• Steel and Composite Structures
• /
• 제3권6호
• /
• pp.439-450
• /
• 2003

The finite strip transition matrix technique, a semi analytical method, is employed to obtain the buckling loads and the natural frequencies of symmetric cross-ply laminated composite plates with edges elastically restrained against both translation and rotation. To illustrate the accuracy and the validation of the method several example of cross play laminated composite plates were analyzed. The buckling loads and the frequency parameters are presented and compared with available results in the literature. The convergence study and the excellent agreement with known results show the reliability of the purposed technique.

• 소음진동
• /
• 제2권4호
• /
• pp.305-315
• /
• 1992

In order to investigate the effects of layer-wise in-plane displacements on vibration and damping characteristics of composite laminated plates, the finite element method based on the generalized laminated plate theory(GLPT) has been formulated. Specific damping capacity of each mode was obtained by modal strain energy method. To see the effect of transverse shear on deformation, the strain energy of stress components was computed. The accuracy of this study was examined for the cylindrical bending vibration of cross-ply plate strip. The results were very accurate compared with 3-D solutions. The numerical results show that through-thickness variation of in-plane displacements has not so much influence on the natural frequency, but has a great influence on the damping of composite plates, especially on the damping of thick composite plates since the damping is affected by local behavior while the natural frequency is affected by global behavior.

• Smart Structures and Systems
• /
• 제25권4호
• /
• pp.409-422
• /
• 2020

This article deals with the flexural analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal loading using a refined plate theory with four variables. In this theory, the undetermined integral terms are used and the number of variables is reduced to four, instead of five or more in other higher-order theories. The boundary conditions on the top and the bottom surfaces of the plate are satisfied; hence the use of the transverse shear correction factors is avoided. The principle of virtual work is used to obtain governing equations and boundary conditions. Navier solution for simply supported plates is used to derive analytical solutions. For the validation of the present theory, numerical results for displacements and stresses are compared with those of classical, first-order, higher-order and trigonometric shear theories reported in the literature.

• Advances in nano research
• /
• 제7권5호
• /
• pp.337-349
• /
• 2019

The size-dependent vibration analysis of a cross-/angle-ply laminated composite plate when embedded on the Pasternak elastic foundation and exposed to an in-plane magnetic field are investigated by adopting an analytical eigenvalue approach. The formulation, which is based on refined-hyperbolic-shear-deformation-plate theory in conjunction with the Eringen Nonlocal Differential Model (ENDM), is tested against considering problems for which numerical/analytical solutions available in the literature. The findings of this study demonstrated the role of magnetic field, size effect, elastic foundation coefficients, geometry, moduli ratio, lay-up numbers and fiber orientations on the nonlocal frequency of cross-/angle-ply laminated composite plates.

• Structural Engineering and Mechanics
• /
• 제74권3호
• /
• pp.365-380
• /
• 2020

The focus of this paper is to develop an analytical approach based on an efficient shear deformation theory with stretching effect for bending stress analysis of cross-ply laminated composite plates subjected to transverse parabolic load and line load by using a new kinematic model, in which the axial displacements involve an undetermined integral component in order to reduce the number of unknowns and a sinusoidal function in terms of the thickness coordinate to include the effect of transverse shear deformation. The present theory contains only five unknowns and satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without using any shear correction factors. The governing differential equations and its boundary conditions are derived by employing the static version of principle of virtual work. Closed-form solutions for simply supported cross-ply laminated plates are obtained applying Navier's solution technique, and the numerical case studies are compared with the theoretical results to verify the utility of the proposed model. Lastly, it can be seen that the present outlined theory is more accurate and useful than some higher-order shear deformation theories developed previously to study the static flexure of laminated composite plates.

• Steel and Composite Structures
• /
• 제41권5호
• /
• pp.697-711
• /
• 2021

In this work, a simple quasi 3-D parabolic shear deformation theory is developed to examine the bending response of antisymmetric cross-ply laminated composite plates under different types of mechanical loading. The main feature of this theory is that, in addition to including the transverse shear deformation and thickness stretching effects, it has only five-unknown variables in the displacement field modeling like Mindlin's theory (FSDT), yet satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without requiring a shear correction factor. The static version of principle of virtual work was employed to derive the governing equations, while the bending problem for simply supported antisymmetric cross-ply laminated plates was solved by a Navier-type closed-form solution procedure. The adequacy of the proposed model is handled by considering the impact of side-to-thickness ratio on bending response of plate through several illustrative examples. Comparison of the obtained numerical results with the other shear deformation theories leads to the conclusion that the present model is more accurate and efficient in predicting the displacements and stresses of laminated composite plates.

• Structural Engineering and Mechanics
• /
• 제18권3호
• /
• pp.377-388
• /
• 2004

Based on the basic equations of elasticity, free-edge effects on stresses in cross-ply laminated plates are found by using the state space method. The laminates are subjected to uniaxial-uniform extension plate, which is a typical example of general plane strain problem. The study takes into account material constants of all individual material layers and the state equation of a laminate is solved analytically in the through thickness direction. By this approach, a composite plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The solution provides a continuous displacement and inter-laminar stress fields across all material interfaces and an approxiamte prediction to the singularity of stresses occurring in the boundary layer region of a free-edge. Numerical solutions are obtained and compared with the results obtained from an alternative numerical method.

• Steel and Composite Structures
• /
• 제22권4호
• /
• pp.713-732
• /
• 2016

A novel four variable refined plate theory is proposed in this work for laminated composite plates. The theory considers a parabolic distribution of the transverse shear strains, and respects the zero traction boundary conditions on the surfaces of the plate without employing shear correction coefficient. The displacement field is based on a novel kinematic in which the undetermined integral terms are used, and only four unknowns are involved. The analytical solutions of antisymmetric cross-ply and angle-ply laminates are determined via Navier technique. The obtained results from the present model are compared with three-dimensional elasticity solutions and results of the first-order and the other higher-order theories reported in the literature. It can be concluded that the developed theory is accurate and simple in investigating the bending and buckling responses of laminated composite plates.

• 항공우주시스템공학회지
• /
• 제1권4호
• /
• pp.28-36
• /
• 2007

This paper presents critical buckling loads of laminated composites under cylindrical bending. In-plane displacements are assumed to vary exponentially through plate thickness. The accuracy of this theory is examined for symmetric/antisymmetric cross-ply, angle-ply and unsymmetric laminates under cylindrical bending. Analytical solutions are provided to investigate the effect of transverse shear deformation on critical buckling loads of the laminated plates, and the results are compared with those obtained from the first-order shear deformation plate theory and the classical laminated plate theory.

• Steel and Composite Structures
• /
• 제17권3호
• /
• pp.321-338
• /
• 2014

In the present study, a new simple first-order shear deformation theory is presented for laminated composite plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher-order shear deformation theories. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions of simply supported antisymmetric cross-ply and angle-ply laminates are obtained and the results are compared with the exact three-dimensional (3D) solutions and those predicted by existing theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of laminated composite plates.