• Advances in materials Research
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• v.5 no.4
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• pp.279-298
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• 2016

Present disquisition proposes an analytical solution method for exploring the buckling characteristics of porous magneto-electro-elastic functionally graded (MEE-FG) plates with various boundary conditions for the first time. Magneto electro mechanical properties of FGM plate are supposed to change through the thickness direction of plate. The rule of power-law is modified to consider influence of porosity according to two types of distribution namely even and uneven. Pores possibly occur inside FGMs due the result of technical problems that lead to creation of micro-voids in these materials. The variation of pores along the thickness direction influences the mechanical and physical properties. Four-variable tangential-exponential refined theory is employed to derive the governing equations and boundary conditions of porous FGM plate under magneto-electrical field via Hamilton's principle. An analytical solution procedure is exploited to achieve the non-dimensional buckling load of porous FG plate exposed to magneto-electrical field with various boundary condition. A parametric study is led to assess the efficacy of material graduation exponent, coefficient of porosity, porosity distribution, magnetic potential, electric voltage, boundary conditions, aspect ratio and side-to-thickness ratio on the non-dimensional buckling load of the plate made of magneto electro elastic FG materials with porosities. It is concluded that these parameters play remarkable roles on the dynamic behavior of porous MEE-FG plates. The results for simpler states are confirmed with known data in the literature. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases.

• Smart Structures and Systems
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• v.23 no.5
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• pp.429-447
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• 2019

The present study analyzed free vibration of the three-layered micro annular/circular plate which its core and face sheets are made of saturated porous materials and FG-CNTRCs, respectively. The structure is subjected to magneto-electric fields and magneto-electro-mechanical pre loads. Mechanical properties of the porous core and also FG-CNTRC face sheets are varied through the thickness direction. Using dynamic Hamilton's principle, the motion equations based on MCS and FSD theories are derived and solved via GDQ as an efficient numerical method. Effect of different parameters such as pores distributions, porosity coefficient, pores compressibility, CNTs distribution, elastic foundation, multi-physical pre loads, small scale parameter and aspect ratio of the plate are investigated. The findings of this study can be useful for designing smart structures such as sensor and actuator.

• Structural Engineering and Mechanics
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• v.66 no.2
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• pp.237-248
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• 2018

This study presents the investigation of wave dispersion characteristics of a magneto-electro-elastic functionally graded (MEE-FG) nanosize beam utilizing nonlocal strain gradient theory (NSGT). In this theory, a material length scale parameter is propounded to show the influence of strain gradient stress field, and likewise, a nonlocal parameter is nominated to emphasize on the importance of elastic stress field effects. The material properties of heterogeneous nanobeam are supposed to vary smoothly through the thickness direction based on power-law form. Applying Hamilton's principle, the nonlocal governing equations of MEE-FG nanobeam are derived. Furthermore, to derive the wave frequency, phase velocity and escape frequency of MEE-FG nanobeam, an analytical solution is employed. The validation procedure is performed by comparing the results of present model with results exhibited by previous papers. Results are rendered in the framework of an exact parametric study by changing various parameters such as wave number, nonlocal parameter, length scale parameter, gradient index, magnetic potential and electric voltage to show their influence on the wave frequency, phase velocity and escape frequency of MEE-FG nanobeams.

• Advanced Composite Materials
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• v.18 no.2
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• pp.153-166
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• 2009

A matrix method for evaluating effective electro-magneto-thermo-elastic properties of a generally anisotropic multilayered composite is presented. Physical variables are categorized into two groups: one that satisfies the continuity across the interface between layers and another that satisfies an average inter-layer compatibility (which is also exact). The coupled electro-magneto-thermo-elastic constitutive equation is accordingly reassembled into submatrices, which leads to the derivation of concise and exact matrix expressions for effective properties of a multilayered composite having the coupled physical effects. Comparing the results for a purely elastic multiplayer with those from other theoretical approaches validates the developed method. Examples are given for a PZT-graphite/epoxy composite and a $BaTiO_3-CoFe_2O_4$ multiplayer which exhibit piezo-thermoelastic and magnetoelectric properties, respectively. The result shows how a strong magnetoelectric effect can be achieved by combining piezoelectric and piezomagnetic materials in a multilayered structure. The magnetoelectric coefficient of the $BaTiO_3-CoFe_2O_4$ multiplayer is compared with those for fibrous and particulate composites fabricated with the same constituents.

• Advances in Computational Design
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• v.3 no.3
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• pp.303-318
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• 2018

This article presents a semi-analytical solution for an exponentially graded piezoelectric hollow sphere. The sphere interacts with electric displacement, elastic deformations, electric potentials, magneto-thermo-elasticity, and hygrothermal influences. The hollow sphere may be standing under both mechanical and electric potentials. Electro-magneto-elastic behavior of magnetic field vector can be described in the hollow sphere. All material, thermal and magnetic properties of hollow sphere are supposed to be graded in radial direction. A semi-analytical technique is improved to deduce all fields in which different boundary conditions for radial stress and electric potential are presented. Numerical examples for radial displacement, radial and hoop stresses, and electric potential are investigated. The influence of many parameters is studied. It is seen that the gradation of all material, thermal and magnetic properties has particular effectiveness in many applications of modern technology.

• Advances in nano research
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• v.5 no.4
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• pp.281-301
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• 2017

In this disquisition, an exact solution method is developed for analyzing the vibration characteristics of magneto-electro-elastic functionally graded (MEE-FG) beams by considering porosity distribution and various boundary conditions via a four-variable shear deformation refined beam theory for the first time. Magneto-electroelastic properties of porous FG beam are supposed to vary through the thickness direction and are modeled via modified power-law rule which is formulated using the concept of even and uneven porosity distributions. Porosities possibly occurring inside functionally graded materials (FGMs) during fabrication because of technical problem that lead to creation micro-voids in FG materials. So, it is necessary to consider the effect of porosities on the vibration behavior of MEE-FG beam in the present study. The governing differential equations and related boundary conditions of porous MEE-FG beam subjected to physical field are derived by Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factor. An analytical solution procedure is used to achieve the natural frequencies of porous-FG beam supposed to magneto-electrical field which satisfies various boundary conditions. A parametric study is led to carry out the effects of material graduation exponent, porosity parameter, external magnetic potential, external electric voltage, slenderness ratio and various boundary conditions on dimensionless frequencies of porous MEE-FG beam. It is concluded that these parameters play noticeable roles on the vibration behavior of MEE-FG beam with porosities. Presented numerical results can be applied as benchmarks for future design of MEE-FG structures with porosity phases.

• Smart Structures and Systems
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• v.26 no.1
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• pp.77-87
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• 2020

By employing a quasi-3D plate formulation, the present research studies static stability of magneto-electro-thermo-elastic functional grading (METE-FG) nano-sized plates. Accordingly, influences of shear deformations as well as thickness stretching have been incorporated. The gradation of piezo-magnetic and elastic properties of the nano-sized plate have been described based on power-law functions. The size-dependent formulation for the nano-sized plate is provided in the context of nonlocal elasticity theory. The governing equations are established with the usage of Hamilton's rule and then analytically solved for diverse magnetic-electric intensities. Obtained findings demonstrate that buckling behavior of considered nanoplate relies on the variation of material exponent, electro-magnetic field, nonlocal coefficient and boundary conditions.

• Steel and Composite Structures
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• v.31 no.5
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• pp.469-488
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• 2019

We in this paper study nonlinear bending of a functionally graded porous nanobeam subjected to multiple physical load based on the nonlocal strain gradient theory. For more reasonable analysis of nanobeams made of porous functionally graded magneto-thermo-electro-elastic materials (PFGMTEEMs), both constituent materials and the porosity appear gradient distribution in the present expression of effective material properties, which is much more suitable to the actual compared with the conventional expression of effective material properties. Besides the displacement function regarding physical neutral surface is introduced to analyze mechanical behaviors of beams made of FGMs. Then we derive nonlinear governing equations of PFGMTEEMs beams using the principle of Hamilton. To obtain analytical solutions, a two-step perturbation method is developed in nonuniform electric field and magnetic field, and then we use it to solve nonlinear equations. Finally, the analytical solutions are utilized to perform a parametric analysis, where the effect of various physical parameters on static bending deformation of nanobeams are studied in detail, such as the nonlocal parameter, strain gradient parameter, the ratio of nonlocal parameter to strain gradient parameter, porosity volume fraction, material volume fraction index, temperature, initial magnetic potentials and external electric potentials.

• Steel and Composite Structures
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• v.33 no.1
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• pp.93-109
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• 2019

In the present study, vibration analysis of double bonded micro sandwich cylindrical shells with saturated porous core and carbon/boron nitride nanotubes (CNT/BNNT) reinforced composite face sheets under multi-physical loadings based on Cooper-Naghdi theory is investigated. The material properties of the micro structure are assumed to be temperature dependent, and each of the micro-tubes is placed on the Pasternak elastic foundations, and mechanical, moisture, thermal, electrical, and magnetic forces are effective on the structural behavior. The distributions of porous materials in three distributions such as non-linear non-symmetric, nonlinear-symmetric, and uniform are considered. The relationship including electro-magneto-hydro-thermo-mechanical loadings based on modified couple stress theory is obtained and moreover the governing equations of motion using the energy method and the Hamilton's principle are derived. Also, Navier's type solution is also used to solve the governing equations of motion. The effects of various parameters such as material length scale parameter, temperature change, various distributions of nanotube, volume fraction of nanotubes, porosity and Skempton coefficients, and geometric parameters on the natural frequency of double bonded micro sandwich cylindrical shells are investigated. Increasing the porosity and the Skempton coefficients of the core in micro sandwich cylindrical shell lead to increase the natural frequency of the structure. Cylindrical shells and porous materials in the industry of filters and separators, heat exchangers and coolers are widely used and are generally accepted today.