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Introduction To Electrodynamics

Honeycombs are ultra-light materials with outstanding mechanical properties, which mainly originate from their unit cell configurations rather than the properties of matrix materials. Honeycombs are triggering in numerous promising applications in the fields of architecture, automotive, railway vehicle, marine, aerospace, satellite, packaging and medical implants, etc. Here we provide an in-depth overview of some important advances in basic structural design to obtain novel honeycombs with various improved mechanical properties. Firstly, the review introduces the classical honeycomb configurations. Then, a clear classification of advanced designs is established and discussed according to the design scale. The designs on the macro scale are divided into hierarchical, graded and disordered, while the designs on the meso scale are grouped as hybrid, curved ligament and reinforced strut. Moreover, the effects of different designs on the mechanical properties of honeycomb are discussed quantitatively. Finally, we summarize the important potential designs to improve the mechanical properties of honeycombs and the challenges in further research.

Advanced honeycomb designs for improving mechanical properties: A review

On the mechanics of functionally graded nanobeams with the account of surface elasticity

Three-dimensional metamaterials with a negative Poisson's ratio and a non-positive coefficient of thermal expansion

On vibrations of functionally graded viscoelastic nanobeams with surface effects

A new non-classical Kirchhoff plate model is developed using a modified couple stress theory, a surface elasticity theory and a two-parameter elastic foundation model. A variational formulation based on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and the complete boundary conditions and provides a unified treatment of the microstructure, surface energy and foundation effects. The new plate model contains a material length scale parameter to account for the microstructure effect, three surface elastic constants to describe the surface energy effect, and two foundation moduli to represent the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the newly developed plate model includes the models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases and recovers the Bernoulli–Euler beam model incorporating the microstructure, surface energy and foundation effects. To illustrate the new model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection of the simply supported plate with or without the elastic foundation predicted by the current model is smaller than that predicted by the classical model. Also, it is observed that the difference in the deflection predicted by the new and classical plate models is very large when the plate thickness is sufficiently small, but it is diminishing with the increase of the plate thickness. For the free vibration problem, it is found that the natural frequency predicted by the new plate model with or without the elastic foundation is higher than that predicted by the classical plate model, and the difference is significant for very thin plates. These predicted trends of the size effect at the micron scale agree with those observed experimentally. In addition, it is shown both analytically and numerically that the presence of the elastic foundation reduces the plate deflection and increases the plate natural frequency, as expected.

A non-classical Kirchhoff plate model incorporating microstructure, surface energy and foundation effects

A new non-classical third-order shear deformation model is developed for Reddy–Levinson beams using a variational formulation based on Hamilton’s principle. A modified couple stress theory and a surface elasticity theory are employed. The equations of motion and complete boundary conditions for the beam are obtained simultaneously. The new model contains a material length scale parameter to account for the microstructure effect and three surface elastic constants to describe the surface energy effect. Also, Poisson’s effect is incorporated in the new beam model. The current non-classical model recovers the classical elasticity-based third-order shear deformation beam model as a special case when the microstructure, surface energy and Poisson’s effects are all suppressed. In addition, the newly developed beam model includes the models considering the microstructure dependence or the surface energy effect alone as limiting cases and reduces to two existing models for Bernoulli–Euler and Timoshenko beams incorporating the microstructure and surface energy effects. To illustrate the new model, the static bending and free vibration problems of a simply supported beam loaded by a concentrated force are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that both the deflection and rotation of the simply supported beam predicted by the current model are smaller than those predicted by the classical model. Also, it is observed that the differences in the deflection and rotation predicted by the two beam models are very large when the beam thickness is sufficiently small, but they are diminishing with the increase in the beam thickness. For the free vibration problem, it is found that the natural frequency predicted by the new model is higher than that predicted by the classical beam model, and the difference is significant for very thin beams. These predicted trends of the size effect at the micron scale agree with those observed experimentally.

A microstructure- and surface energy-dependent third-order shear deformation beam model

A transversely isotropic magneto-electro-elastic Timoshenko beam model incorporating microstructure and foundation effects§

Band gaps for elastic wave propagation in a periodic composite beam structure incorporating microstructure and surface energy effects

A new model for anisotropic magneto-electro-elastic Mindlin plates is developed by using an extended modified couple stress theory. The equations of motion and complete boundary conditions are simultaneously obtained by a variational formulation based on Hamilton’s principle. The new anisotropic magneto-electro-elastic plate model includes the models for orthotropic and transversely isotropic magneto-electro-elastic Mindlin plates and the model for isotropic Mindlin plates, all incorporating the microstructure effect, as special cases. To illustrate the new model, the static bending and free vibration problems of a simply supported transversely isotropic magneto-electro-elastic plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection, rotation, electric potential, and magnetic potential of the simply supported plate predicted by the current non-classical model are always smaller than those predicted by the classical elasticity-based model, and the differences are significant when the plate thickness is very small but is diminishing as the thickness increases. For the free vibration problem, it is found that the natural frequency predicted by the new plate model is higher than that predicted by the classical model, and the difference is quite large for very thin plates.

G. Y. Zhang

Papers

A non-classical Kirchhoff plate model incorporating microstructure, surface energy and foundation effects

A microstructure- and surface energy-dependent third-order shear deformation beam model

A transversely isotropic magneto-electro-elastic Timoshenko beam model incorporating microstructure and foundation effects§

Band gaps for elastic wave propagation in a periodic composite beam structure incorporating microstructure and surface energy effects

A microstructure-dependent anisotropic magneto-electro-elastic Mindlin plate model based on an extended modified couple stress theory