Techno Press

Steel and Composite Structures   Volume 27, Number 2, April25 2018, pages 201-216
Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles
Behrouz Karami, Maziar Janghorban and Abdelouahed Tounsi

Abstract     [Full Text]
    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 (r, θ, φ), 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 (r, θ, φ) 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.
Key Words
    three-dimensional elasticity theory; nonlocal strain gradient theory; spherical coordinate; anisotropic material; nanoparticles
(1) Behrouz Karami, Maziar Janghorban:
Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran;
(2) Abdelouahed Tounsi:
Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria.

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