• Steel and Composite Structures
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• v.43 no.1
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• pp.79-90
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• 2022

In this study, the dynamic behavior of functionally graded layered deep beams with viscoelastic core is investigated including the porosity effect. The material properties of functionally graded layers are assumed to vary continuously through thickness direction according to the power-law function. To investigate porosity effect in functionally graded layers, three different distribution models are considered. The viscoelastically cored deep beam is exposed to harmonic sinusoidal load. The composite beam is modeled based on plane stress assumption. The dynamic equations of motion of the composite beam are derived based on the Hamilton principle. Within the framework of the finite element method (FEM), 2D twelve -node plane element is exploited to discretize the space domain. The discretized finite element model is solved using the Newmark average acceleration technique. The validity of the developed procedure is demonstrated by comparing the obtained results and good agreement is detected. Parametric studies are conducted to demonstrate the applicability of the developed methodology to study and analyze the dynamic response of viscoelastically cored porous functionally graded deep beams. Effects of viscoelastic parameter, porosity parameter, graduation index on the dynamic behavior of porous functionally graded deep beams with viscoelastic core are investigated and discussed. Material damping and porosity have a significant effect on the forced vibration response under harmonic excitation force. Increasing the material viscosity parameters results in decreasing the vibrational amplitudes and increasing the vibration time period due to increasing damping effect. Obtained results are supportive for the design and manufacturing of such type of composite beam structures.

• Steel and Composite Structures
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• v.48 no.3
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• pp.335-351
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• 2023

This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin-Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke's law, and von-Kármán equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated.

• Steel and Composite Structures
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• v.32 no.5
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• pp.633-642
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• 2019

In this work, lightweight sandwich plates consisting of a functionally graded porous (FGP) core and two laminated composite face sheets resting on elastic foundation have been proposed. Three different profiles are considered for the distributions of porosities along core thickness. The main aim of this paper is the investigation of the buckling behavior of the proposed porous sandwich plates (PSPs) by reporting their critical mechanical loads and their corresponding mode shapes. A finite element method (FEM) based on first order shear deformation theories (FSDT) is developed to discretize governing equations for the buckling behavior of the proposed sandwich plates. The effects of porosity dispersion and volume, the numbers and angles of laminated layers, sandwich plate geometrical dimensions, elastic foundation coefficients, loading and boundary conditions are studied. The results show that the use of FGP core can offer a PSP with half weight core and only 5% reduction in critical buckling loads. Moreover, stacking sequences with only ${\pm}45$ orientation fibers offer the highest values of buckling loads.

• Advances in materials Research
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• v.11 no.4
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• pp.279-298
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• 2022

In this paper, the important novelty and the defining a physical phenomenon of the resent research is the development of nonlocal stress and strain parameters on the porous sandwich beam with functionally graded materials in the top and bottom face sheets.Also, various beam models including Euler-Bernoulli, Reddy and the generalized formulation of two-variable beam theories are obtained in this research. According to a nonlocal strain elasticity theory, the strain at a reference point in the body is dependent not only on the stress state at that point, but also on the stress state at all of the points throughout the body. Thus, the nonlocal stress-strain elasticity theory is defined that can be actual at micro/nano scales. It can be seen that the critical buckling load and transverse deflection of sandwich beam by considering both nonlocal stress-strain parameters is higher than the nonlocal stress parameter. On the other hands, it is noted that by considering the nonlocal stress-strain parameters simultaneously becomes the actual case.

• Steel and Composite Structures
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• v.46 no.2
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• pp.263-277
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• 2023

Free vibration analysis of multi-directional porous functionally graded (FG) sandwich plate has been performed for two cases namely: FG skin with homogeneous core and FG core with homogeneous skin. Hamilton's principle was employed and the solution was obtained using Navier's technique. This theory imposes traction-free boundary conditions on the surfaces and does not require shear correction factors. The results obtained are validated with those available in the literature. The composition of metal-ceramic-based functionally graded material (FGM) changes in longitudinal and transverse directions according to the power law. Imperfections in the functionally graded material introduced during the fabrication process were modeled with different porosity laws such as evenly, unevenly distributed, and logarithmic uneven distributions. The effect of porosity laws and geometry parameters on the natural frequency was investigated. On comparing the natural frequency of two cases for perfect and imperfect sandwich plates a reverse trend in natural frequency result was seen. The finding shows a multidirectional functionally graded structures perform better compared to uni-directional gradation. Hence, critical grading parameters and imperfection types have been identified which will guide experimentalists and researchers in selecting fabrication routes for improving the performance of such structures.

• Steel and Composite Structures
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• v.35 no.5
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• pp.659-670
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• 2020

This paper proposes the use of a porous core between layers of laminated composite plates to examine its effect on the natural frequencies of the resulted porous laminated composite sandwich plate (PLCSP) resting on a two-parameter elastic foundation. Moreover, it has been suggested that the dispersion of porosity has two different functionally graded (FG) patterns which are compared with a uniformly dispersed (UD) profile to find their best vibrational efficiency in the proposed PLCSPs. In FG patterns, two types of dispersions, including symmetric (FG-S) and asymmetric (FG-A) patterns have been considered. To derive the governing Eigen value equation of such structures, the first order shear deformation theory (FSDT) of plates has been employed. Accordingly, a finite element method (FEM) is developed to solve the derived Eigen value equation. Using the mentioned theory and method, the effects of porosity parameters, fiber orientation of laminated composite, geometrical dimensions, boundary conditions and elastic foundation on the natural frequencies of the proposed PLCSPs have been studied. It is observed that embedding porosity in core layer leads to a significant improvement in the natural frequencies of PLCSPs. Moreover, the natural frequencies of PLCSPs with FG porous core are higher than those with UD porous core.

• Structural Engineering and Mechanics
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• v.77 no.4
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• pp.549-557
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• 2021

In this study, it is aimed to analyze the bending of porous sandwich plates using the four-variable shear deformation theory. The core of the sandwich plate is assumed to be functionally graded, and face sheets are assumed to be isotropic. The pore distribution of the sandwich plate is considered even and uneven type of porosity distribution. Displacement fields are defined with four variable shear deformation theory. Equilibrium equations of porous sandwich plates are derived from virtual displacement principle. An analytical solution is obtained by Navier's approach. Results are presented for uniformly and sinusoidally distributed loaded porous sandwich plates. Face sheet -core thickness ratio, porosity distribution, amount of porosity is investigated.

• Coupled systems mechanics
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• v.8 no.3
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• pp.259-271
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• 2019

This paper presents forced vibration analysis of sandwich deep beams made of functionally graded material (FGM) in face layers and a porous material in core layer. The FGM sandwich deep beam is subjected to a harmonic dynamic load. The FGM in the face layer is graded though the layer thickness. In order to get more realistic result for the deep beam problem, the plane solid continua is used in the modeling of The FGM sandwich deep beam. The equations of the problem are derived based the Hamilton procedure and solved by using the finite element method. The novelty in this paper is to investigate the dynamic responses of sandwich deep beams made of FGM and porous material by using the plane solid continua. In the numerical results, the effects of different material distributions, porosity coefficient, geometric and dynamic parameters on the dynamic responses of the FGM sandwich deep beam are investigated and discussed.

• Steel and Composite Structures
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• v.32 no.5
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• pp.595-610
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• 2019

This paper deals with the static and dynamic behavior of Functionally Graded Carbon Nanotubes (FG-CNT)-reinforced porous sandwich (PMPV) polymer plate. The model of nanocomposite plate is investigated within the first order shear deformation theory (FSDT). Two types of porous sandwich plates are supposed (sandwich with face sheets reinforced / homogeneous core and sandwich with homogeneous face sheets / reinforced core). Functionally graded Carbon Nanotubes (FG-CNT) and uniformly Carbon Nanotubes (UD-CNT) distributions of face sheets or core porous plates with uniaxially aligned single-walled carbon nanotubes are considered. The governing equations are derived by using Hamilton's principle. The solution for bending and vibration of such type's porous plates are obtained. The detailed mathematical derivations are provided and the solutions are compared to some cases in the literature. The effect of the several parameters of reinforced sandwich porous plates such as aspect ratios, volume fraction, types of reinforcement, number of modes and thickness of plate on the bending and vibration analyses are studied and discussed. On the question of porosity, this study found that there is a great influence of their variation on the static and vibration of porous sandwich plate.

• Advances in nano research
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• v.7 no.2
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• pp.109-123
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• 2019

In this article, the free vibration analysis of annular sandwich plates with various functionally graded (FG) porous cores and carbon nanotubes reinforced composite (CNTRC) facesheets is investigated based on modified couple stress theory (MCST) and first order shear deformation theories (FSDT). The annular sandwich plate is composed of two face layers and a functionally graded porous core layer which contains different porosity distributions. Various approaches such as extended mixture rule (EMR), Eshelby-Mori-Tanaka (E-M-T), and Halpin-Tsai (H-T) are used to determine the effective material properties of microcomposite circular sandwich plate. The governing equations of motion are extracted by using Hamilton's principle and FSDT. A Ritz method has been utilized to calculate the natural frequency of an annular sandwich plate. The effects of material length scale parameters, boundary conditions, aspect and inner-outer radius ratios, FG porous distributions, pore compressibility and volume fractions of CNTs are considered. The results are obtained by Ritz solutions that can be served as benchmark data to validate their numerical and analytical methods in the future work and also in solid-state physics, materials science, and micro-electro-mechanical devices.