Interaction between two nanoscale elliptical holes with surface tension

2018 ◽  
Vol 24 (5) ◽  
pp. 1556-1566 ◽  
Author(s):  
Shuang Wang ◽  
Cun-Fa Gao ◽  
Zeng-Tao Chen
Keyword(s):  
Surface Tension ◽  
Stress Field ◽  
Hoop Stress ◽  
Elliptical Hole ◽  
Integral Form ◽  
Maximum Hoop Stress ◽  
Stress Boundary Condition ◽  
Elliptical Holes ◽  
Basic Equations ◽  
Stress Boundary

In this paper, the plane problem of two elliptical nanoscale holes with surface tension is investigated. Firstly, the basic equations are given via the complex variable methods. Then, the stress boundary condition caused by surface tension is derived through the integral-form Gurtin–Murdoch model. The problem is finally solved by the conformal mapping along with the series expansion methods. The results show that the stress field decreases as the two holes become further away from each other. When the distance between the two holes is more than three times the sum of their sizes, the interaction between the two holes can be neglected. In addition, the stress field is greatly influenced by the orientation, aspect ratio and size of the holes. The positions of the maximum hoop stress are also discussed. When the two elliptical holes are put close horizontally, the hoop stress around one hole usually obtain its maximum at the endpoint close to the other hole. However, if one elliptical hole is not horizontal, the hoop stress around it will no longer attain its maximum at the endpoints. Another exception is that when one elliptical hole becomes larger, the hoop stress around the smaller hole would tend to achieve a local minimum at the endpoint close to the larger hole.

Micro-Stress-Field of Lamellar Inclusion in Eutectic Composite Ceramic

2012 ◽  
Vol 204-208 ◽  
pp. 4433-4436 ◽  
Author(s):  
Xie Quan Liu ◽  
Xin Hua Ni ◽  
Jing Zhang ◽  
Xiang Feng Meng
Keyword(s):  
Stress Field ◽  
Composite Ceramic ◽  
Apparent Size ◽  
Phase Cell ◽  
Ceramic Analysis ◽  
Eutectic Composite ◽  
Three Phase ◽  
Stress Boundary Condition ◽  
Stress Boundary ◽  
Remote Stress

According to the interaction between lamellar inclusion and interphase, forth-phase model is suggested to determine the micro-stress-field distribution of three-phase cell in eutectic composite ceramic. On the basis of the volumetric average strain, the effective compliance tensor increment of eutectic composite ceramic is obtained. The remote stress boundary condition of the eutectic composite ceramic is accounted for getting the micro-stress-field of lamellar inclusion in eutectic composite ceramic. Analysis shows that the micro-stress-field of the lamellar inclusion in eutectic composite ceramic is associated with the stiffness and the volume fractions of each component in eutectic composite ceramic, the shape of interphase and lamellar inclusion. The-micro-stress field has apparent size effect: three direction stresses increase with the thickness of lamellar inclusion.

Size Dependent Micro-Stress-Field of Fibers in Eutectic Ceramic Rod

2010 ◽  
Vol 168-170 ◽  
pp. 226-229
Author(s):  
Hai Xing Lu ◽  
Xie Quan Liu ◽  
Xin Hua Ni ◽  
Tao Sun ◽  
Bao Feng Li
Keyword(s):  
Stress Field ◽  
Local Stress ◽  
Apparent Size ◽  
Average Strain ◽  
Size Dependent ◽  
Three Phase ◽  
Stress Boundary Condition ◽  
Stress Boundary ◽  
Remote Stress ◽  
Local Stress Field

Considering the interaction between fiber-inclusion and strong constraining interphase, forth-phase model is suggested to determine the local stress field distribution of three-phase element in eutectic ceramic rod. On the basis of the volumetric average strain, the effective compliance tensor increment of eutectic ceramic rod is obtained. The remote stress boundary condition of the eutectic ceramic rod is accounted for getting the micro stress field of fibers in eutectic ceramic rod. The results show the micro stress field of the fiber-inclusion in eutectic ceramic rod is associated with the stiffness and the volume fractions of each component in eutectic ceramic rod, the shape of interphase and fiber. The micro stress field has apparent size effect: three direction stresses increase with the diameter of fiber- inclusion.

The Mechanical-Stress-Field of Matrix in Eutectic Ceramic Composite

2011 ◽  
Vol 121-126 ◽  
pp. 3607-3611
Author(s):  
Zhao Gang Cheng ◽  
Xin Hua Ni ◽  
Xie Quan Liu
Keyword(s):  
Stress Field ◽  
Mechanical Stress ◽  
Ceramic Composite ◽  
Composite Ceramic ◽  
Composite Ceramics ◽  
Eutectic Composite ◽  
Nano Fiber ◽  
The Matrix ◽  
Stress Boundary Condition ◽  
Stress Boundary

Based on the interaction between nano-fiber and eutectic interphase, forth-phase mode is used to get the mechanical stress field of matrix in eutectic composite ceramics. The effective flexibility increment tensor of eutectic ceramic composite is obtained by the volumetric average strain. The remote stress boundary condition of the eutectic composite ceramis is accounted for getting the mechanical stress field in matrix. The results show the mechanical stress field of the matrix is associated with the stiffness and the volume fractions of each component in eutectic composite ceramic , the shape of interphase and nano-fiber. The stresses in matrix will decrease due to the strong constraining effects of the eutectic interphase. The eutectic interphase make the eutectic composite ceramics strengthen.

scholarly journals Capillary retraction of the edge of a stretched viscous sheet

2018 ◽  
Vol 844 ◽  
Author(s):  
James P. Munro ◽  
John R. Lister
Keyword(s):  
Boundary Condition ◽  
Surface Tension ◽  
Stokes Flow ◽  
Similarity Solution ◽  
Far Field ◽  
Long Wavelength ◽  
Stress Boundary Condition ◽  
Stress Boundary

Surface tension causes the edge of a fluid sheet to retract. If the sheet is also stretched along its edge then the flow and the rate of retraction are modified. A universal similarity solution for the Stokes flow in a stretched edge shows that the scaled shape of the edge is independent of the stretching rate, and that it decays exponentially to its far-field thickness. This solution justifies the use of a stress boundary condition in long-wavelength models of stretched viscous sheets, and gives the detailed shape of the edge of such a sheet, resolving the position of the sheet edge to the order of the thickness.

Analysis of the Electro-Mechanical Responses of the Piezoelectric Motor Based on Finite Element Method

2014 ◽  
Vol 697 ◽  
pp. 181-186
Author(s):  
Zi Lei Wang ◽  
Tian De Qiu
Keyword(s):  
Finite Element ◽  
Coupling Effect ◽  
Complex Stress ◽  
Piezoelectric Resonator ◽  
Element Analysis ◽  
Mechanical Coupling ◽  
Mechanical Responses ◽  
Stress Boundary Condition ◽  
Piezoelectric Field ◽  
Stress Boundary

The piezoelectric field and structure field of piezoelectric resonator of ultrasonic motor are intercoupling. It is difficult to obtain the solution under some circumstances because of the complex stress boundary condition and the influence of coupling effect. An electro-mechanical coupling finite-element dynamic equation is established on the basis of the Hamilton’s Principle about piezoceramic and elastomer. The equation is decoupled through the shock excitation of the piezoelectric resonator and the piezoelectricity element and material provided by finite-element analysis. As a result, an admittance curve as well as the distribution status of the nodal DOF is obtained, which provides an effective method to solve electro-mechanical coupling problems.

scholarly journals Marangoni Convection of Dust Particles in the Boundary Layer of Maxwell Nanofluids with Varying Surface Tension and Viscosity

Coatings ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 1072
Author(s):  
Khaled S. AlQdah ◽  
Naseer M. Khan ◽  
Habib Ben Bacha ◽  
Jae-Dong Chung ◽  
Nehad Ali Shah
Keyword(s):  
Surface Tension ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Dust Particles ◽  
Physical Parameters ◽  
Temperature Dependent Viscosity ◽  
Liquid Phases ◽  
Variable Surface ◽  
Basic Equations ◽  
Dependent Viscosity

The flow of nanofluids is very important in industrial refrigeration systems. The operation of nuclear reactors and the cooling of the entire installation to improve safety and economics are entirely dependent on the application of nanofluids in water. Therefore, a model of Maxwell’s dusty nanofluid with temperature-dependent viscosity, surface suction and variable surface tension under the action of solar radiation is established. The basic equations of momentum and temperature of the dust and liquid phases are solved numerically using the MATLAB bvp4c scheme. In the current evaluation, taking into account variable surface tension and varying viscosity, the effect of dust particles is studied by immersing dust particles in a nanofluid. Qualitative and quantitative discussions are provided to focus on the effect of physical parameters on mass and heat transfer. The propagation results show that this mixing effect can significantly increase the thermal conductivity of nanofluids. With small changes in the surface tension parameters, a stronger drop in the temperature distribution is observed. The suction can significantly reduce the temperature distribution of the liquid and dust phases. The stretchability of the sheet is more conducive to temperature rise. The tables are used to explain how physical parameters affect the Nusselt number and mass transfer. The increased interaction of the liquid with nanoparticles or dust particles is intended to improve the Nusselt number. This model contains features that have not been previously studied, which stimulates demand for this model among all walks of life now and in the future.

Surface effect on deformation around an elliptical hole by surface energy density theory

2019 ◽  
Vol 25 (2) ◽  
pp. 337-347
Author(s):  
Liyuan Wang
Keyword(s):  
Energy Density ◽  
Surface Energy ◽  
Hoop Stress ◽  
Surface Effect ◽  
Plane Deformation ◽  
Surface Elasticity ◽  
Closed Form Solution ◽  
Elliptical Hole ◽  
External Loading ◽  
Surface Energy Density

The finite plane deformation of nanomaterial surrounding an elliptical hole subjected to remote loading is systematically investigated using a recently developed continuum theory. A complex variable formulation is utilized to obtain a closed-form solution for the hoop stress along the edge of the hole. The results show that when the size of the hole reduces to the same order as the ratio of the surface energy density to the applied remote stress, the influence of the surface energy density plays an even more significant role, and the shape of the hole coupled with surface energy density has a significant effect on the elastic state around the hole. Surprisingly, in the absence of any external loading, the hoop stress induced solely by surface effects is identical to that for a hole with surface energy in a linearly elastic solid derived by the Gurtin–Murdoch surface elasticity model. The results in this paper should be useful for the precise design of nanodevices and helpful for the reasonable assessment of test results of nano-instruments.

Analytic stress solution for a circular tunnel in half plane with a concentrated force

2019 ◽  
Vol 24 (12) ◽  
pp. 3862-3879
Author(s):  
Hui Cai ◽  
Ai-zhong Lu ◽  
Yao-cai Ma
Keyword(s):  
Boundary Condition ◽  
Stress Distribution ◽  
Half Plane ◽  
Analytic Functions ◽  
Surrounding Rock ◽  
Circular Tunnel ◽  
Concentrated Force ◽  
Stress Solution ◽  
Stress Boundary Condition ◽  
Stress Boundary

An analytic stress solution is presented for a circular tunnel problem in a half plane with a concentrated force acting on any position in the field under gravity. The solution uses the complex variable method and the power series method. The influence of the unbalanced force system on the tunnel boundary is considered. The relationship between two analytic functions is established by using surface stress boundary condition. The analytic functions can be determined from the tunnel stress boundary condition. Based on the principle of superposition, the stresses of the surrounding rock can be calculated by superimposing three partial solutions which are obtained separately. The examples give contour plots of the principal stresses in the surrounding rock, focus on the stress distribution on the ground surface and the tunnel boundary and analyze the effect on the stress distribution of some main parameters.

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