The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common...The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.展开更多
Micro-hotplate (MHP) technology is one key part in the manufacturing of gas sensors. The pursuit of analytical solutions for the temperature distribution and also thermal stresses within the MHP is of intrinsic scie...Micro-hotplate (MHP) technology is one key part in the manufacturing of gas sensors. The pursuit of analytical solutions for the temperature distribution and also thermal stresses within the MHP is of intrinsic scientific interest. In this study, analytical solutions for the temperature field, and both radial and tangential stresses and van Mises stress for circular MHP were obtained. Two geometries were considered: one had a circular heater at the center and the other had a circular heater at the center and an annular heater within the membrane part. Internal heat generation was incorporated in the energy equation for the MHP and different values of convection heat transfer coefficient were used at the upper and lower surfaces of the MHP. It has been shown that the MHP with two heaters can provide more uniform temperature field compared with the MHP with one heater. The main objective of this work is to provide an exact analytical solution for thermal stresses within the circular micro-hcater with a simple geometry as a benchmark, from mathematical point of view, against which the accuracy of new numerical schemes can be checked. To make sure that the analytical procedure is correct, the analytical results are checked against numerical solutions derived from finite element simulation. Since the analytical models for the temperature field and especially for the thermal stresses of MHP ace seldom investigated in the literature, the obtained results are believed to facilitate the design and performance evaluation of MHPs as well.展开更多
This paper presents an analytical solution for the thermoelastic stress in a typical in-plane's thin-film micro- thermoelectric cooling device under different operating con- ditions. The distributions of the permissi...This paper presents an analytical solution for the thermoelastic stress in a typical in-plane's thin-film micro- thermoelectric cooling device under different operating con- ditions. The distributions of the permissible temperature fields in multilayered thin-films are analytically obtained, and the characteristics, including maximum temperature dif- ference and maximum refrigerating output of the thermo- electric device, are discussed for two operating conditions. Analytical expressions of the thermoelastic stresses in the layered thermoelectric thin-films induced by the tempera- ture difference are formulated based on the theory of mul- tilayer system. The results demonstrate that, the geometric dimension is a significant factor which remarkably affects the thermoelastic stresses. The stress distributions in layers of semiconductor thermoelements, insulating and support- ing membrane show distinctly different features. The present work may profitably guide the optimization design of high- efficiency micro-thermoelectric cooling devices.展开更多
A new analytical study on stresses around a post-tensioned anchor in rocks with two perpendicular joint sets is presented. The assumptions of orthotropic elastic rock with plane strain conditions are made in derivatio...A new analytical study on stresses around a post-tensioned anchor in rocks with two perpendicular joint sets is presented. The assumptions of orthotropic elastic rock with plane strain conditions are made in derivation of the formulations. A tri-linear bond-slip constitutive law is used for modeling the tendon-grout interface behavior and debonding of this interface. The bearing plate width is also considered in the analysis. The obtained solutions are in the integral forms and numerical techniques that have been used for evaluation. In the illustrative example given, the major principal stress is compressive in the anchor free zone and compressive stress concentrations of 815 k Pa and 727 k Pa(for the anchor load of 300 k N) are observed under the bearing plate and the bond length proximal end, respectively. However, large values of tensile stresses with the maximum of-434 k Pa are formed at the bond length distal end. The results obtained using the proposed solution are compared very those of numerical method(FEM).展开更多
According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surf...According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant's theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab. When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the famous Lame solution can be induced from this limit. The above work paves the way for mathematic model building of hollow cylinder and for the analytic solution of hollow cvlinder with randomly uneven pressure.展开更多
In this paper, a 3-node triangular element for couple stress theory is proposed based on the assumed stress quasi-conforming method. The formulation starts from polynomial approx- imation of stresses. Then the stress-...In this paper, a 3-node triangular element for couple stress theory is proposed based on the assumed stress quasi-conforming method. The formulation starts from polynomial approx- imation of stresses. Then the stress-function matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the string-net functions are introduced to calculate strain integration and the stress smooth technique is adopted to improve the stress accuracy. Numerical results show that the proposed new model can pass the Co- 1 patch test with excellent precision, does not exhibit extra zero energy modes and can cap- ture the scale effects of microstructure.展开更多
基金Projects(50874047,51074014,51174014)supported by the National Natural Science Foundation of China
文摘The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.
文摘Micro-hotplate (MHP) technology is one key part in the manufacturing of gas sensors. The pursuit of analytical solutions for the temperature distribution and also thermal stresses within the MHP is of intrinsic scientific interest. In this study, analytical solutions for the temperature field, and both radial and tangential stresses and van Mises stress for circular MHP were obtained. Two geometries were considered: one had a circular heater at the center and the other had a circular heater at the center and an annular heater within the membrane part. Internal heat generation was incorporated in the energy equation for the MHP and different values of convection heat transfer coefficient were used at the upper and lower surfaces of the MHP. It has been shown that the MHP with two heaters can provide more uniform temperature field compared with the MHP with one heater. The main objective of this work is to provide an exact analytical solution for thermal stresses within the circular micro-hcater with a simple geometry as a benchmark, from mathematical point of view, against which the accuracy of new numerical schemes can be checked. To make sure that the analytical procedure is correct, the analytical results are checked against numerical solutions derived from finite element simulation. Since the analytical models for the temperature field and especially for the thermal stresses of MHP ace seldom investigated in the literature, the obtained results are believed to facilitate the design and performance evaluation of MHPs as well.
基金supported by the National Basic Research Program of China(2007CB607506)the Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China(111005)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(11121202)
文摘This paper presents an analytical solution for the thermoelastic stress in a typical in-plane's thin-film micro- thermoelectric cooling device under different operating con- ditions. The distributions of the permissible temperature fields in multilayered thin-films are analytically obtained, and the characteristics, including maximum temperature dif- ference and maximum refrigerating output of the thermo- electric device, are discussed for two operating conditions. Analytical expressions of the thermoelastic stresses in the layered thermoelectric thin-films induced by the tempera- ture difference are formulated based on the theory of mul- tilayer system. The results demonstrate that, the geometric dimension is a significant factor which remarkably affects the thermoelastic stresses. The stress distributions in layers of semiconductor thermoelements, insulating and support- ing membrane show distinctly different features. The present work may profitably guide the optimization design of high- efficiency micro-thermoelectric cooling devices.
文摘A new analytical study on stresses around a post-tensioned anchor in rocks with two perpendicular joint sets is presented. The assumptions of orthotropic elastic rock with plane strain conditions are made in derivation of the formulations. A tri-linear bond-slip constitutive law is used for modeling the tendon-grout interface behavior and debonding of this interface. The bearing plate width is also considered in the analysis. The obtained solutions are in the integral forms and numerical techniques that have been used for evaluation. In the illustrative example given, the major principal stress is compressive in the anchor free zone and compressive stress concentrations of 815 k Pa and 727 k Pa(for the anchor load of 300 k N) are observed under the bearing plate and the bond length proximal end, respectively. However, large values of tensile stresses with the maximum of-434 k Pa are formed at the bond length distal end. The results obtained using the proposed solution are compared very those of numerical method(FEM).
文摘According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant's theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab. When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the famous Lame solution can be induced from this limit. The above work paves the way for mathematic model building of hollow cylinder and for the analytic solution of hollow cvlinder with randomly uneven pressure.
基金supported by the Fundamental Research Funds for the Central Universities (DUT16LK27,DUT17RC(4)59)the National Natural Science Foundation of China (No.11472071)
文摘In this paper, a 3-node triangular element for couple stress theory is proposed based on the assumed stress quasi-conforming method. The formulation starts from polynomial approx- imation of stresses. Then the stress-function matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the string-net functions are introduced to calculate strain integration and the stress smooth technique is adopted to improve the stress accuracy. Numerical results show that the proposed new model can pass the Co- 1 patch test with excellent precision, does not exhibit extra zero energy modes and can cap- ture the scale effects of microstructure.