The duality solution for elasticity and the biorthogonality relationship have been well researched. Now the couple stress theory becomes a new research spot but there is few research for the biorthogonality relationsh...The duality solution for elasticity and the biorthogonality relationship have been well researched. Now the couple stress theory becomes a new research spot but there is few research for the biorthogonality relationship for couple stress theory comparing to classical elasticity. A new state vector is presented for three dimensional couple stress problems of prismatic structures. A new biorthogonality relation- ship of couple stress is discovered. The dual partial differential equations of couple stress problem are derived by the new state vector. By two important identical equations the new biorthogonality rela- tionship is proved based on the method of separation of variables. The symplectic orthogonality rela- tionship to three dimensional couple stress theory may be decomposed into two independently and symmetrically orthogonality relationships. The new biorthogonality relationship includes the symplec- tic orthogonality relationship. The biorthogonality relationship of couple stress may also be degener- ated into the theory of elasticity. The new state vector and biorthogonality relationship provide theo- retic foundation for the research on the schemes of separation of variables and eigenfunction expan- sion of couple stress theory.展开更多
Thin film lubrication (TFL) is a condition in which the lubricating features between two surfaces in relative motion are determined by the combination of the properties of the surfaces and the lubricant and viscosity ...Thin film lubrication (TFL) is a condition in which the lubricating features between two surfaces in relative motion are determined by the combination of the properties of the surfaces and the lubricant and viscosity of the lubricant. The effects imposed by couple stress on lubrication characteristics cannot be disregarded in this regime where the ordered molecules dominate the fluid field. There are different tensor measures and constitutive equations in this case other than Newtonian case. The lubrication of two-phase (solid phase and liquid phase) fluid is investigated in this paper. The existence of couple stress will enhance the lubricant viscosity and hence increase the film thickness and improve the load-carrying capability. Size-dependent effects can be seen in the lubrication with couple stress, and the thinner the lubricating film is, the more obvious the effect will be.展开更多
In the coastal saline soils,moisture and salinity are the functions of groundwater depth affecting crop growth and yield.Accordingly,the objectives of this study were to:1)investigate the combined effects of moisture ...In the coastal saline soils,moisture and salinity are the functions of groundwater depth affecting crop growth and yield.Accordingly,the objectives of this study were to:1)investigate the combined effects of moisture and salinity stresses on wheat growth as affected by groundwater depth,and 2)find the optimal groundwater depth for wheat growth in coastal saline soils.The groundwater depths(0.7,1.1,1.5,1.9,2.3,and 2.7 m during 2013-2014(Y1)and 0.6,1.0,1.4,1.8,2.2,and 2.6 m during 2014-2015(Y2))of the field experiment were maintained by soil columns.There was a positive correlation between soil moisture and salinity.Water logging with high salinity(groundwater depth at 0.7 m in Y1 and 0.6 m in Y2)showed a greater decline towards wheat growth than that of slight drought with medium(2.3 m in Y1)or low salinity(2.7 m in Y1,2.2 and 2.6 m in Y2).The booting stage was the most sensitive stage of wheat crop under moisture and salinity stresses.Data showed the most optimal rate of photosynthesis,grain yield,and flour quality were obtained under the groundwater depth(ditch depth)of 1.9 m(standard soil moisture with medium salinity)and 2.3 m(slight drought with medium salinity)in Y1 and 1.8 m(standard soil moisture with medium salinity)and 2.2 m(slight drought with low salinity)in Y2.The corresponding optimal soil relative moisture content and conductivity with the 1:5 distilled water/soil dilution,in the depth of 0-20 cm and 20-40 cm in coastal saline soils,were equal to 58.67-63.07%and 65.51-72.66%in Y1,63.09-66.70%and 69.75-74.72%in Y2;0.86-1.01 dS m^-1 and 0.63-0.77 dS m^-1 in Y1,0.57-0.93 dS m^-1 and 0.40-0.63 dS m^-1 in Y2,respectively.展开更多
Chemical mechanical polishing (CMP) is a manufacturing process used to achieve high levels of global and local planarity. Currently, the slurries used in CMP usually contain nanoscale particles to accel-erate the remo...Chemical mechanical polishing (CMP) is a manufacturing process used to achieve high levels of global and local planarity. Currently, the slurries used in CMP usually contain nanoscale particles to accel-erate the removal ratio and to optimize the planarity, whose rheological properties can no longer be accu-rately modeled with Newtonian fluids. The Reynolds equation, including the couple stress effects, was de-rived in this paper. The equation describes the mechanism to solve the CMP lubrication equation with the couple stress effects. The effects on load and moments resulting from the various parameters, such as pivot height, roll angle, and pitch angle, were subsequently simulated. The results show that the couple stress can provide higher load and angular moments. This study sheds some lights into the mechanism of the CMP process.展开更多
According to the prominent characteristic of rapid heating and cooling velocity in process of laser phase transformation hardening, it is important and necessary to consider the couple relation among temperature, phas...According to the prominent characteristic of rapid heating and cooling velocity in process of laser phase transformation hardening, it is important and necessary to consider the couple relation among temperature, phase transformation and stress. Based on the above, a mathematical model to analyze transformation and to reflect its characteristic is presented. Also temperature field control equation relative to stress and phase transformation is set up and thermal elastoplastic constitutive equation containing phase transformation was derived, In a given yield condition, temperature and stress field are numerically calculated by means of Finite Element Method. The result indicates the calculation value coincides with result of test Stress especially thermal stress varied violently in process of laser phase transformation hardening, which leaded to the residual stress on the surface and accorded to the fact. This process can improve the characteristic of material, so it is significant to study on thermal stress of laser quenching, to discuss the effect of phase transformation and stress on temperature, to optimize the laser quenching process and to improve the synthetic mechanic properties of quenching material.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 50778071)the Hunan Provincial Natural Science Foundation of China (Grant No. 08JJ3011)the Research Committee of City University of Hong Kong (Grant No. 7002315)
文摘The duality solution for elasticity and the biorthogonality relationship have been well researched. Now the couple stress theory becomes a new research spot but there is few research for the biorthogonality relationship for couple stress theory comparing to classical elasticity. A new state vector is presented for three dimensional couple stress problems of prismatic structures. A new biorthogonality relation- ship of couple stress is discovered. The dual partial differential equations of couple stress problem are derived by the new state vector. By two important identical equations the new biorthogonality rela- tionship is proved based on the method of separation of variables. The symplectic orthogonality rela- tionship to three dimensional couple stress theory may be decomposed into two independently and symmetrically orthogonality relationships. The new biorthogonality relationship includes the symplec- tic orthogonality relationship. The biorthogonality relationship of couple stress may also be degener- ated into the theory of elasticity. The new state vector and biorthogonality relationship provide theo- retic foundation for the research on the schemes of separation of variables and eigenfunction expan- sion of couple stress theory.
基金Nomenclature: τ, stress tensor ρ, density+7 种基金 a, acceleration (m/s2)f, body force (N)p, pressure (Pa) λ, second viscosity coefficient d, strain tensor δ, sign function η, material constant responsible for couple stress parameter μ dynamic visc
文摘Thin film lubrication (TFL) is a condition in which the lubricating features between two surfaces in relative motion are determined by the combination of the properties of the surfaces and the lubricant and viscosity of the lubricant. The effects imposed by couple stress on lubrication characteristics cannot be disregarded in this regime where the ordered molecules dominate the fluid field. There are different tensor measures and constitutive equations in this case other than Newtonian case. The lubrication of two-phase (solid phase and liquid phase) fluid is investigated in this paper. The existence of couple stress will enhance the lubricant viscosity and hence increase the film thickness and improve the load-carrying capability. Size-dependent effects can be seen in the lubrication with couple stress, and the thinner the lubricating film is, the more obvious the effect will be.
基金funded by the National Key R&D Program of China (2017YFD0201900)the Fundamental Research Funds for the Central Universities, China (KYYJ201802)the earmarked fund for China Agriculture Research System (CARS-15-14)
文摘In the coastal saline soils,moisture and salinity are the functions of groundwater depth affecting crop growth and yield.Accordingly,the objectives of this study were to:1)investigate the combined effects of moisture and salinity stresses on wheat growth as affected by groundwater depth,and 2)find the optimal groundwater depth for wheat growth in coastal saline soils.The groundwater depths(0.7,1.1,1.5,1.9,2.3,and 2.7 m during 2013-2014(Y1)and 0.6,1.0,1.4,1.8,2.2,and 2.6 m during 2014-2015(Y2))of the field experiment were maintained by soil columns.There was a positive correlation between soil moisture and salinity.Water logging with high salinity(groundwater depth at 0.7 m in Y1 and 0.6 m in Y2)showed a greater decline towards wheat growth than that of slight drought with medium(2.3 m in Y1)or low salinity(2.7 m in Y1,2.2 and 2.6 m in Y2).The booting stage was the most sensitive stage of wheat crop under moisture and salinity stresses.Data showed the most optimal rate of photosynthesis,grain yield,and flour quality were obtained under the groundwater depth(ditch depth)of 1.9 m(standard soil moisture with medium salinity)and 2.3 m(slight drought with medium salinity)in Y1 and 1.8 m(standard soil moisture with medium salinity)and 2.2 m(slight drought with low salinity)in Y2.The corresponding optimal soil relative moisture content and conductivity with the 1:5 distilled water/soil dilution,in the depth of 0-20 cm and 20-40 cm in coastal saline soils,were equal to 58.67-63.07%and 65.51-72.66%in Y1,63.09-66.70%and 69.75-74.72%in Y2;0.86-1.01 dS m^-1 and 0.63-0.77 dS m^-1 in Y1,0.57-0.93 dS m^-1 and 0.40-0.63 dS m^-1 in Y2,respectively.
基金Supported by the National Natural Science Foundation of China (major program No. 50390060) and the Postdoctoral Fund of China
文摘Chemical mechanical polishing (CMP) is a manufacturing process used to achieve high levels of global and local planarity. Currently, the slurries used in CMP usually contain nanoscale particles to accel-erate the removal ratio and to optimize the planarity, whose rheological properties can no longer be accu-rately modeled with Newtonian fluids. The Reynolds equation, including the couple stress effects, was de-rived in this paper. The equation describes the mechanism to solve the CMP lubrication equation with the couple stress effects. The effects on load and moments resulting from the various parameters, such as pivot height, roll angle, and pitch angle, were subsequently simulated. The results show that the couple stress can provide higher load and angular moments. This study sheds some lights into the mechanism of the CMP process.
文摘According to the prominent characteristic of rapid heating and cooling velocity in process of laser phase transformation hardening, it is important and necessary to consider the couple relation among temperature, phase transformation and stress. Based on the above, a mathematical model to analyze transformation and to reflect its characteristic is presented. Also temperature field control equation relative to stress and phase transformation is set up and thermal elastoplastic constitutive equation containing phase transformation was derived, In a given yield condition, temperature and stress field are numerically calculated by means of Finite Element Method. The result indicates the calculation value coincides with result of test Stress especially thermal stress varied violently in process of laser phase transformation hardening, which leaded to the residual stress on the surface and accorded to the fact. This process can improve the characteristic of material, so it is significant to study on thermal stress of laser quenching, to discuss the effect of phase transformation and stress on temperature, to optimize the laser quenching process and to improve the synthetic mechanic properties of quenching material.
