Abstract
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.
Highlights
Due to attractive structural properties like high strength-to-weight and high stiffness-to-weight ratios, the demand of composite materials is increased in many engineering industries such as mechanical engineering, marine engineering, civil engineering, aerospace engineering, etc
4) The present theory is strongly recommended for the analysis of laminated composite and sandwich plates, because it yields accurate prediction of displacements and stresses compared to existing non-polynomial type theories
The accuracy of the solution is checked by comparing results obtained using the present theory (FOSNDT) with the other theories and the exact elasticity solution wherever available in the literature
Summary
Due to attractive structural properties like high strength-to-weight and high stiffness-to-weight ratios, the demand of composite materials is increased in many engineering industries such as mechanical engineering, marine engineering, civil engineering, aerospace engineering, etc. The FSDT shows constant variation of transverse shear stress through the thickness of the plate and required shear correction factor to properly account the strain energy due to shear deformation These limitations of CLPT and FSDT leads to the development of higher order refined plate theories. To prove the efficiency of the present theory, the non-dimensional displacements and stresses obtained for laminated composite and sandwich plates and are compared with existing exact elasticity solutions and other theories. The important contributions in the present study are summarized as follows: 1) In the present study, a new higher-order shear and normal deformation theory is developed and applied for the bi-directional bending of laminated composite and sandwich plates subjected to transverse loadings. 4) The present theory is strongly recommended for the analysis of laminated composite and sandwich plates, because it yields accurate prediction of displacements and stresses compared to existing non-polynomial type theories. 5) The most important feature of the present theory is it predicts accurate interlaminar shear stresses as compared to any other refined plate theories available in the literature
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