https://northumbria-test.eprints-hosting.org/id/document/265204

A review of continuum mechanics models for size-dependent analysis of beams and plates

On the effect of viscoelasticity on behavior of gyroscopes

Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory

A three-dimensional finite element (FE) model for armchair, zigzag single-walled carbon nanotubes (SWCNTs) is proposed. The model development is based on the assumption that carbon nanotubes, when subjected to loading, behave like space-frame structures. The bonds between carbons atoms are considered as connecting load-carrying members, while the carbon atoms as joints of the members. To create the FE models, nodes are placed at the locations of carbon atoms and the bonds between them are modeled using three-dimensional elastic beam elements. The elastic moduli of beam elements are determined by using a linkage between molecular and continuum mechanics. In order to evaluate the FE model and demonstrate its performance, the influence of tube wall thickness, diameter on the elastic moduli (Young’s modulus and shear modulus) of SWCNTs is investigated. It is found that the choice of wall thickness significantly affects the calculation of Young’s modulus. For the values of wall thickness used in the literature, the obtained values of Young’s modulus agree very well with the corresponding theoretical results and many experimental measurements. Dependence of elastic moduli to diameter of the nanotubes is also obtained. With increased tube diameter, the elastic moduli of the SWCNTs increase. The results show that armchair nanotube exhibit slightly higher values of Young’s modulus than zigzag ones for small values of radius, but their shear modulus are identical based on the present study. The presented results demonstrate that the proposed FE model may provide a valuable tool for studying the mechanical behavior of carbon nanotubes and their integration in nano-composites.

Finite element modeling of single-walled carbon nanotubes

In the present investigation, a new first-order shear deformation theory (OVFSDT) on the basis of the in-plane stability of the piezo-magnetoelectric composite nanoplate (PMEN) has been developed, and its precision has been evaluated. The OVFSDT has many advantages compared to the conventional first-order shear deformation theory (FSDT) such as needless of shear correction factors, containing less number of unknowns than the existing FSDT and strong similarities with the classical plate theory (CPT). The composite nanoplate consisted of BaTiO3-CoFe2O4 , a kind of material by which coupling between piezoelectric and piezomagnetic in nanosize was established. The plate is surrounded by a motionless and stationary matrix that is embedded in a hygrothermal surround in order to keep it more stable, and to take into consideration the influences of the moisture and temperature on the plate's mechanical behavior. The governing equilibrium equations for the smart composite plate have been formulated using the higher-order nonlocal strain gradient theory within which both stress nonlocality and second strain gradient size-dependent terms are taken into account by using three independent length scale parameters. The extracted equations are solved by utilizing the analytical approaches by which numerical results are obtained with various boundary conditions. In order to evaluate the proposed theory and methods of solution, the outcomes in terms of critical buckling loads are compared with those from several available well-known references. Finally, after determining the accuracy of the results of the new plate theory, several parameters are investigated to show the influences of material properties of the ceramic composite nanoplate on the critical buckling loads.

Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory

In this research, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and non-linear strains of Von-Karman was studied. The bi-layer carbon sheets was modeled as a double-layered plate, and van der Waals forces between layers were considered. The governing equations and boundary conditions were obtained using the first order shear deformation theory. For calculation of critical temperature and critical shear load, the equations were divided for two states via adjacent equilibrium criterion, pre-buckling and stability. The stability equations were discretized by differential quadrature method which is a high accurate numerical method. The equations were solved for various boundary conditions, such as free edges. Finally, the small scale parameter effect due to length to the width ratio, stiffness of elastic medium on the critical load was considered. The shear buckling results showed that the effect of type of shear loading on the nonlocal results is more than local results. Also, in thermal buckling analysis, the most important results being that whether the boundary conditions have more flexibility, by increasing the dimensions ratio, the results of critical temperature were tightly close together in nonlocal and local analysis.

Non-linear static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum

In this paper, the nonlinear bending behavior of bilayer orthotropic rectangular graphene sheets resting on a two parameter elastic foundation is studied subjected to uniform transverse loads using the non-local elasticity theory. The non-local theory consider the small scale effects. Considering the non-local differential constitutive relations of Eringen theory based on first order shear deformation theory (FSDT) and using the von-Karman strain field, the nonlinear formulations are derived. Equilibrium partial differential equations are expressed in terms of generalized displacements and rotations. Because of nonlinear partial differential equations, if it is not impossible but it is too complicated to find an analytical solution, so, the differential quadrature method (DQM) that is a high accurate numerical method is investigated to solve the governing equations. The Newton–Raphson iterative scheme is applied to solve the obtained nonlinear algebraic equations system. Different boundary conditions including clamped, simply supports and free edges are considered. Since there is not any researches available for nonlinear bending of bilayer rectangular graphene sheets with FSD theory, so considering the monolayer, the results are compared with available papers. Finally, the small scale effect parameter due to various types of conditions such as thickness ratio, boundary conditions, stiffness of elastic foundation, the van der Waals interactions between the layers, nonlinear to linear FSDT analysis and the differences between non-local and local elasticity theories are investigated.

Nonlinear bending analysis of bilayer orthotropic graphene sheets resting on Winkler–Pasternak elastic foundation based on non-local continuum mechanics

Nonlinear static analysis of single layer annular/circular graphene sheets embedded in Winkler–Pasternak elastic matrix based on non-local theory of Eringen

Non-linear bending analysis of multi-layer orthotropic annular/circular graphene sheets embedded in elastic matrix in thermal environment based on non-local elasticity theory

M Jabbarzadeh

Papers

Non-linear static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum

Nonlinear bending analysis of bilayer orthotropic graphene sheets resting on Winkler–Pasternak elastic foundation based on non-local continuum mechanics

Nonlinear static analysis of single layer annular/circular graphene sheets embedded in Winkler–Pasternak elastic matrix based on non-local theory of Eringen

Non-linear bending analysis of multi-layer orthotropic annular/circular graphene sheets embedded in elastic matrix in thermal environment based on non-local elasticity theory

The density effect of van der Waals forces on the elastic modules in graphite layers