Self-instability and bending behaviors of nano plates

This paper aims at investigating the size-dependent self-buckling and bending behaviors of nano plates through incorporating surface elasticity into the elasticity with residual stress fields. In the absence of external loading, positive surface tension induces a compressive residual stress field in the bulk of the nano plate and there may be self-equilibrium states corresponding to the plate self-buckling. The self-instability of nano plates is investigated and the critical self-instability size of simply supported rectangular nano plates is determined. In addition, the residual stress field in the bulk of the nano plate is usually neglected in the existing literatures, where the elastic response of the bulk is often described by the classical Hooke’s law. The present paper considered the effect of the residual stress in the bulk induced by surface tension and adopted the elasticity with residual stress fields to study the bending behaviors of nano plates without buckling. The present results show that the surface effects only modify the coefficients in corresponding equations of the classical Kirchhoff plate theory.

A micromechanical damage theory for brittle materials with small cracks

For brittle solids containing numerous small cracks, a micromechanical damage theory is presented which accounts for the interactions between different small cracks and the effect of the boundary of a finite solid, and includes growth of the pre-existing small cracks. The analysis is based on a superposition scheme and series expansions of the complex potentials. The small crack evolution process is simulated through the use of fracture mechanics incorporating appropriate failure criteria. The stress-strain relations are obtained from the micromechanics analysis. Typical examples are given to illustrate the potential capability of the proposed theory. These results show that the present method provides a direct and efficient approach to deal with brittle finite solids containing multiple small cracks. The stress-strain relation curves are evaluated for a rectangular plate containing small cracks.

Size Effects in Micro-bending Deformation of MEMS Devices Based on the Discrete Dislocation Theory

In the present research, the discrete dislocation theory is used to analyze the size effect phenomena for the MEMS devices undergoing micro-bending load. A consistent result with the experimental one in literature is obtained. In order to check the effectiveness to use the discrete dislocation theory in predicting the size effect, both the basic version theory and the updated one are adopted simultaneously. The normalized stress-strain relations of the material are obtained for different plate thickness or for different obstacle density. The prediction results are compared with experimental results.

Bending solution of high-order refined shear deformation-theory for rectangular composite plates

A new high-order refined shear deformation theory based on Reissner's mixed variational principle in conjunction with the state- space concept is used to determine the deflections and stresses for rectangular cross-ply composite plates. A zig-zag shaped function and Legendre polynomials are introduced to approximate the in-plane displacement distributions across the plate thickness. Numerical results are presented with different edge conditions, aspect ratios, lamination schemes and loadings. A comparison with the exact solutions obtained by Pagano and the results by Khdeir indicates that the present theory accurately estimates the in-plane responses.

Approximate theory of natural-convection with small grashof number

To gain some insight into the behaviour of low-gravity flows in the material processing in space, an approximate theory has been developed for the convective motion of fluids with a small Grashof number Gr. The expansion of the variables into a series of Gr reduces the Boussinesq equation to a system of weakly coupled linearly inhomogeneous equations. Moreover, the analogy concept is proposed and utilized in the study of the plate bending problems in solid mechanics. Two examples are investigated in detail, i. e. the 2-dimensional steady flows in either circular or square infinite closed cylinder, which is horizontally imposed at a specified temperature of linear distribution on the boundaries. The results for stream function ψ, velocity u and temperature T are provided. The analysis of the influences of some parameters such as the Grashof number Gr and the Prandtl number Pr, on motions will lead to several interesting conclusions. The theory seems to be useful for seeking for an analytical solutions. At least, it will greatly simplify the complicated problems originally governed by the Navier-Stokes equation including buoyancy. It is our hope that the theory might be applicable to unsteady or 3-dimensional cases in future.

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.