• Geomechanics and Engineering
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• v.7 no.6
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• pp.665-678
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• 2014

In discrete element modeling, 2D software has been widely used in order to gain further insights into the fundamental mechanisms with less computational time. The porosities used in 2D DEM studies should be determined with appropriate approaches based on 3D laboratory porosities. This paper summarizes the main approaches for converting porosities from 3D to 2D for DEM studies and theoretical evaluations show that none of the current approaches can be widely used in dealing with soil mechanical problems. Therefore, a parabolic equation and a criterion have been suggested for the determination of 2D porosities in this paper. Moreover, a case study has been used to validate that the 2D porosity obtained from the above suggestion to be rational with both the realistic contact force distribution in the specimen and the good agreement of the DEM simulation results of direct shear tests with the corresponding experimental data. Therefore, the parabolic equation and the criterion are suggested for the determination of 2D porosities in a wide range of polydisperse particle systems, especially in dealing with soil mechanical problems.

• Steel and Composite Structures
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• v.46 no.5
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• pp.611-619
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• 2023

In the present work, the flutter characteristics of porous nanocomposite cylindrical shells, reinforced with graphene platelets (GPLs) in supersonic airflow, have been investigated. Different distributions for GPLs and porosities have been considered which are named uniform and non-uniform distributions thorough the shell's thickness. The effective material properties have been determined via Halpin-Tsai micromechanical model. The cylindrical shell formulation considering supersonic airflow has been developed in the context of first-order shell and first-order piston theories. The governing equations have been solved using Galerkin's method to find the frequency-pressure plots. It will be seen that the flutter points of the shell are dependent on the both amount and distribution of porosities and GPLs and also shell geometrical parameters.

• Structural Engineering and Mechanics
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• v.88 no.6
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• pp.551-567
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• 2023

In this work, the free vibration analysis of functionally graded material (FGM) sandwich plates with porosity is conducted using the p-version of the finite element method (FEM), which is based on the first-order shear deformation theory (FSDT). The sandwich plate consists of two face-sheet layers of FGM and a homogeneous core layer. The obtained results are validated using convergence and comparison studies with previously published results. Five porosities distribution models of FGM sandwich plates are assumed and analyzed. The effect of the thickness ratio, boundary conditions, volume fraction exponents, and porosity coefficients of the top and bottom layers of FGM sandwich plates on the natural frequency are addressed.

• Advances in materials Research
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• v.6 no.1
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• pp.45-63
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• 2017

In this article, static deflection and buckling of functionally graded (FG) nanoscale beams made of porous material are carried out based on the nonlocal Timoshenko beam model which captures the small scale influences. The exact position of neutral axis is fixed, to eliminate the stretching and bending coupling due to the unsymmetrical material change along the FG nanobeams thickness. The material properties of FG beam are graded through the thickness on the basis of the power-law form, which is modified to approximate the material properties with two models of porosity phases. By employing Hamilton's principle, the nonlocal governing equations of FG nanobeams are obtained and solved analytically for simply-supported boundary conditions via the Navier-type procedure. Numerical results for deflection and buckling of FG nanoscale beams are presented and validated with those existing in the literature. The influences of small scale parameter, power law index, porosity distribution and slenderness ratio on the static and stability responses of the FG nanobeams are all explored.

• Wind and Structures
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• v.25 no.4
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• pp.329-342
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• 2017

This work presents a static and free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. A new displacement field containing integrals is proposed which involves only three variables. Based on the suggested theory, the equations of motion are derived from Hamilton's principle. This theory involves only three unknown functions and accounts for parabolic distribution of transverse shear stress. In addition, the transverse shear stresses are vanished at the top and bottom surfaces of the beam. The Navier solution technique is adopted to derive analytical solutions for simply supported beams. The accuracy and effectiveness of proposed model are verified by comparison with previous research. A detailed numerical study is carried out to examine the influence of the deflections, stresses and natural frequencies on the bending and free vibration responses of functionally graded beams.

• Geomechanics and Engineering
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• v.9 no.3
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• pp.361-372
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• 2015

In this paper, a refined exponential shear deformation theory for free vibration analysis of functionally graded beam with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Coupled systems mechanics
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• v.13 no.2
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• pp.171-186
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• 2024

In the present paper, thermal buckling characteristics of functionally graded rectangular plates made of porous material that are integrated with surface-bonded piezoelectric actuators subjected to the combined action of thermal load and constant applied actuator voltage are investigated by utilizing a Navier solution method. The uniform temperature rise loading is considered. Thermomechanical material properties of FGM plates are assumed to be temperature independent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of stability for the piezoelectric FGM plate are derived based on higher order shear deformation plate theory. Influences of several important parameters on the critical thermal buckling temperature are investigated and discussed in detail.

• Steel and Composite Structures
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• v.21 no.1
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• pp.123-136
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• 2016

This work focuses on the behavior of the static analysis of functionally graded plates materials (FGMs) with porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose a new refined plate theory is used in this work, it contains only four unknowns, unlike five unknowns for other theories. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The parabolic distribution of transverse shear stresses along the thickness of the plate is taken into account in this analysis; the material properties of the FGM plate vary a power law distribution in terms of volume fraction of the constituents. The rule of mixture is modified to describe and approximate material properties of the FG plates with porosity phases. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, 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.

• Advances in nano research
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• v.7 no.1
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• pp.25-38
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• 2019

This research is aimed at studying the asymmetric thermal buckling of porous functionally graded (FG) annular nanoplates resting on an elastic substrate which are made of two different sets of porous distribution, based on nonlocal elasticity theory. Porosity-dependent properties of inhomogeneous nanoplates are supposed to vary through the thickness direction and are defined via a modified power law function in which the porosities with even and uneven type are approximated. In this model, three types of thermal loading, i.e., uniform temperature rise, linear temperature distribution and heat conduction across the thickness direction are considered. Based on Hamilton's principle and the adjacent equilibrium criterion, the stability equations of nanoporous annular plates on elastic substrate are obtained. Afterwards, an analytical solution procedure is established to achieve the critical buckling temperatures of annular nanoplates with porosities under different loading conditions. Detailed numerical studies are performed to demonstrate the influences of the porosity volume fraction, various thermal loading, material gradation, nonlocal parameter for higher modes, elastic substrate coefficients and geometrical dimensions on the critical buckling temperatures of a nanoporous annular plate. Also, it is discussed that because of present of thermal moment at the boundary conditions, porous nanoplate with simply supported boundary condition doesn't buckle.

• Structural Engineering and Mechanics
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• v.82 no.2
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• pp.151-161
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• 2022

In this study, the effect of porosity distribution pattern on the free vibration analysis of porous FG plates with various boundary conditions is studied. The material properties of the plate and the porosities within the plate are considered to vary continuously through the thickness direction according to the volume fraction of constituents defined by the modified rule of the mixture, this includes porosity volume fraction with four different types of porosity distribution over the cross-section. The governing partial differential equation of motion for the free vibration analysis is obtained using hyperbolic shear deformation theory. An analytical solution is presented for the governing PDEs for various boundary conditions. Results of the presented solution are compared and validated by the available results in the literature. Moreover, the effects of material and porosity distribution and geometrical parameters on vibrational properties are investigated.