• Wind and Structures
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• v.27 no.5
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• pp.311-324
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• 2018

This work examines vibration and bending response of carbon nanotube-reinforced composite plates resting on the Pasternak elastic foundation. Four types of distributions of uni-axially aligned single-walled carbon nanotubes are considered to reinforce the plates. Analytical solutions determined from mathematical formulation based on hyperbolic shear deformation plate theory are presented in this study. An accuracy of the proposed theory is validated numerically by comparing the obtained results with some available ones in the literature. Various considerable parameters of carbon nanotube volume fraction, spring constant factors, plate thickness and aspect ratios, etc. are considered in the present investigation. According to the numerical examples, it is revealed that the vertical displacement of the plates is found to diminish as the increase of foundation parameters; while, the natural frequency increase as the increment of the parameters for every type of plate.

• Steel and Composite Structures
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• v.38 no.1
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• pp.1-15
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• 2021

In this paper, a higher order shear deformation theory for bending analysis of functionally graded plates resting on Pasternak foundation and under various boundary conditions is exposed. The proposed theory is based on the assumption that porosities can be produced within functionally graded plate which may lead to decline in strength of materials. In this research a novel distribution of porosity according to the thickness of FG plate are supposing. Governing equations of the present theory are derived by employing the virtual work principle, and the closed-form solutions of functionally graded plates have been obtained using Navier solution. Numerical results for deflections and stresses of several types of boundary conditions are presented. The exactitude of the present study is confirmed by comparing the obtained results with those available in the literature. The effects of porosity parameter, slenderness ratio, foundation parameters, power law index and boundary condition types on the deflections and stresses are presented.

• Advances in aircraft and spacecraft science
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• v.6 no.3
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• pp.257-272
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• 2019

Numerical study of the flutter of a plate on a viscoelastic foundation is carried out in the paper. Critical velocity of the flutter of a plate on an elastic and viscoelastic foundation is determined. The mathematical model for the investigation of viscoelastic plates is based on the Marguerre's theory applied to the study of the problems of strength, rigidity and stability of thin-walled structures such as aircraft wings. Aerodynamic pressure is determined in accordance with the A.A. Ilyushin's piston theory. Using the Bubnov - Galerkin method, the basic resolving systems of nonlinear integro-differential equations (IDE) are obtained. At wide ranges of geometric and physical parameters of viscoelastic plates, their influence on the flutter velocity has been studied in detail.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.819-822
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• 2006

This paper has the objects of deciding dynamic instability regions of thick plates on inhomogeneous Pasternak foundation by finite element method and providing kinematic design data for mats and slabs of building structures. In this paper, dynamic stability analysis of tapered opening thick plate is done by use of Serendipity finite element with 8 nodes considering shearing strain of plate. To verify this finite element method, buckling stress and natural frequencies of thick pate with or without in-plane stress are compared with existing solutions. The results are as follow that this finite element solutions with $4{\times}4$ meshes are shown the error of maximum 0.56% about existing solutions, and the larger foundation parameters, the farther dynamic instability regions are from vertical axis of graph presented relation of ${\beta}\;and\;\overline{\omega}/\omega$.

• Steel and Composite Structures
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• v.27 no.3
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• pp.311-325
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• 2018

This article presents the bending analysis of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment. Theoretical formulations are based on a recently developed refined shear deformation theory. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. The present theory satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modeled as non-uniform foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermo-mechanical behavior of functionally graded plates. Numerical results show that the present theory can archive accuracy comparable to the existing higher order shear deformation theories that contain more number of unknowns.

• Steel and Composite Structures
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• v.22 no.3
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• pp.691-712
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• 2016

In this editorial, buckling analytical investigation of the nanocomposite plate with square cut out reinforced by carbon nanotubes (CNTs) surrounded by Pasternak foundation is considered. The plate is presumed has square cut out in center and resting on Pasternak foundation. CNTs are used as amplifier in plate for diverse distribution, such as uniform distribution (UD) and three patterns of functionally graded (FG) distribution types of CNTs (FG-X, FG-A and FG-O). Moreover, the effective mechanical properties of nanocomposite plate are calculated from the rule of mixture. Domain decomposition method and orthogonal polynomials are applied in order to define the shape function of nanocomposite plate with square cut out. Finally, Rayleigh-Ritz energy method is used to obtain critical buckling load of system. A detailed parametric study is conducted to explicit the effects of the dimensions of plate, length of square cut out, different distribution of CNTs, elastic medium and volume fraction of CNTs. It is found from results that increase the dimensions of plate and length of square cut out have negative impact on buckling behavior of system but considering CNTs in plate has positive influence.

• Advances in nano research
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• v.7 no.5
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• pp.293-310
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• 2019

In this paper, thermal-buckling behavior of the functionally graded (FG) nanocomposite plates reinforced with graphene oxide powder (GOP) is studied under three types of thermal loading once the plate is supposed to be rested on a two-parameter elastic foundation. The effective material properties of the nanocomposite plate are considered to be graded continuously through the thickness according to the Halpin-Tsai micromechanical scheme. Four types of GOPs' distribution namely uniform (U), X, V and O, are considered in a comparative way in order to find out the most efficient model of GOPs' distribution for the purpose of improving the stability limit of the structure. The governing equations of the plate have been derived based on a refined higher-order shear deformation plate theory incorporated with Hamilton's principle and solved analytically via Navier's solution for a simply supported GOP reinforced (GOPR) nanocomposite plate. Some new results are obtained by applying different thermal loadings to the plate according to the GOPs' negative coefficient of thermal expansion and considering both Winkler-type and Pasternak-type foundation models. Besides, detailed parametric studies have been carried out to reveal the influences of the different types of thermal loading, weight fraction of GOP, aspect and length-to-thickness ratios, distribution type, elastic foundation constants and so on, on the critical buckling load of nanocomposite plates. Moreover, the effects of thermal loadings with various types of temperature rise are investigated comparatively according to the graphical results. It is explicitly shown that the buckling behavior of an FG nanocomposite plate is significantly influenced by these effects.

• Steel and Composite Structures
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• v.43 no.6
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• pp.821-837
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• 2022

This research is devoted to study the effects of humidity and temperature on the bending behavior of functionally graded (FG) ceramic-metal porous plates resting on Pasternak elastic foundation using a quasi-3D hyperbolic shear deformation theory developed recently. The present plate theory with only four unknowns, takes into account both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the functionally graded plate without using shear correction factors. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. The governing differential equations are obtained using the "principle of virtual work". Analytically, the Navier method is used to solve the equations that govern a simply supported FG porous plate. The obtained results are checked by comparing the results determined for the perfect and imperfect FG plates with those available in the scientific literature. Effects due to material index, porosity factors, moisture and thermal loads, foundation rigidities, geometric ratios on the FG porous plate are all examined. Finally, this research will help us to design advanced functionally graded materials to ensure better durability and efficiency for hygro-thermal environments.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.73-79
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• 1997

It is one of classical problems in the elastic theory to analyze contact stresses between elastic bodies. Concrete pavements under traffic wheel loads can be considered as one of these typical Problems. In the paper, Mindlin plate theory is used to consider the transverse shear effect, 8-node isoparametric plate bending element is adopted in this study, and an elastic plate resting on tensionless elastic half-space is analyzed by finite element method. The Boussineq's solution of elastic half-space is used to evaluate the flexibility of foundation. To obtain the boundary of contact area, the flexibility matrix of foundation is modified after each cycle of analysis iteratively. A Numerical example is presented by using these method.

• The Journal of Engineering Geology
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• v.15 no.4 s.42
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• pp.423-433
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• 2005

For the design of spread foundation and the stability evaluation, we compared and analyzed it for theoretical, empirical bearing capacity formulas, and various settlement computation formulas, by conducting the plate bearing test at the site of A and B, which consisted of gneiss weathered soil. In addition, we considered the effective method of stability evaluation by carrying out the plate bearing test carried out on the ground consisted of weathering soil of gneiss. Consequently, it was found out that the allowablebearing capacity by the theoretical formula of Terzaghi was too excessive in comparison with the result of the plate bearing test and the Terzaghi-Peck method, which was used widely domestically in designing the spread foundation. It was more effective for a stable design. As a result of the plate bearing test carried out, on the ground consisted of weathering soil. It was found that reviewing the stability by the bearing capacity calculated with load-settlement curve. It is evaluated in a safer side than the point of view of the settlement.