• Steel and Composite Structures
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• v.42 no.5
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• pp.711-722
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• 2022

In this paper, hyperbolic shear deformation plate theory is developed for thermal buckling of functionally graded plates with porosity by dividing transverse displacement into bending and shear parts. The present theory is variationally consistent, and accounts for a quadratic variation of the transverse shearstrains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Three different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. The logarithmic-uneven porosities for first time is mentioned. Equilibrium and stability equations are derived based on the present theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, aspect ratio and side-to-thickness ratio on the buckling temperature difference of imperfect FG plates.

• Computers and Concrete
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• v.25 no.3
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• pp.215-224
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• 2020

In the present study, according to the important of porosity in low specific weight in comparison of high stiffness of carbon nanotubes reinforced composite, buckling and free vibration analysis of sandwich composite beam in two configurations, of laminates using differential quadrature method (DQM) is studied. Also, the effects of porosity coefficient and three types of porosity distribution on critical buckling load and natural frequency are discussed. It is shown the buckling loads and natural frequencies of laminate 1 are significantly larger than the results of laminate 2. When configuration 2 (the core is made of FRC) and laminate 1 ([0/90/0/45/90]_s) are used, the first natural frequency rises noticeably. It is also demonstrated that the influence of the core height in the case of lower carbon volume fractions is negligible. Even though, when volume fraction of fiber increases, the critical buckling load enhances smoothly. It should be noticed the amount of decline has inverse relationship with the beam aspect ratio. Investigating three porosity patterns, beam with the distribution of porosity Type 2 has the maximum critical buckling load and first natural frequency. Among three elastic foundations (constant, linear and parabolic), buckling load and natural frequency in linear variation has the least amount. For all kind of elastic foundations, when the porosity coefficient increases, critical buckling load and natural frequency decline significantly.

• Steel and Composite Structures
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• v.33 no.6
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• pp.865-875
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• 2019

The current article proposed to develop a geometrical model for the analysis and modelling of the uniaxial functionally graded structure using the higher-order displacement kinematics with and without the presence of porosity including the distribution. Additionally, the formulation is capable of modelling three different kinds of grading patterns i.e., Power-law, sigmoid and exponential distribution of the individual constituents through the thickness direction. Also, the model includes the distribution of porosity (even and uneven kind) through the panel thickness. The structural governing equation of the porous graded structure is obtained (Hamilton's principle) and solved mathematically by means of the isoparametric finite element technique. Initially, the linear frequency parameters are obtained for different geometrical configuration via own computer code. The comparison and the corresponding convergence studies are performed for the unidirectional FG structure for the validation purpose. Finally, the impact of different influencing parameters like aspect ratio (O), thickness ratio (S), curvature ratio (R/h), porosity index (λ), type of porosity (even or uneven), power-law exponent (n), boundary condition on the free vibration characteristics are obtained for the FG panel and discussed in details.

• Structural Engineering and Mechanics
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• v.87 no.1
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• pp.85-94
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• 2023

In the present work, thermal buckling and post-buckling behaviors of imperfect graphene platelet reinforced metal foams (GPRMFs) doubly curved shells are examined. Material properties of GPRMFs doubly curved shells are presumed to be the function of the thickness. Reddy' shell theory incorporating geometric nonlinearity is utilized to derive the governing equations. Various types of the graphene platelets (GPLs) distribution patterns and doubly curved shell types are taken into account. The nonlinear equations are discretized for the case of simply supported boundary conditions. The thermal post-buckling response are presented to analyze the effects of GPLs distribution patterns, initial geometric imperfection, GPLs weight fraction, porosity coefficient, porosity distribution forms, doubly curved shell types. The results show that these factors have significant effects on the thermal post-buckling problems.

• Steel and Composite Structures
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• v.43 no.1
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• pp.31-54
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• 2022

This paper is concerned with the buckling behavior of functionally graded graphene reinforced porous nanocomposite beams based on the finite element method (FEM) using two variables trigonometric shear deformation theory. Both Young's modulus and material density of the FGP beam element are simultaneously considered as grading through the thickness of the beam. The finite element approach is developed using a nonlocal strain gradient theory. The governing equations derived here are solved introducing a 3-nodes beam element, and then the critical buckling load is calculated with different porosity distributions and GPL dispersion patterns. After a convergence and validation study to verify the accuracy of the present model, a comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern of GPL reinforcements on the Buckling behavior of the nanocomposite beam. The effects of various structural parameters such as the dispersion patterns for the graphene and porosity, thickness ratio, boundary conditions, and nonlocal and strain gradient parameters are brought out. The results indicate that porosity distribution and GPL pattern have significant effects on the response of the nanocomposite beams, and the results allows to identify the most effective way to achieve improved buckling behavior of the porous nanocomposite beam.

• Advances in nano research
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• v.14 no.4
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• pp.375-389
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• 2023

In this study, free vibration analysis of functionally graded (FG) porous truncated conical shell panels reinforced by graphene platelets (GPLs) has been investigated for the first time. Additionally, the effect of three different types of porosity distribution and five different types of GPLs patterns on dynamic response of the shell are also studied. Halpin-Tsai micromechanical model and Voigt's rule are used to determine Young modulus, shear modulus and Poisson's ratio with mass densities of the shell, respectively. The main novelties of present study are: applying 3D elasticity theory and the finite element method in conjunction with Rayleigh-Ritz method to give more accurate results unlike other simplified shell theories, and also presenting a general 3D solution in cylindrical coordinate system that can be used for analyses of different structures such as circular, annular and annular sector plates, cylindrical shells and panels, and conical shells and panels. A convergence study is performed to justify the correctness of the obtained solution and numerical results. The impact of porosity and GPLs patterns, the volume of voids, the weight fraction of graphene nanofillers, semi vertex and span angles of the cone, and various boundary conditions on natural frequencies of the functionally graded panel have been comprehensively studied and discussed. The results show that the most important parameter on dynamic response of FG porous truncated conical panel is the weight fraction of nanofiller and adding 1% weight fraction of nanofiller could increase 57% approximately the amounts of natural frequencies of the shell. Moreover, the porosity distribution has great effect on the value of natural frequency of structure rather than the porosity coefficient.

• Steel and Composite Structures
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• v.39 no.3
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• pp.275-290
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• 2021

The main purpose of this research work is to investigate the critical buckling load of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using generalized differential quadrature (GDQ) method at thermal condition. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the plate thickness direction. Generally, the thermal distribution is considered to be nonlinear and the temperature changing continuously through the thickness of the nanocomposite plates according to the power-law distribution. To model closed cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme are used, through which mechanical properties of the structures can be extracted. Based on the third order shear deformation theory (TSDT) and the Hamilton's principle, the equations of motion are established and solved for various boundary conditions (B.Cs). The fast rate of convergence and accuracy of the method are investigated through the different solved examples and validity of the present study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns through the thickness, porosity coefficient and distribution of porosity on critical buckling load. Results reveal that the importance of thermal condition on of the critical load of FGP-GPL reinforced nanocomposite plates.

• Advances in nano research
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• v.8 no.1
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• pp.59-68
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• 2020

In the present study, buckling analysis of sandwich composite (carbon nanotube reinforced composite and fiber reinforced composite) Euler-Bernoulli beam in two configurations (core and layers material), three laminates (combination of different angles) and two models (relative thickness of core according to peripheral layers) using differential quadrature method (DQM) is studied. Also, the effects of porosity coefficient and different types of porosity distribution on critical buckling load are discussed. Using sandwich beam, it shows a considerable enhancement in the critical buckling load when compared to ordinary composite. Actually, resistance against buckling in sandwich beam is between two to four times more. It is also showed the critical buckling loads of laminate 1 and 3 are significantly larger than the results of laminate 2. When Configuration 2 is used, the critical buckling load rises about 3 percent in laminate 1 and 3 compared to the results of configuration 1. The amount of enhancement for laminate 3 is about 17 percent. It is also demonstrated that the influence of the core height (thickness) in the case of lower carbon volume fractions is ignorable. Even though, when volume fraction of fiber increases, differences grow smoothly. It should be noticed the amount of decline has inverse relationship with the beam aspect ratio. Among three porosity patterns investigated, beam with the distribution of porosity Type 2 (downward parabolic) has the maximum critical buckling load. At the end, the first three modes of buckling will be demonstrated to investigate the effect of spring constants.

• Steel and Composite Structures
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• v.35 no.1
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• pp.111-127
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• 2020

The goal of this study is to fill this apparent gap in the area about investigating the effect of porosity distributions on vibrational behavior of FG sectorial plates resting on a two-parameter elastic foundation. The response of the elastic medium is formulated by the Winkler/Pasternak model. The internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The model is proposed with material parameters varying in the thickness of plate to achieve graded distributions in both porosity and nanofillers. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. The 2-D differential quadrature method as an efficient and accurate numerical approach is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution. Results show that for better understanding of mechanical behavior of nanocomposite plates, it is crucial to consider porosities inside the material structure.

• Structural Engineering and Mechanics
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• v.69 no.2
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• pp.231-241
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• 2019

In this paper, a new higher order shear deformation model is developed for static and free vibration analysis of functionally graded beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. Different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. In addition, the effect of different micromechanical models on the bending and 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 higher-order shear deformation model, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain displacement, stresses and frequencies, and the numerical results are compared with those available in the literature. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, micromechanical models, mode numbers, and geometry on the bending and natural frequencies of imperfect FG beams.