• Geomechanics and Engineering
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• v.14 no.6
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• pp.519-532
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• 2018

In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton's principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.

• Smart Structures and Systems
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• v.26 no.1
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• pp.77-87
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• 2020

By employing a quasi-3D plate formulation, the present research studies static stability of magneto-electro-thermo-elastic functional grading (METE-FG) nano-sized plates. Accordingly, influences of shear deformations as well as thickness stretching have been incorporated. The gradation of piezo-magnetic and elastic properties of the nano-sized plate have been described based on power-law functions. The size-dependent formulation for the nano-sized plate is provided in the context of nonlocal elasticity theory. The governing equations are established with the usage of Hamilton's rule and then analytically solved for diverse magnetic-electric intensities. Obtained findings demonstrate that buckling behavior of considered nanoplate relies on the variation of material exponent, electro-magnetic field, nonlocal coefficient and boundary conditions.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.571-589
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• 2019

This paper aims to develop a quasi-3D shear deformation theory for the study of bending, buckling and free vibration responses of functionally graded (FG) sandwich thick plates. For that, in the present theory, both the components of normal deformation and shear strain are included. The displacement field of the proposed model contains undetermined integral terms and involves only four unknown functions with including stretching effect. Using Navier's technique the solution of the problem is derived for simply supported sandwich plate. Numerical results have been reported, and compared with those available in the open literature were excellent agreement was observed. Finally, a detailed parametric study is presented to demonstrate the effect of the different parameters on the flexural responses, free vibration and buckling of a simply supported sandwich plates.

• Advances in nano research
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• v.7 no.1
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• pp.63-75
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• 2019

This article represents a quasi-3D theory for the buckling investigation of magneto-electro-elastic functionally graded (MEE-FG) nanoplates. All the effects of shear deformation and thickness stretching are considered within the presented theory. Magneto-electro-elastic material properties are considered to be graded in thickness direction employing power-law distribution. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of such nanoplates. Using Hamilton's principle, the nonlocal governing equations based on quasi-3D plate theory are obtained for the buckling analysis of MEE-FG nanoplates including size effect and they are solved applying analytical solution. It is found that magnetic potential, electric voltage, boundary conditions, nonlocal parameter, power-law index and plate geometrical parameters have significant effects on critical buckling loads of MEE-FG nanoscale plates.

• Smart Structures and Systems
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• v.22 no.3
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• pp.303-314
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• 2018

An original quasi-3D hyperbolic shear deformation theory for simply supported functionally graded plates is proposed in this work. The theory considers both shear deformation and thickness-stretching influences by a hyperbolic distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower surfaces of the plate without using any shear correction coefficient. By expressing the shear parts of the in-plane displacements with the integral term, the number of unknowns and equations of motion of the proposed theory is reduced to four as against five in the first shear deformation theory (FSDT) and common quasi-3D theories. Equations of motion are obtained from the Hamilton principle. Analytical solutions for dynamic problems are determined for simply supported plates. Numerical results are presented to check the accuracy of the proposed theory.

• Structural Engineering and Mechanics
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• v.83 no.6
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• pp.771-788
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• 2022

This research investigates the free vibration of porous advanced composite plates resting on Winkler/Pasternak/ Kerr foundations by using a new hyperbolic quasi three dimensional (quasi-3D) shear deformation theory. The present theory, which does not require shear correction factor, accounts for shear deformation and thickness stretching effects by parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate. In this work, we consider imperfect FG plates with porosities embedded within elastic Winkler, Pasternak or Kerr foundations. Implementing an analytical approach, the obtained governing equations from Hamilton's principle according to FG plates are derived. The closed form solutions are obtained by using Navier technique, and natural frequencies of FG plates are found, for simply supported plates, by solving the results of eigenvalue problems. A comprehensive parametric study is presented to evaluate effects of the geometry of material, mode numbers, porosity volume fraction, Power-law index and stiffness of foundations parameters on free vibration characteristics of FG plates.

• Structural Engineering and Mechanics
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• v.85 no.6
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• pp.765-780
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• 2023

In this work, a novel combined logarithmic, secant and tangential 2D and quasi-3D refined higher order shear deformation theory is proposed to examine the buckling analysis of simply supported uniform functionally graded plates under uniaxial and biaxial loading. The proposed formulations contain a reduced number of variables compared to others similar solutions. The combined function employed in this study ensures automatically the zero-transverse shear stresses at the free surfaces of the structure. Various models of the material distributions are considered (linear, quadratic, cubic inverse quadratic and power-law). The differentials stability equations are derived via virtual work principle with including the stretching effect. The Navier's approach is applied to solve the governing equations which satisfying the boundary conditions. Several comparative and parametric studies are performed to illustrates the validity and efficacity of the proposed model and the various factors influencing the critical buckling load of thick FG plate.

• Geophysics and Geophysical Exploration
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• v.4 no.3
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• pp.70-79
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• 2001

The integral equation method is a powerful tool for numerical electromagnetic modeling. But the difficulty of this technique is the size of the linear equations, which demands excessive memory and calculation time to invert. This limitation of the integral equation method becomes critical in inverse problem. The conventional Born approximation, where the electric field in the anomalous body is approximated by the background field, is very rapid and easy to compute. However, the technique is inaccurate when the conductivity contrast between the body and the background medium is large. Quasi-linear, quasi-analytical and extended Born approximations are novel approaches to 3-D EM modeling based on the linearization of the integral equations for scattered EM field. These approximation methods are much less time consuming than full integral equation method and more accurate than conventional Born approximation. They we, however, still approximate methods for 3-D EM modeling. Iterative series methods such as modified Born, quasi-linear and quasi-analytical can be used to increase the accuracy of various approximation methods. Comparisons of numerical performance against a full integral equation and various approximation codes show that the iterative series methods are very accurate and almost always converge. Furthermore, they are very fast and easy to implement on a computer. In this study, extended Born series method is developed and it shows more accurate result than that of other series methods. Therefore, Iterative series methods, including extended Born series, open principally new possibilities for fast and accurate 3-D EM modeling and inversion.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.3
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• pp.92-98
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• 1998

This paper presents three boundary techniques which are useful for FEM analysis of composite laminates: 1) a rotational symmetric boundary technique . 2) a quasi three-dimensional boundary technique and 3) a contact boundary technique. The use of the rotational symmetric boundary technique is possible for a smaller FEM model. With the use of the quasi three-dimensional boundary tecnique. quasi three dimensional analysis of composite laminates can be performed on the conventional 3-D FEM program These techniques can readily be adopted to FEM programs.

• Steel and Composite Structures
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• v.45 no.6
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• pp.839-850
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• 2022

This paper presents an analytical solution to study the combined effect of non-local and stretching effect on the vibration of advanced functionally graded (FG) nanoplates. A new quasi-3D plate theory is presented; there are only five unknowns and any shear correction factor is used. A new displacement field with a new shear warping function is proposed. The equilibrium equations of the FG nanoplates are obtained using the Hamilton principle and solved numerically using the Navier technique. The material properties of functionally graded nanoplates are presumed to change according to the power-law distribution of ceramic and metal constituents. The numerical results of this work are compared with those of other published results to indicate the accuracy and convergence of this theory. Hence, a profound parameterstudy is also performed to show the influence of many parameters of the functionally graded nanoplates on the free vibration responses is investigated.