinate. The governing equations and boundary conditions of the theory are derived using the virtual work principle. System of governing equations, for simply supported conditions, Navier's solution technique is used to obtain results. Plate material properties vary across thickness direction according to exponential distribution law. In the current theory, transverse shear stresses are distributed accurately through the plate thickness, hence obviates the need for a shear correction factor. TSDT results are compared with those from other theories to ensure the accuracy and effectiveness of the present theory. The current theory is in excellent agreement with the semi-analytical theory.