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
This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredepend...This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.展开更多
A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress the...A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).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
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
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supported by a grant from the National Science and Technology Council of the Republic of China(Grant Number:MOST 112-2221-E-006-048-MY2).
文摘This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.
基金the National Natural Science Foundation of China(Nos.11602204 and 12102373)the Fundamental Research Funds for the Central Universities of China(Nos.2682022ZTPY081 and 2682022CX056)the Natural Science Foundation of Sichuan Province of China(Nos.2023NSFSC0849,2023NSFSC1300,2022NSFSC1938,and 2022NSFSC2003)。
文摘A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).
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.
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.
