On exact wave propagation analysis of triclinic material using three-dimensional bi-Helmholtz gradient plate model

Behrouz Karami,Maziar Janghorban,Abdelouahed Tounsi 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.69 No.5

Rapid advances in the engineering applications can bring further areas to provide the opportunity to manipulate anisotropic structures for direct productivity in design of micro/nano-structures. For the first time, magnetic affected wave characteristics of nanosize plates made of anisotropic material is investigated via the three-dimensional bi-Helmholtz nonlocal strain gradient theory. Three small scale parameters are used to predict the size-dependent behavior of the nanoplates more accurately. After owing governing equations of wave motion, an analytical approach based harmonic series is utilized to fine the wave frequency as well as phase velocity. It is observed that the small scale parameters, magnetic field and wave number have considerable influence on the wave characteristics of anisotropic nanoplates. Due to the lack of any study on the mechanics of three-dimensional bi-Helmholtz gradient plates made of anisotropic materials, it is hoped that the present exact model may be used as a benchmark for future works of such nanostructures.

Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles

Behrouz Karami,Maziar Janghorban,Abdelouahed Tounsi 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.27 No.2

In this paper, three-dimensional (3D) elasticity theory in conjunction with nonlocal strain gradient theory (NSGT) is developed for mechanical analysis of anisotropic nanoparticles. The present model incorporates two scale coefficients to examine the mechanical characteristics much accurately. All the elastic constants are considered and assumed to be the functions of (<i>r</i>, <i>θ</i>, <i>φ</i>), so all kind of anisotropic structures can be modeled. Moreover, all types of functionally graded spherical structures can be investigated. To justify our model, our results for the radial vibration of spherical nanoparticles are compared with experimental results available in the literature and great agreement is achieved. Next, several examples of the radial vibration and wave propagation in spherical nanoparticles including nonlocal strain gradient parameters are presented for more than 10 different anisotropic nanoparticles. From the best knowledge of authors, it is the first time that 3D elasticity theory and NSGT are used together with no approximation to derive the governing equations in the spherical coordinate. Moreover, up to now, the NSGT has not been used for spherical anisotropic nanoparticles. It is also the first time that all the 36 elastic constants as functions of (<i>r</i>, <i>θ</i>, <i>φ</i>) are considered for anisotropic and functionally graded nanostructures including size effects. According to the lack of any common approximations in the displacement field or in elastic constant, present theory can be assumed as a benchmark for future works.

A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates

Behrouz Karami,Maziar Janghorban,Davood Shahsavari,Abdelouahed Tounsi 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.28 No.1

In this paper, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment. This quasi-3D plate theory considers both thickness stretching influences and shear deformation with the variations of displacements in the thickness direction as a parabolic function. Moreover, the stress-free boundary conditions on both sides of the plate are satisfied without using a shear correction factor. This theory includes five independent unknowns with results in only five governing equations. Size effects are obtained via a higher-order nonlocal strain gradient theory of elasticity. A variational approach is adopted to owning the governing equations employing Hamilton's principle. Solving analytically via Fourier series, these equations gives wave frequencies and phase velocities as a function of wave numbers. The validity of the present results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for material composition, size dependency, two parametric elastic foundation, temperature and moisture differences, and wave number. Some conclusions are drawn from the parametric studies with respect to the wave characteristics.

A new size-dependent shear deformation theory for wave propagation analysis of triclinic nanobeams

Behrouz Karami,Maziar Janghorban 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.32 No.2

For the first time, longitudinal and transverse wave propagation of triclinic nanobeam is investigated via a size-dependent shear deformation theory including stretching effect. Furthermore, the influence of initial stress is studied. To consider the size-dependent effects, the nonlocal strain gradient theory is used in which two small scale parameters predict the behavior of wave propagation more accurately. The Hamiltonian principle is adopted to obtain the governing equations of wave motion, then an analytic technique is applied to solve the problem. It is demonstrated that the wave characteristics of the nanobeam rely on the wave number, nonlocal parameter, strain gradient parameter, initial stress, and elastic foundation. From this paper, it is concluded that the results of wave dispersion in isotropic and anisotropic nanobeams are almost the same in the presented case study. So, in this case, triclinic nanobeam can be approximated with isotropic model.

Effects of triaxial magnetic field on the anisotropic nanoplates

Behrouz Karami,Maziar Janghorban,Abdelouahed Tounsi 국제구조공학회 2017 Steel and Composite Structures, An International J Vol.25 No.3

In this study, the influences of triaxial magnetic field on the wave propagation behavior of anisotropic nanoplates are studied. In order to include small scale effects, nonlocal strain gradient theory has been implemented. To study the nanoplate as a continuum model, the three-dimensional elasticity theory is adopted in Cartesian coordinate. In our study, all the elastic constants are considered and assumed to be the functions of (x, y, z), so all kind of anisotropic structures such as hexagonal and trigonal materials can be modeled, too. Moreover, all types of functionally graded structures can be investigated. eigenvalue method is employed and analytical solutions for the wave propagation are obtained. To justify our methodology, our results for the wave propagation of isotropic nanoplates are compared with the results available in the literature and great agreement is achieved. Five different types of anisotropic structures are investigated in present paper and then the influences of wave number, material properties, nonlocal and gradient parameter and uniaxial, biaxial and triaxial magnetic field on the wave propagation analysis of anisotropic nanoplates are presented. From the best knowledge of authors, it is the first time that three-dimensional elasticity theory and nonlocal strain gradient theory are used together with no approximation to derive the governing equations. Moreover, up to now, the effects of triaxial magnetic field have not been studied with considering size effects in nanoplates. According to the lack of any common approximations in the displacement field or in elastic constant, present theory has the potential to be used as a bench mark for future works.

Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation

Behrouz Karami,Maziar Janghorban,Abdelouahed Tounsi 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.70 No.1

This work deals with the size-dependent wave propagation analysis of functionally graded (FG) anisotropic nanoplates based on a nonlocal strain gradient refined plate model. The present model incorporates two scale coefficients to examine wave dispersion relations more accurately. Material properties of FG anisotropic nanoplates are exponentially varying in the z-direction. In order to solve the governing equations for bulk waves, an analytical method is performed and wave frequencies and phase velocities are obtained as a function of wave number. The influences of several important parameters such as material graduation exponent, geometry, Winkler-Pasternak foundation parameters and wave number on the wave propagation of FG anisotropic nanoplates resting on the elastic foundation are investigated and discussed in detail. It is concluded that these parameters play significant roles on the wave propagation behavior of the nanoplates. From the best knowledge of authors, it is the first time that FG nanoplate made of anisotropic materials is investigated, so, presented numerical results can serve as benchmarks for future analysis of such structures.

Dynamic analysis of isotropic nanoplates subjected to moving load using state-space method based on nonlocal second order plate theory

Mohammad Rahim Nami,Maziar Janghorban 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.6

In this work, dynamic analysis of rectangular nanoplates subjected to moving load is presented. In order to derive the governing equationsof motion, second order plate theory is used. To capture the small scale effects, the nonlocal elasticity theory is adopted. It is assumedthat the nanoplate is subjected to a moving concentrated load with the constant velocity V in the x direction. To solve the governingequations, state-space method is used to find the deflections of rectangular nanoplate under moving load. The results obtained herereveal that the nonlocality has significant effect on the deflection of rectangular nanoplate subjected to moving load.

On buckling analysis of laminated composite plates using a nonlocal refined four-variable model

Davood Shahsavari,Behrouz Karami,Maziar Janghorban 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.32 No.2

This study is concerned with the stability of laminated composite plates modelled using Eringen’s nonlocal differential model (ENDM) and a novel refined-hyperbolic-shear-deformable plate theory. The plate is assumed to be lying on the Pasternak elastic foundation and is under the influence of an in-plane magnetic field. The governing equations and boundary conditions are obtained through Hamilton’s principle. An analytical approach considering Navier series is used to fine the critical bucking load. After verifying with existing results for the reduced cases, the present model is then used to study buckling of the laminated composite plate. Numerical results demonstrate clearly for the first time the roles of size effects, magnetic field, foundation parameters, moduli ratio, geometry, lay-up numbers and sequences, fiber orientations, and boundary conditions. These results could be useful for designing better composites and can further serve as benchmarks for future studies on the laminated composite plates.

Approximated 3D non-homogeneous model for the buckling and vibration analysis of femur bone with femoral defects

Mobasseri, Saleh,Sadeghi, Mehdi,Janghorban, Maziar,Tounsi, Abdelouahed Techno-Press 2020 Biomaterials and Biomechanics in Bioengineering Vol.5 No.1

We carry the knowledge that the skeleton bones of the human body are not always without defects and some various defects could occur in them. In the present paper, as the first endeavor, free vibration and buckling analysis of femur bones with femoral defects are investigated. A major strength of this study is the modeling of defects in femur bones. Materialise Mimics software is adopted to model the bone geometry and the SOLIDWORKS software is used to generate the defects in bones. Next, the ABAQUS software is employed to study the behaviors of bones with defects.

Several models for bending and buckling behaviors of FG-CNTRCs with piezoelectric layers including size effects

Heidari, Farshad,Afsari, Ahmad,Janghorban, Maziar Techno-Press 2020 Advances in nano research Vol.9 No.3

In this research, beside presenting real images of produced Functionally Graded Carbon Nanotube-Reinforced Composites (FG-CNTRCs) and a brief review of the synthesis method of FG-CNTRCs, static and buckling analysis of FG-CNTRC with piezoelectric layers are investigated. It is assumed that the material properties of FG-CNTRC are varied through the thickness direction using four different distributions of Carbon Nanotubes (CNTs). To capture the size effects, nonlocal elasticity theory proposed by A.C. Eringen is also adopted in our model. One of the topics in our paper is using a higher order theory with eight different displacement fields and comparing their results with each other. To solve the governing equations, an analytical method is used to find the deflections and critical buckling loads of FG-CNTRCs. To show the accuracy of present methodology, our results are compared with the results of simply supported rectangular nano plates available in the literature. In this research, the effects of aspect ratio, piezoelectric layer and nonlocal parameter are also studied. It is hoped that this work leads to more accurate models on FG-CNTRC.