• 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.

• Advances in concrete construction
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• v.14 no.3
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• pp.169-183
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• 2022

In this article, vibrational behavior and wave propagation characteristics in (FG) functionally graded plates resting on Kerr foundation with three parameters is studied using a 2D dimensional (HSDT) higher shear deformation theory. The new 2D higher shear deformation theory has only four variables in field's displacement, which means has few numbers of unknowns compared with others theories. The shape function used in this theory satisfies the nullity conditions of the shear stresses on the two surfaces of the FG plate without using shear correction factors. The FG plates are considered to rest on the Kerr layer, which is interconnected with a Pasternak-Kerr shear layer. The FG plate is materially inhomogeneous. The material properties are supposed to vary smoothly according to the thickness of the plate by a Voigt's power mixing law of the volume fraction. The equations of motion due to the dynamics of the plate resting on a three-parameter foundation are derived using the principle of minimization of energies; which are then solved analytically by the Navier technique to find the vibratory characteristics of a simply supported plate, and the wave propagation results are derived by using the dispersion relations. Perceivable numerical results are fulfilled to evaluate the vibratory and the wave propagation characteristics in functionally graded plates and some parameters such wave number, thickness ratio, power index and foundation parameters are discussed in detail.

• Structural Engineering and Mechanics
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• v.89 no.2
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• pp.103-119
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• 2024

The present research investigates the thermodynamically bending behavior of FG sandwich plates, laying on the Winkler/Pasternak/Kerr foundation with various boundary conditions, subjected to harmonic thermal load varying through thickness. The supposed FG sandwich plate has three layers with a ceramic core. The constituents' volume fractions of the lower and upper faces vary gradually in the direction of the FG sandwich plate thickness. This variation is performed according to various models: a Power law, Trigonometric, Viola-Tornabene, and the Exponential model, while the core is constantly homogeneous. The displacement field considered in the current work contains integral terms and fewer unknowns than other theories in the literature. The corresponding equations of motion are derived based on Hamilton's principle. The impact of the distribution model, scheme, aspect ratio, side-to-thickness ratio, boundary conditions, and elastic foundations on thermodynamic bending are examined in this study. The deflections obtained for the sandwich plate without elastic foundations have the lowest values for all boundary conditions. In addition, the minimum deflection values are obtained for the exponential volume fraction law model. The sandwich plate's non-dimensional deflection increases as the aspect ratio increases for all distribution models.

• Steel and Composite Structures
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• v.37 no.1
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• pp.27-35
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• 2020

This study examines the wave propagation of the functionally graded polymer composite (FG-PC) nanoplates reinforced with graphene nanoplatelets (GNPs) resting on elastic foundations in the framework of the nonlocal strain gradient theory incorporating both stiffness hardening and softening mechanisms of nanostructures. To this end, the material properties are based on the Halpin-Tsai model, and the expressions for the classical and higher-order stresses and strains are consistently derived employing the second-order shear deformation theory. The equations of motion are then consistently derived using Hamilton's principle of variation. These governing equations are solved with the help of Trial function method. Extensive numerical discussions are conducted for wave propagation of the nanoplates and the influences of different parameters, such as the nonlocal parameter, strain gradient parameter, weight fraction of GNPs, uniform and non-uniform distributions of GNPs, elastic foundation parameters as well as wave number.

• Advances in nano research
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• v.11 no.6
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• pp.581-593
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• 2021

This model is proposed to describe the buckling behavior of Carbon Nanotubes (CNTs) embedded in an elastic medium taking into account the combined effects of the magnetic field, the temperature, the nonlocal parameter, the number of walls. Using Eringen's nonlocal elasticity theory, thin cylindrical shell theory and Van der Waal force (VdW) interactions, we develop a system of partial differential equations governing the buckling response of CNTs embedded on Winkler, Pasternak, and Kerr foundations in a thermal-magnetic environment. The pre-buckling stresses are obtained by applying airy's stress function and an adjacent equilibrium criterion. To estimate the nonlocal critical buckling load of CNTs under the simultaneous effects of the magnetic field, the temperature change, and the number of walls, an optimization technique is proposed. Furthermore, analytical formulas are developed to obtain the buckling behavior of SWCNTs embedded in an elastic medium without taking into account the effects of the nonlocal parameter. These formulas take into account VdW interactions between adjacent tubes and the effect of terms involving differences in tube radii generally neglected in the derived expressions of the critical buckling load published in the literature. Most scientific research on modeling the effects of magnetic fields is based on beam theories, this motivation pushes me to develop a cylindrical shell model for studying the effect of the magnetic field on the static behavior of CNTs. The results show that the magnetic field has significant effects on the static behavior of CNTs and can lead to slow buckling. On the other hand, thermal effects reduce the critical buckling load. The findings in this work can help us design of CNTs for various applications (e.g. structural, electrical, mechanical and biological applications) in a thermal and magnetic environment.

• Computers and Concrete
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• v.25 no.1
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• pp.37-57
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• 2020

This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.

• Structural Engineering and Mechanics
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• v.84 no.5
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• pp.685-697
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• 2022

Nanotechnology has become one of the interesting technique used in material science and engineering. However, it is low used in civil engineering structures. The purpose of the present study is to investigate the static behavior of concrete plates reinforced with silica-nanoparticles. Due to agglomeration effect of silica-nanoparticles in concrete, Voigt's model is used for obtaining the equivalent nano-composite properties. Furthermore, the plate is simulated mathematically with higher order shear deformation theory. For a large use of this study, the concrete plate is assumed resting on a Pasternak elastic foundation, including a shear layer, and Winkler spring interconnected with a Kerr foundation. Using the principle of virtual work, the equilibrium equations are derived and by the mean of Hamilton's principle the energy equations are obtained. Finally, based on Navier's technique, closed-form solutions of simply supported plates have been obtained. Numerical results are presented considering the effect of different parameters such as volume percent of SiO₂ nanoparticles, mechanical loads, geometrical parameters, soil medium, on the static behavior of the plate. The most findings of this work indicate that the use of an optimum amount of SiO₂ nanoparticles on concretes increases better mechanical behavior. In addition, the elastic foundation has a significant impact on the bending of concrete slabs.