• Structural Engineering and Mechanics
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• v.49 no.5
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• pp.661-672
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• 2014

Laminated Rectangular plates embedded in elastic foundations are used in many mechanical structures. This study presents an analytical approach for transverse bending analysis of an embedded symmetric laminated rectangular plate using Mindlin plate theory. The surrounding elastic medium is simulated using Pasternak foundation. Adopting the Mindlin plate theory, the governing equations are derived based on strain-displacement relation, energy method and Hamilton's principle. The exact analysis is performed for this case when all four ends are simply supported. The effects of the plate length, elastic medium and applied force on the plate transverse bending are shown. Results indicate that the maximum deflection of the laminated plate decreases when considering an elastic medium. In addition, the deflection of the laminated plate increases with increasing the plate width and length.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.8
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• pp.763-770
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• 2012

The free vibration characteristics of fluid-filled cylindrical shells on partial elastic foundations are investigated by an analytical method. The cylindrical shell is fully or partially surrounded by the elastic foundations, these are represented by the Winkler or Pasternak model. The motion of shell is represented by the first order shear deformation theory to account for rotary inertia and transverse shear strains. The steady flow of fluid is described by the classical potential flow theory. The fluid-structure interaction is considered in the analysis. The effect of internal fluid can be considered by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. To validate the present method, the numerical example is presented and compared with the available existing results.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.69-86
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• 2007

A four-noded plate bending quadrilateral (PBQ4) and an eight-noded plate bending quadrilateral (PBQ8) element based on Mindlin plate theory have been adopted for modeling the thick plates on elastic foundations using Winkler model. Transverse shear deformations have been included, and the stiffness matrices of the plate elements and the Winkler foundation stiffness matrices are developed using Finite Element Method based on thick plate theory. A computer program is coded for this purpose. Various loading and boundary conditions are considered, and examples from the literature are solved for comparison. Shear locking problem in the PBQ4 element is observed for small value of subgrade reaction and plate thickness. It is noted that prevention of shear locking problem in the analysis of the thin plate is generally possible by using element PBQ8. It can be concluded that, the element PBQ8 is more effective and reliable than element PBQ4 for solving problems of thin and thick plates on elastic foundations.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.137-146
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• 2017

The size-dependent behavior of single walled carbon nanotubes (SWCNT) embedded in the elastic medium and subjected to the initial axial force is investigated using the mixed finite element method. The SWCNT is assumed to be Euler-Bernoulli beam incorporating nonlocal theory developed by Eringen. The mixed finite element model shows its great advantage of dealing with nonlocal behavior of SWCNT subjected to a concentrated load owing to the existence of two coefficients ${\alpha}_1$ and ${\alpha}_2$. This is the first numerical approach to deal with a puzzling fact of nonlocal theory with concentrated load. Numerical examples are performed to show the accuracy and efficiency of the present method. In addition, parametric study is carefully carried out to point out the influences of nonlocal effect, the elastic medium, and the initial axial force on the behavior of the carbon nanotubes.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.12
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• pp.947-955
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• 2003

This research analyzes the dynamic stability of stiffened plates on elastic foundations using the finite element method. For analyzing the stiffened plates, both the Mindlin plate theory and Timoshenko beam-column theory were applied. In application of the finite element method, 8-nodes serendipity element system and 3-nodes finite element system were used for plate and beam elements, respectively Elastic foundations were modeled as the Pasternak foundations in which the continuity effect of foundation is considered. In order to verify the theory of this study, solutions obtained by this analysis were compared with the classical solutions in open literature and experimental solutions. The dynamic stability legions of stiffened plates on Pasternak foundations were determined according to changes of in-plane stresses, foundation parameters and dimensions of stiffener.

• Steel and Composite Structures
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• v.23 no.6
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• pp.623-631
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• 2017

Present paper deals with the temperature-dependent buckling analysis of sandwich nanocomposite plates resting on elastic medium subjected to magnetic field. The lamina layers are reinforced with carbon nanotubes (CNTs) as uniform and functionally graded (FG). The elastic medium is considered as orthotropic Pasternak foundation with considering the effects of thermal loading on the spring and shear constants of medium. Mixture rule is utilized for obtaining the effective material properties of each layer. Adopting the Reddy shear deformation plate theory, the governing equations are derived based on energy method and Hamilton's principle. The buckling load of the structure is calculated with the Navier's method for the simply supported sandwich nanocomposite plates. Parametric study is conducted on the combined effects of the volume percent and distribution types of the CNTs, temperature change, elastic medium, magnetic field and geometrical parameters of the plates on the buckling load of the sandwich structure. The results show that FGX distribution of the CNTs leads to higher stiffness and consequently higher buckling load. In addition, considering the magnetic field increases the buckling load of the sandwich nanocomposite plate.

• Steel and Composite Structures
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• v.44 no.1
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• pp.17-31
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• 2022

This investigation studies the characteristics of wave dispersion in sigmoid functionally graded (SFG) curved beams lying on an elastic substrate for the first time. Homogenization process was performed with the help of sigmoid function and two power laws. Moreover, various materials such as Zirconia, Alumina, Monel and Nickel steel were explored as curved beams materials. In addition, curved beams were rested on an elastic substrate which was modelled based on Winkler-Pasternak foundation. The SFG curved beams' governing equations were derived according to Euler-Bernoulli curved beam theory which is known as classic beam theory and Hamilton's principle. The resulted governing equations were solved via an analytical method. In order to validate the utilized method, the obtained outcomes were compared with other researches. Finally, the influences of various parameters, including wave number, opening angle, gradient index, Winkler coefficient and Pasternak coefficient were evaluated and indicated in the form of diagrams.

• 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.

• Steel and Composite Structures
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• v.34 no.4
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• pp.511-524
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• 2020

In this research, a simple four-variable trigonometric integral shear deformation model is proposed for the static behavior of advanced functionally graded (AFG) ceramic-metal plates supported by a two-parameter elastic foundation and subjected to a nonlinear hygro-thermo-mechanical load. The elastic properties, including both the thermal expansion and moisture coefficients of the plate, are also supposed to be varied within thickness direction by following a power law distribution in terms of volume fractions of the components of the material. The interest of the current theory is seen in its kinematics that use only four independent unknowns, while first-order plate theory and other higher-order plate theories require at least five unknowns. The "in-plane displacement field" of the proposed theory utilizes cosine functions in terms of thickness coordinates to calculate out-of-plane shear deformations. The vertical displacement includes flexural and shear components. The elastic foundation is introduced in mathematical modeling as a two-parameter Winkler-Pasternak foundation. The virtual displacement principle is applied to obtain the basic equations and a Navier solution technique is used to determine an analytical solution. The numerical results predicted by the proposed formulation are compared with results already published in the literature to demonstrate the accuracy and efficiency of the proposed theory. The influences of "moisture concentration", temperature, stiffness of foundation, shear deformation, geometric ratios and volume fraction variation on the mechanical behavior of AFG plates are examined and discussed in detail.

• Geomechanics and Engineering
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• v.22 no.5
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• pp.415-431
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• 2020

In this study, dynamics responses of advanced composite plates resting variable elastic foundations via a quasi-3D theory are developed using an analytical approach. This higher shear deformation theory (HSDT) is included the shear deformation theory and effect stretching that has five unknowns, which is even inferior to normal deformation theories found literature and other theories. The quasi-three-dimensional (quasi-3D) theory accounts for a parabolic distribution of the transverse shear deformation and satisfies the zero traction boundary conditions on the surfaces of the advanced composite plate without needing shear correction factors. The plates assumed to be rest on two-parameter elastic foundations, the Winkler parameter is supposed to be constant but the Pasternak parameter varies along the long side of the plate with three distributions (linear, parabolic and sinusoidal). The material properties of the advanced composite plates gradually vary through the thickness according to two distribution models (power law and Mori-Tanaka). Governing differential equations and associated boundary conditions for dynamics responses of the advanced composite plates are derived using the Hamilton principle and are solved by using an analytical solution of Navier's technique. The present results and validations of our modal with literature are presented that permitted to demonstrate the accuracy of the present quasi-3D theory to predict the effect of variables elastic foundation on dynamics responses of advanced composite plates.