• Computers and Concrete
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• 제24권6호
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• pp.579-586
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• 2019

In this research paper, the free vibrational behavior of the simply supported FG nano-plate is studied using the nonlocal two variables integral refined plate theory. The present model takes into account the small scale effect. The effective's properties of the plate change according to the power law variation (P-FGM). The equations of motion of the system are determined and resolved via Hamilton's principle and Navier procedure, respectively. The validity and efficiency of the current model are confirmed by comparing the results with those given in the literature. At the last section, several numerical results are presented to show the various parameters influencing the vibrational behavior such as the small-scale effect, geometry ratio, material index and aspect ratio.

• Coupled systems mechanics
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• 제9권3호
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• pp.265-280
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• 2020

In this paper, a new refined hyperbolic shear deformation beam theory for the free vibration analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equations of motion are derived from the Hamilton's principle. Navier type solution method was used to obtain frequencies, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the free vibration response of a simply supported FG beams.

• Earthquakes and Structures
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• 제16권2호
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• pp.177-183
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• 2019

In this paper, a new refined hyperbolic shear deformation beam theory for the bending analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the bending response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equilibrium equations are derived from the principle of virtual work. Navier type solution method was used to obtain displacement and stresses, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG beams.

• Coupled systems mechanics
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• 제9권6호
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• pp.575-597
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• 2020

Equilibrium equations of a porous FG plate resting on Winkler-Pasternak foundations with various boundary conditions are derived using a new refined shear deformation theory. Different types of porosity distribution rate are considered. Governing equations are obtained including the plate-foundation interaction. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The novel rule of mixture is proposed to describe and approximate material properties of the FG plates with different distribution case of porosity. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature. Effects of variation of porosity distribution rate, boundary conditions, foundation parameter, power law index, plate aspect ratio, side-to-thickness ratio on the deflections and stresses are all discussed.

• Steel and Composite Structures
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• 제44권6호
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• pp.829-843
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• 2022

This manuscript work presents a comprehensive continuum model capable to investigate the effect of porosity on vibro-acoustic behaviour of functionally graded (FG) beams resting on an elastic foundation subjected to thermal and mechanical loadings. Effects of uniform temperature rise and edge compressive load on the sound radiation characteristics are studied in a comparative manner. The numerical analysis is carried out by combining finite element method with Rayleigh's integral. Detailed parametric studies are accomplished, and influences of power law index, porosity volume, porosity distribution and boundary conditions on the vibro-acoustic response characteristics are analyzed. It is found that the vibro-acoustic response under mechanical edge compression is entirely different compared to from that under the thermal load. Furthermore, nature of grading of porosity affects the sound radiation behaviour for both the loads. The proposed model can be used to obtain the suppression performance of vibration and noise FG porous beams under thermal and mechanical loads.

• Coupled systems mechanics
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• 제13권2호
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• pp.115-132
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• 2024

This paper introduces an improved shear deformation theory for analyzing the buckling behavior of functionally graded plates subjected to varying temperatures. The transverse shear strain functions employed satisfy the stress-free condition on the plate surfaces without requiring shear correction factors. The material properties and thermal expansion coefficient of the porous functionally graded plate are assumed temperature-dependent and exhibit continuous variation throughout the thickness, following a modified power-law distribution based on the volume fractions of the constituents. Moreover, the study considers the influence of porosity distribution on the buckling of the functionally graded plates. Thermal loads are assumed to have uniform, linear, and nonlinear distributions through the thickness. The obtained results, considering the effect of porosity distribution, are compared with alternative solutions available in the existing literature. Additionally, this study provides comprehensive discussions on the influence of various parameters, emphasizing the importance of accounting for the porosity distribution in the buckling analysis of functionally graded plates.

• Structural Engineering and Mechanics
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• 제73권3호
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• pp.225-238
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• 2020

This work treats the axisymmetric buckling of functionally graded (FG) porous annular/circular nanoplates based on modified couple stress theory (MCST). The nanoplate is located at the elastic medium which is simulated by Kerr foundation with two spring and one shear layer. The material properties of the porous FG nanostructure are assumed to vary through the nanoplate thickness based on power-law rule. Based on two variables refined plate theory, the governing equations are derived by utilizing Hamilton's principle. Applying generalized differential quadrature method (GDQM), the buckling load of the annular/circular nanoplates is obtained for different boundary conditions. The influences of different involved parameters such as boundary conditions, Kerr medium, material length scale parameter, geometrical parameters of the nanoplate, FG power index and porosity are demonstrated on the nonlinear buckling load of the annular/circular nanoplates. The results indicate that with increasing the porosity of the nanoplate, the nonlinear buckling load is decreased. In addition, with increasing the material length scale parameter to thickness ratio, the effect of spring constant of Kerr foundation on the buckling load becomes more prominent. The present results are compared with those available in the literature to validate the accuracy and reliability. A good agreement is observed between the two sets of the results.

• Structural Engineering and Mechanics
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• 제60권3호
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• pp.489-505
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• 2016

Sinusoidal shear deformation theory (SSDT) is developed here for dynamic buckling of functionally graded (FG) nano-plates. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. In order to present a realistic model, the structural damping of nano-structure is considered using Kelvin-Voigt model. The surrounding elastic medium is modeled with a novel foundation namely as orthotropic visco-Pasternak medium. Size effects are incorporated based on Eringen'n nonlocal theory. Equations of motion are derived from the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is applied for obtaining the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, orthotropic visco-Pasternak foundation, power index of FG plate, structural damping and boundary conditions on the dynamic instability of system. The results are compared with those of first order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the dynamic buckling responses of system.

• Steel and Composite Structures
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• 제41권6호
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• pp.787-803
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• 2021

The size-dependent nonlinear thermomechanical vibration analysis of pre- and post-buckled tapered two-directional functionally graded (2D-FG) microbeams is presented in this study. In the context of the modified couple stress theory, the formulations are derived based on the parabolic shear deformation beam theory and von Karman nonlinear strains. Different thermomechanical material properties are assumed to be temperature-dependent and smoothly vary in both length and thickness directions using the power law and the physical neutral axis concept is employed. The nonlinear governing equations are derived using the Hamilton principle and the resulting variable coefficient equations of motion are solved using the differential quadrature method (DQM) and iterative Newton's method for clamped-clamped and simply supported boundary conditions. Comparison studies are presented to validate the derived model and solution procedure. The impacts of induced thermal moments, temperature power index, two gradient indices, nonuniform cross-section, and microstructure length scale parameter on the frequency-temperature configurations are explored for both clamped and simply supported microbeams.

• Structural Engineering and Mechanics
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• 제48권4호
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• pp.547-567
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• 2013

Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain-displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.