• Steel and Composite Structures
• /
• v.21 no.6
• /
• pp.1347-1368
• /
• 2016

In this article, an exact analytical solution for mechanical buckling analysis of symmetrically cross-ply laminated plates including curvature effects is presented. The equilibrium equations are derived according to the refined nth-order shear deformation theory. The present refined nth-order shear deformation theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments The most interesting feature of this theory is that it accounts for a parabolic variation 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. Buckling of orthotropic laminates subjected to biaxial inplane is investigated. Using the Navier solution method, the differential equations have been solved analytically and the critical buckling loads presented in closed-form solutions. The sensitivity of critical buckling loads to the effects of curvature terms and other factors has been examined. The analysis is validated by comparing results with those in the literature.

• Advances in nano research
• /
• v.7 no.5
• /
• pp.351-364
• /
• 2019

In this work, dynamic behavior of functionally graded (FG) porous nano-beams is studied based on nonlocal nth-order shear deformation theory which takes into the effect of shear deformation without considering shear correction factors. It has been observed that during the manufacture of "functionally graded materials" (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the dynamic analysis of FG beams taking into account the influence of these imperfections is established. Material characteristics of the FG beam are supposed to be vary continuously within thickness direction according to a "power-law scheme" which is modified to approximate material characteristics for considering the influence of porosities. A comparative study with the known results in the literature confirms the accuracy and efficiency of the current nonlocal nth-order shear deformation theory.

• Geomechanics and Engineering
• /
• v.13 no.3
• /
• pp.385-410
• /
• 2017

This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Earthquakes and Structures
• /
• v.17 no.3
• /
• pp.257-270
• /
• 2019

The purpose of this work is to analyze the bending behavior of laminated composite plates using the refined fourvariable theory and the finite element method approach using an ANSYS 12 computational code. The analytical model is based on the multilayer plate theory of shear deformation of the nth-order proposed by Xiang et al 2011 using the theory principle developed by Shimpi and Patel 2006. Unlike other theories, the number of unknown functions in the present theory is only four, while five or more in the case of other theories of shear deformation. The formulation of the present theory is based on the principle of virtual works, it has a strong similarity with the classical theory of plates in many aspects, it does not require shear correction factor and gives a parabolic description of the shear stress across the thickness while filling the condition of zero shear stress on the free edges. The analysis is validated by comparing results with those in the literature.

• Wind and Structures
• /
• v.29 no.6
• /
• pp.371-387
• /
• 2019

In the present paper, a simple refined nth-higher-order shear deformation theory is applied for the free vibration analysis of laminated composite plates. The proposed displacement field is based on a novel kinematic in which include the undetermined integral terms and contains only four unknowns, as against five or more in case of other higher-order theories. The present theory accounts for adequate distribution of the transverse shear strains through the plate thickness and satisfies the shear stress-free boundary conditions on the top and bottom surfaces of the plate, therefore, it does not require problem dependent shear correction factor. The governing equations of motion are derived from Hamilton's principle and solved via Navier-type to obtain closed form solutions. The numerical results of non-dimensional natural frequencies obtained by using the present theory are presented and compared with those of other theories available in the literature to verify the validity of present solutions. It can be concluded that the present refined theory is accurate and efficient in predicting the natural frequencies of isotropic, orthotropic and laminated composite plates.

• Computers and Concrete
• /
• v.33 no.1
• /
• pp.27-39
• /
• 2024

In this study, the authors investigate the free vibration behavior of three-phases functionally graded sandwich plates using a novel nth-order shear deformation theory. These plates are composed of a homogeneous core and two face-sheet layers made of different functionally graded materials. This is the novel type of the sandwich structures that can be applied in many fields of mechanical engineering and industrial. The proposed theory only requires four unknown displacement functions, and the transverse displacement does not need to be separated into bending and shear parts, simplifying the theory. One noteworthy feature of the proposed theory is its ability to capture the parabolic distribution of transverse shear strains and stresses throughout the plate's thickness while ensuring zero values on the two free surfaces. By eliminating the need for shear correction factors, the theory further enhances computational efficiency. Equations of motion are established using Hamilton's principle and solved via Navier's solution. The accuracy and efficiency of the proposed theory are verified by comparing results with available solutions. The authors then use the proposed theory to investigate the free vibration characteristics of three-phases functionally graded sandwich plates, considering the effects of parameters such as aspect ratio, side-to-thickness ratio, skin-core-skin thicknesses, and power-law indexes. Through careful analysis of the free vibration behavior of three-phases functionally graded sandwich plates, the work highlighted the significant roles played by individual material ingredients in influencing their frequencies.

• Smart Structures and Systems
• /
• v.25 no.2
• /
• pp.197-218
• /
• 2020

In this work, thermomechanical flexural analysis of functionally graded material sandwich plates with P-FGM face sheets and E-FGM and symmetric S-FGM core is performed by employing a nth-order shear deformation theory. A novel type of S-FGM sandwich plates, namely, both P-FGM face sheets and a symmetric S-FGM hard core are considered. By employing only four unknown variables, the governing equations are obtained based on the principle of virtual work and then Navier method is used to solve these equations. Analytical solutions are deduced to compute the stresses and deflections of simply supported S-FGM sandwich plates. The effects of volume fraction variation, geometrical parameters and thermal load on thermomechanical flexural behavior of the symmetric FGM sandwich plates are investigated.