A review on the mechanics of functionally graded nanoscale and microscale structures

https://northumbria-test.eprints-hosting.org/id/document/268107

A review on the mechanics of nanostructures

In this study, the free vibration and buckling responses of functionally graded nanoplates with magneto-electro-elastic coupling are studied for the first time using a nonlocal modified sinusoidal shear deformation plate theory including the thickness stretching effect. The constitutive relations for these kind of structures are defined. The equations of motion for rectangular sandwich plates in macro and nano scale are derived using a modified dynamic version of Hamilton's principle including a contribution of the electric and magnetic fields. The closed-form analytical solution to simply supported plates is obtained using Navier solution technique. A power-law distribution and a half cosine variation are used to model the variation of materials properties and electric/magnetic potentials, respectively. The analytical solutions are verified with well-known solutions in the literature. A parametric study was conducted to show the effect of nonlocal parameter, power-law index, predefined electric and magnetic fields, axial compressive and tensile forces, the aspect ratio of plates, and volume ratio of functionally graded and piezomagnetic layers on mechanical behaviors of nanoplates. Obtained numerical results can be used as benchmark values for validation of correctness of diverse analytical and numerical methods applied for design and analysis of composite nanoelectromechanical systems.

Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory

Recently, advanced materials whose properties vary within a continuous pattern have been put to use to design and manufacture modern structures. In the current investigation, size dependencies are captured in the nonlinear free vibration characteristics of micro/nano-beams made of bi-directional functionally graded materials (2D-FGM). With the aid of the nonlocal strain gradient elasticity theory and the variational principle, the size-dependent nonlinear differential equations of motion are derived within the framework of the refined hyperbolic shear deformation beam theory. It is supposed that the material properties are distributed exponentially along longitudinal direction, and vary based on the power law function in lateral direction. Moreover, the deviation of the associated physical neutral plane from the mid-plane counterpart is taken into consideration. By employing a numerical solution methodology on the basis of the generalized differential quadrature method (GDQM) together with Galerkin technique and pseudo arc-length continuation method, the nonlocal strain gradient frequency-deflection responses of 2D-FGM micro/nano-beam are obtained corresponding to various values of longitudinal and lateral material property indexes and small scale parameters. It is revealed that the increment made by the strain gradient size dependency in the value of the nonlinear frequency is more than the reduction caused by the nonlocality, especially for the lower maximum deflection imposed to the 2D-FGM micro/nano-beam. Also, it is indicated that for lower values of the material property gradient indexes, the reduction in the nonlinear frequency caused by the lateral functionally graded pattern in the absence of the axial functionally graded pattern is more than that made by the vice versa case. However, for higher values of the material property gradient indexes, an opposite observation is seen.

Nonlinear free vibrations of bi-directional functionally graded micro/nano-beams including nonlocal stress and microstructural strain gradient size effects

The present study deals with the size-dependent nonlinear buckling and postbuckling characteristics of magneto-electro-elastic cylindrical composite nanoshells incorporating simultaneously the both of hardening-stiffness and softening-stiffness size effects. To accomplish this purpose, the nonlocal strain gradient elasticity theory is applied to the classical shell theory. Via the virtual work's principle, the size-dependent governing differential equations are constructed including the coupling terms between the axial mechanical compressive load, external magnetic potential and external electrical potential. The nonlinear prebuckling deformations and the large postbuckling deflections are taken into consideration based upon the boundary layer theory of shell buckling. Finally, an improved perturbation technique is employed to achieve explicit analytical expressions for nonlocal strain gradient stability curves of magneto-electro-elastic nanoshells under various surface electric and magnetic voltages. It is seen that a positive electric potential and a negative magnetic potential cause to increase both of the nonlocality and strain gradient size dependencies in the nonlinear instability behavior of axially loaded magneto-electro-elastic composite nanoshells, while a negative electric potential and a positive magnetic potential play an opposite role.

Nonlocal strain gradient shell model for axial buckling and postbuckling analysis of magneto-electro-elastic composite nanoshells

Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates

A new approach to consider the influence of aging state on Lithium-ion battery state of power estimation for hybrid electric vehicle

Accurate estimation of the State of Power (SoP) can ensure safe and efficient operation of Lithium-ion batteries in Electric Vehicles (EVs) and Hybrid Electric Vehicles (HEVs). The cell-to-cell variation within a battery pack is a major challenge towards accurate estimation of the SoP, particularly when the cells get aged. This paper presents a hybrid model predictive and fuzzy logic based control system to accurately estimate the SoP for series-connected Lithium-ion cells. The estimation strategy consists of two steps; the power capability for a single new cell is first reckoned under the light of the model predictive control algorithm. The second step is devoted to designation of a model-less fuzzy logic based control system to compensate for the concurrent aging state and State of Charge (SoC) differences among the cells. Accordingly, the present approach only utilizes the actual values of current and cell voltages together with the Electric Circuit Model (ECM) parameters of the new cell, which are identified off-line. Moreover, it benefits from a closed-loop framework which ends in an accurate and reliable SoP estimation. An experimental setup consisting of fresh and aged LiFePO4 cell samples is designed and the extracted data are utilized to verify the proposed estimation method in a feed-forward simulation model for a HEV. The results indicate that the proposed method can estimate the pack SoP accurately while the safe operation for the cells is guaranteed.

A hybrid model predictive and fuzzy logic based control method for state of power estimation of series-connected Lithium-ion batteries in HEVs

Passive dynamic walking originally was introduced to describe some natural stable periodic gaits in straight walking. However, in this research, we have extended this notion to curved walking, wherein some novel three-dimensional (3D) periodic gaits with natural stability have been realized. For this aim, the simplest bipedal walking model, i.e. a rimless spoked-wheel, in its general 3D form, has been considered on a straight slope surface. Then, two kinds of stable passive turning, i.e. limited and circular continuous have been discussed. The first kind is actually a transfer among two-dimensional (2D) periodic motions and can be implemented on such straight slope surface. It is shown that the second kind is related to novel 3D periodic motions and can be just recognized on a special surface profile namely ‘helical slope’. The latter are interpreted as 3D fixed points of a Poincare return map. Results not only show asymptotical stability of such periodic motions, but also surprisingly indicate that the s...

Passive turning motion of 3D rimless wheel: novel periodic gaits for bipedal curved walking

Passive dynamic walking usually refers to a kind of walking where a biped walker is able to walk downhill, without any actuation or control, just due to the gravity. Although most of works done in this regard have concentrated on passive walking along a straight line, in this paper we extend this concept to a more general case of locomotion, i.e. turning or walking along curved path. We call the novel extension passive turning, and categorize it to two types of finite and infinite. We showed that the finite type is still applicable on a typical downhill or ramp, while the infinite type is only practical on a specific surface profile that we call it helical ramp. Furthermore, several stability and parameter analysis are also conducted to evaluate more aspects of this notion. We highlighted that surprisingly, the passive straight walking is actually a special case of passive turning, just with infinite radius of turn and less asymptotical stability. It should be noted that the present study is perfo...

M. R. Hairi Yazdi

Papers

Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates

A new approach to consider the influence of aging state on Lithium-ion battery state of power estimation for hybrid electric vehicle

A hybrid model predictive and fuzzy logic based control method for state of power estimation of series-connected Lithium-ion batteries in HEVs

Passive turning motion of 3D rimless wheel: novel periodic gaits for bipedal curved walking

Passive dynamic turning in 3D biped locomotion: an extension to passive dynamic walking