• Structural Engineering and Mechanics
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• 제71권2호
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• pp.185-196
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• 2019

In this investigation, study of the static and dynamic behaviors of functionally graded beams (FGB) is presented using a hyperbolic shear deformation theory (HySDT). The simply supported FG-beam is resting on the elastic foundation (Winkler-Pasternak types). The properties of the FG-beam vary according to exponential (E-FGB) and power-law (P-FGB) distributions. The governing equations are determined via Hamilton's principle and solved by using Navier's method. To show the accuracy of this model (HySDT), the current results are compared with those available in the literature. Also, various numerical results are discussed to show the influence of the variation of the volume fraction of the materials, the power index, the slenderness ratio and the effect of Winkler spring constant on the fundamental frequency, center deflection, normal and shear stress of FG-beam.

• Steel and Composite Structures
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• 제49권3호
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• pp.307-323
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• 2023

In this research, the study of the thermoelastic flexural analysis of silicon carbide/Aluminum graded (FG) sandwich 2D uniform structure (plate) under harmonic sinusoidal temperature load over time is presented. The plate is modeled using a simple two dimensional integral shear deformation plate theory. The current formulation contains an integral terms whose aim is to reduce a number of variables compared to others similar solutions and therefore minimize the computation time. The transverse shear stresses vary according to parabolic distribution and vanish at the free surfaces of the structure without any use of correction factors. The external load is applied on the upper face and varying in the thickness of the plates. The structure is supposed to be composed of "three layers" and resting on nonlinear visco-Pasternak's-foundations. The governing equations of the system are deduced and solved via Hamilton's principle and general solution. The computed results are compared with those existing in the literature to validate the current formulation. The impacts of the parameters (material index, temperature exponent, geometry ratio, time, top/bottom temperature ratio, elastic foundation type, and damping coefficient) on the dynamic flexural response are studied.

• Steel and Composite Structures
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• 제52권3호
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• pp.273-291
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• 2024

This paper presents a three-dimensional displacement-based formulation to investigate the free vibration of functionally graded nanoplates resting on a Winkler-Pasternak foundation based on the nonlocal elasticity theory. The material properties of the FG nanoplate are considered to vary continuously through the thickness of the nanoplate according to the power-law distribution model. A general three-dimensional displacement field is considered for the plate, which takes into account the out-of-plane strains of the plate as well as the in-plane strains. Unlike the shear deformation theories, in the present formulation, no predetermined form for the distribution of displacements and transverse strains is considered. The equations of motion for functionally graded nanoplate are derived based on Hamilton's principle. The solution is obtained for simply-supported nanoplate, and the predicted results for natural frequencies are compared with the predictions of shear deformation theories which are available in the literature. The predictions of the present theory are discussed in detail to investigate the effects of power-law index, length-to-thickness ratio, mode numbers and the elastic foundation on the dynamic behavior of the functionally graded nanoplate. The present study presents a three-dimensional solution that is able to determine more accurate results in predicting of the natural frequencies of flexural and thickness modes of nanoplates. The effects of parameters that play a key role in the analysis and mechanical design of functionally graded nanoplates are investigated.

• Earthquakes and Structures
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• 제13권5호
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• pp.509-518
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• 2017

The objective of the present paper is to investigate the bending behavior with stretching effect of carbon nanotube-reinforced composite (CNTRC) beams. The beams resting on the Pasternak elastic foundation, including a shear layer and Winkler spring, are considered. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are estimated by using the rule of mixture. The significant feature of this model is that, in addition to including the shear deformation effect and stretching effect it deals with only 4 unknowns without including a shear correction factor. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are assessed by employing the rule of mixture. The equilibrium equations have been obtained using the principle of virtual displacements. The mathematical models provided in this paper are numerically validated by comparison with some available results. New results of bending analyses of CNTRC beams based on the present theory with stretching effect is presented and discussed in details. the effects of different parameters of the beam on the bending responses of CNTRC beam are discussed.

• Steel and Composite Structures
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• 제34권1호
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• pp.75-89
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• 2020

The current paper illustrates the effect of in-plane varying compressive force on critical buckling loads and buckling modes of sandwich composite laminated beam rested on elastic foundation. To generalize a proposed model, unified higher order shear deformation beam theories are exploited through analysis; those satisfy the parabolic variation of shear across the thickness. Therefore, there is no need for shear correction factor. Winkler and Pasternak elastic foundations are presented to consider the effect of any elastic medium surrounding beam structure. The Hamilton's principle is proposed to derive the equilibrium equations of unified sandwich composite laminated beams. Differential quadrature numerical method (DQNM) is used to discretize the differential equilibrium equations in spatial direction. After that, eigenvalue problem is solved to obtain the buckling loads and associated mode shapes. The proposed model is validated with previous published works and good matching is observed. The numerical results are carried out to show effects of axial load functions, lamination thicknesses, orthotropy and elastic foundation constants on the buckling loads and mode shapes of sandwich composite beam. This model is important in designing of aircrafts and ships when non-uniform compressive load and shear loading is dominated.

• Steel and Composite Structures
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• 제20권3호
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• pp.513-543
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• 2016

Third order shear deformation theory is used to evaluate electro-elastic solution of a sandwich plate with considering functionally graded (FG) core and composite face sheets made of piezoelectric layers. The plate is resting on the Pasternak foundation and subjected to normal pressure. Short circuited condition is applied on the top and bottom of piezoelectric layers. The governing differential equations of the system can be derived using Hamilton's principle and Maxwell's equation. The Navier's type solution for a sandwich rectangular thick plate with all edges simply supported is used. The numerical results are presented in terms of varying the parameters of the problem such as two elastic foundation parameters, thickness ratio ($h_p/2h$), and power law index on the dimensionless deflection, critical buckling load, electric potential function, and the natural frequency of sandwich rectangular thick plate. The results show that the dimensionless natural frequency and critical buckling load diminish with an increase in the power law index, and vice versa for dimensionless deflection and electrical potential function, because of the sandwich thick plate with considering FG core becomes more flexible; while these results are reverse for thickness ratio.

• Steel and Composite Structures
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• 제48권2호
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• pp.191-206
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• 2023

The present research investigates how micromechanical models affect the behavior of Functionally Graded (FG) plates under different boundary conditions. The study employs diverse micromechanical models to assess the effective material properties of a two-phase particle composite featuring a volume fraction of particles that continuously varies throughout the thickness of the plate. Specifically, the research examines the vibrational response of the plate on a Winkler-Pasternak elastic foundation, considering different boundary conditions. To achieve this, the governing differential equations and boundary conditions are derived using Hamilton's principle, which is based on a four-variable shear deformation refined plate theory. Additionally, the Galerkin method is utilized to compute the plate's natural frequencies. The study explores how the plate's natural frequencies are influenced by various micromechanical models, such as Voigt, Reuss, Hashin-Shtrikman bounds, and Tamura, as well as factors such as boundary conditions, elastic foundation parameters, length-to-thickness ratio, and aspect ratio. The research results can provide valuable insights for future analyses of FG plates with different boundaries, utilizing different micromechanical models.

• Structural Engineering and Mechanics
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• 제85권4호
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• pp.433-443
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• 2023

The current paper discusses the dynamic and stability responses of cross-ply composite laminated plates by employing a refined quasi-3D trigonometric shear deformation theory. The proposed theory takes into consideration shear deformation and thickness stretching by a trigonometric variation of in-plane and transverse displacements through the plate thickness and assures the vanished shear stresses conditions on the upper and lower surfaces of the plate. The strong point of the new formulation is that the displacements field contains only 4 unknowns, which is less than the other shear deformation theories. In addition, the present model considers the thickness extension effects (ε_z≠0). The presence of the Winkler-Pasternak elastic base is included in the mathematical formulation. The Hamilton's principle is utilized in order to derive the four differentials' equations of motion, which are solved via Navier's technique of simply supported structures. The accuracy of the present 3-D theory is demonstrated by comparing fundamental frequencies and critical buckling loads numerical results with those provided using other models available in the open literature.

• Coupled systems mechanics
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• 제5권3호
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• pp.269-283
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• 2016

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. The influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• Wind and Structures
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• 제22권3호
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• pp.329-348
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• 2016

This work presents a simple hyperbolic shear deformation theory for analysis of functionally graded plates resting on elastic foundation. The proposed model contains fewer number of unknowns and equations of motion than the first-order shear deformation model, but the transverse shear stresses account for a hyperbolic variation and respect the tangential stress-free boundary conditions on the plate boundary surface without introducing shear correction factors. Equations of motion are obtained from Hamilton's principle. The Navier-type analytical solutions for simply-supported plates are compared with the existing solutions to demonstrate the accuracy of the proposed theory.