In this paper, the Ritz method has been employed to analyze the free in-plane vibration of heterogeneous (non-uniform) rectangular nanoplates corresponding to Eringen’s nonlocal elasticity theory. The non-uniformity is taken into account using combinations of linear and quadratic forms in the thickness, material density and Young’s modulus. Two-dimensional boundary characteristic orthogonal pol...

The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of investigation was initiated for the space of elasticity tensors. Since then, different authors solved this problem for other kinds of physics such as photoelectricity, ...

In this paper, buckling and free vibration analysis of a circular tapered nanoplate subjected to in-plane forces were studied. The linear variation of the plate thickness was considered in radial direction. Nonlocal elasticity theory was employed to capture size-dependent effects. The Raleigh-Ritz method and differential transform method were utilized to obtain the frequency equations for simpl...

In this paper, axisymmetric free vibration analysis of a circular Nano-plate having variable thickness was studied. The variation in thickness of plate was considered as a linearly in radial direction. Nonlocal elasticity theory was utilized to take into account size-dependent effects. Ritz functions was utilized to obtain the frequency equations for simply supported and clamped boundary. To ve...

In this work, nonlocal vibration of double of carbon nanotubes (CNTs) system conveying fluid coupled by visco-Pasternak medium is carried out based on nonlocal elasticity theory where CNTs are placed in uniform temperature change and magnetic field. Considering Euler-Bernoulli beam (EBB) model and Knudsen number, the governing equations of motion are discretized and Ritz method is applied to ob...

In the present study, the buckling analysis of the rectangular nanoplate under biaxial non-uniform compression using the modified couple stress continuum theory with various boundary conditions has been considered. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using the Hamilton’s principle. An analytic...

We give an overview on existence results in nonlinear peridynamics, a nonlocal elasticity theory, and compare these results with those known for classical nonlinear elastodynamics. In peridynamics, it is possible to obtain stronger results under equal or even less restrictive assumptions on the stress.

The following article investigates nonlinear symmetric buckling of moderately thick circular Nano plates with an orthotropic property under uniform radial compressive in-plane mechanical load. Taking into account Eringen nonlocal elasticity theory, principle of virtual work, first order shear deformation plate theory (FSDT) and nonlinear Von-Karman strains, the governing equations are obtained ...

Abstract In this manuscript two BMO estimates are obtained, one for Linear Elasticity and Nonlinear Elasticity. It is first shown that the BMO-seminorm of gradient a vector-valued mapping bounded above by constant times symmetric part its gradient, is, Korn inequality in BMO. The uniqueness equilibrium finite deformation whose principal stresses everywhere nonnegative then considered. when seco...

The free vibration analysis of rotating functionally graded (FG) nano-beams under an in-plane thermal loading is provided for the first time in this paper. The formulation used is based on Euler-Bernoulli beam theory through Hamilton’s principle and the small scale effect has been formulated using the Eringen elasticity theory. Then, they are solved by a generalized differential quadrature meth...