The natural element method （NEM） is a newly- developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functi...The natural element method （NEM） is a newly- developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic the- orem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nons- moothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.展开更多
The prediction of central bursting defects in the rod extrusion process through conical dies using the upper bound analysisis investigated. A kinematically admissible velocity field, including the radial and angular v...The prediction of central bursting defects in the rod extrusion process through conical dies using the upper bound analysisis investigated. A kinematically admissible velocity field, including the radial and angular velocity components, is proposed. A newcriterion is presented to predict the occurrence of the central bursting defects. Parameter bobt, which represents the risk probability ofcracking, is proposed. It is calculated using the shape of the boundary at the entrance by minimizing the total power dissipationduring the extrusion process. When bobt is equal to or greater than bcr, central bursting occurs. Furthermore, the quantitativerelationships between central bursting defects and process parameters （semi die angle, reduction in area and frictional factor） arestudied. The results show that the central bursting defects are affected primarily by the reduction in area and the friction factor. Thepresented criterion is verified by comparing with the FEM simulation data and the results of the published paper.展开更多
At present, associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line...At present, associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line. It is proved that geotechnical materials do not abide by the associated flow rule. It is impossible for the stress characteristic line to conform to the velocity line. Generalized plastic mechanics theoretically proved that plastic potential surface intersects the Mohr-Coulomb yield surface with an angle, so that the velocity line must be studied by non-associated flow rule. According to limit analysis theory, the theory of slip line field is put forward in this paper, and then the ultimate beating capacity of strip footing is obtained based on the associated flow rule and the non-associated flow nile individually. These two results are identical since the ultimate bearing capacity is independent of flow role. On the contrary, the velocity fields of associated and non-associated flow rules are different which shows the velocity field based on the associat- ed flow rule is incorrect.展开更多
It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based ...It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based on the lower and upper bounds is presented in this paper, which can obtain the system reliability analytically without concerning the structure of the complex system. The method has been applied to a real system and the reliability results are compared with those acquired by the classical method and the parametric method. The effectiveness and accuracy of the proposed method have been testified.展开更多
The tiered geosynthetic-reinforced soil (GRS) walls have been increasingly applied in the high and steep retaining soil structures. However, very little is known about the design method for the tiered GRS wall in prac...The tiered geosynthetic-reinforced soil (GRS) walls have been increasingly applied in the high and steep retaining soil structures. However, very little is known about the design method for the tiered GRS wall in practice. This study is aimed at proposing an upper-bound stability analysis method of a tiered GRS wall. The proposed method was firstly validated by the existing results from the centrifuge test and the numerical method, and then a parametric study was performed to investigate the effects of the cohesionless backfill friction angle φ1 and the wall geometric parameters including the offset distance, the total wall height, the batter angle δ, the number of tiers n, and wall height ratio of adjacent tiers on the dimensionless equivalent earth pressure coefficient KT. The analysis results demonstrated that as the φ1 increases, the shear strength of backfill is enhanced and thus the KT or the total reinforcement tensile force decreases, and the KT decreases with the increase of the offset distance at the initial stage and then becomes stable when it reaches a certain critical value. For a fixed offset distance, the KT or the total reinforcement tensile force decreases with the increase of the δ. For the two-tiered GRS walls having the offset distance less than the critical value, the wall with the smaller wall height ratio has a larger KT. Further, the variation of the location of the critical failure surfaces of tiered GRS walls was presented in this study with the variation of the φ1 and the wall geometry.展开更多
A more universal and flexible method of constructing the streamlined die surfaces is presented. The streamlined die surfaces are interpolated by the arbitrarily cross sectional shapes of the die entrance and exit. Th...A more universal and flexible method of constructing the streamlined die surfaces is presented. The streamlined die surfaces are interpolated by the arbitrarily cross sectional shapes of the die entrance and exit. The boundaries of the die entrance and exit are represented by Ferguson curves with tension parameters. By adjusting the tension parameter, the cross sectional shapes of the die entrance and exit with line segments can be accurately constructed. The upper bound method is used to analyze the procedure of extrusion, the pseudo independent parameters in kinematically admissible velocity and die surface are computed by minimizing the extrusion load, so the optimum die surface is obtained. The effects of frictional condition, die length, area reduction and product shaped complexity are discussed in relation to the extrusion load.展开更多
The variation principle is discussed and Rayleigh-Ritz method is proposed for construction of veloci ty field. A kinematically admissible velocity field based on polynomials was appIied to the determina tion of forgin...The variation principle is discussed and Rayleigh-Ritz method is proposed for construction of veloci ty field. A kinematically admissible velocity field based on polynomials was appIied to the determina tion of forging load and deformed buIge profile during upset forging of blocks. Simulation of upsetforging of rectangular blocks under various friction condjtions was performed. Comparison of the computed results with experiments and FEM shows good agreement. It is shown that this techniquecan be used for 3D simulation of metal forming process.展开更多
The focal point of this paper is to present the theoretical aspects of the building blocks of the upper bounds of ISD （integer sub-decomposition） method defined by kP = k11P ＋ k12ψ1 （P） ＋ k21P ＋ k22ψ2 （P） w...The focal point of this paper is to present the theoretical aspects of the building blocks of the upper bounds of ISD （integer sub-decomposition） method defined by kP = k11P ＋ k12ψ1 （P） ＋ k21P ＋ k22ψ2 （P） with max {｜k11｜, ｜k12｜} 〈 Ca√n and max{｜k21｜, ｜k22｜}≤C√, where C=I that uses efficiently computable endomorphisms ψj for j=1,2 to compute any multiple kP of a point P of order n lying on an elliptic curve E. The upper bounds of sub-scalars in ISD method are presented and utilized to enhance the rate of successful computation of scalar multiplication kP. Important theorems that establish the upper bounds of the kernel vectors of the ISD reduction map are generalized and proved in this work. The values of C in the upper bounds, that are greater than 1, have been proven in two cases of characteristic polynomials （with degree 1 or 2） of the endomorphisms. The upper bound of ISD method with the case of the endomorphism rings over an integer ring Z results in a higher rate of successful computations kP. Compared to the case of endomorphism rings, which is embedded over an imaginary quadratic field Q = [4-D]. The determination of the upper bounds is considered as a key point in developing the ISD elliptic scalar multiplication technique.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle ...By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle of virtual power, the upper bound solution for surrounding rock pressure of shallow unsymmetrical loading tunnel was derived and verified by an example. The results indicate that the calculated results of the derived upper bound method for surrounding rock pressure of shallow unsymmetrical loading tunnels are relatively close to those of the existing "code method" and test results, which means that the proposed method is feasible. The current code method underestimates the unsymmetrical loading feature of surrounding rock pressure of shallow unsymmetrical loading tunnels, so it is unsafe; when the burial depth is less or greater than two times of the tunnel span and the unsymmetrical loading angle is less than 45°, the upper bound method or the average value of the results calculated by the upper bound method and code method respectively, is comparatively reasonable. When the burial depth is greater than two times of the tunnel span and the unsymmetrical loading angle is greater than 45°, the code method is more suitable.展开更多
The extrusion process of hybrid sheet metals through arbitrarily curved dies was analyzed by the method of upper bound. The material under deformation was divided into two deformation regions, bimetal and mono-metal r...The extrusion process of hybrid sheet metals through arbitrarily curved dies was analyzed by the method of upper bound. The material under deformation was divided into two deformation regions, bimetal and mono-metal regions, and the flow of the material in each region was assumed as plane strain state. The internal, shearing and frictional power terms were derived and they were used in the upper bound model. The extrusion forces for two types of die shapes, an optimum wedge shaped die and an optimum streamlined die shape for a hybrid sheet composed of copper as sleeve and aluminum as core were determined. The corresponding results for those two die shapes were also determined by using the finite element code, ABAQUS, and compared with the upper bound results. These comparisons show a good agreement.展开更多
Based on the nonlinear failure criterion and the upper bound theorem, the modified tangential technique method was proposed to derive the expression of supporting pressure acting on shallow tunnel. Instead of the same...Based on the nonlinear failure criterion and the upper bound theorem, the modified tangential technique method was proposed to derive the expression of supporting pressure acting on shallow tunnel. Instead of the same stress state, different normal stresses on element boundaries were used. In order to investigate the influence of different factors on supporting pressures, the failure mechanism was established. The solution of supporting pressure, with different parameters, was obtained by optimization theory. The corresponding failure mechanism and numerical results were presented. In comparison with the results using the single tangential technique method, it is found that the proposed method is effective, and the good agreement shows that the present solution of supporting pressure is reliable.展开更多
Given the extensive utilization of cantilever retaining walls in construction and development projects,their optimal design and analysis with proper attention to seismic loads is a typical engineering problem.This res...Given the extensive utilization of cantilever retaining walls in construction and development projects,their optimal design and analysis with proper attention to seismic loads is a typical engineering problem.This research presents a new algorithm for pseudo-static analysis of retaining walls employing upper bound method.The algorithm can be utilized to design and check the external and internal stability of the wall based on the proposed mechanism.One of the main features of this algorithm is its ability to determine the critical condition of failure wedges,the minimum safety factor and maximum force acting on the wall,as well as the minimum weight of the wall,simultaneously,by effectively using the multi-objective optimization.The results obtained by the proposed failure mechanisms show that,while using the upper bound limit analysis approach,the active force should be maximized concurrent with optimizing the direction of the plane passing through the back of the heel.The present study also applies the proposed algorithm to determine the critical direction of the earthquake acceleration coefficient.The critical direction of earthquake acceleration coefficient is defined as the direction that maximizes the active force exerted on the wall and minimizes the safety factor for wall stability.The results obtained in this study are in good agreement with those of similar studies carried out based on the limit equilibrium method and finite element analysis.The critical failure mechanisms were determined via optimization with genetic algorithm.展开更多
Considering the variation of cohesion along the depth,the upper bound solution of active earth pressure for a rough inclined wall with sloped backfill is formulated based on a log-spiral failure mechanism.For a more a...Considering the variation of cohesion along the depth,the upper bound solution of active earth pressure for a rough inclined wall with sloped backfill is formulated based on a log-spiral failure mechanism.For a more accurate prediction,the influence of intermediate principal stress is taken into consideration using the unified strength theory.Converting the search for the active pressure to an optimization problem,the most critical failure surface can be located by a natural selection-based gravitational search algorithm(GSA).The proposed method is validated compared with existing methods for noncohesive and cohesive cases and proved to be more accordance with the limit equilibrium solution.The influences of the variation of soil cohesion and intermediate principal stress on active earth pressure coefficient are then fully studied.It can be concluded that both the variations of soil cohesion and intermediate principal stress have a significant influence on the active earth pressure coefficient.展开更多
Based on the upper bound theorem of limit analysis,the factor of safety for shallow tunnel in saturated soil is calculated in conjunction with the strength reduction technique.To analyze the influence of the pore pres...Based on the upper bound theorem of limit analysis,the factor of safety for shallow tunnel in saturated soil is calculated in conjunction with the strength reduction technique.To analyze the influence of the pore pressure on the factor of safety for shallow tunnel,the power of pore pressure is regarded as a power of external force in the energy calculation.Using the rigid multiple-block failure mechanism,the objective function for the factor of safety is constructed and the optimal solutions are derived by employing the sequential quadratic programming.According to the results of optimization calculation,the factor of safety of shallow tunnel for different pore pressure coefficients and variational groundwater tables are obtained.The parameter analysis shows that the pore pressure coefficient and the location of the groundwater table have significant influence on the factor of safety for shallow tunnel.展开更多
A recently developed backward extrusion method entitled “modified backward extrusion” was presented using an upper bound analysis. For this purpose deformation area was divided into four distinct zones and a kinemat...A recently developed backward extrusion method entitled “modified backward extrusion” was presented using an upper bound analysis. For this purpose deformation area was divided into four distinct zones and a kinematically admissible velocity field for each of them was suggested. Total dissipated power was calculated for the deformation zones and the extrusion power wascomputed. The correlations of important geometrical parameters with extrusion force and dissipated powers were shown. Finding the initial billet size, a challenging area in the modified backward extrusion method, was discussed and the optimum billet radius was obtained, considering the minimum relative extrusion pressure. Finite element analyses were conducted and the results werecompared with the upper bound analysis. Finally, experiments were executed on commercially pure aluminium and a good agreement between upper bound and finite element analyses with experimental values was observed.展开更多
An analysis of tunnel face stability generally assumes a single homogeneous rock mass.However,most rock tunnel projects are excavated in stratified rock masses.This paper presents a two-dimensional(2D)analytical model...An analysis of tunnel face stability generally assumes a single homogeneous rock mass.However,most rock tunnel projects are excavated in stratified rock masses.This paper presents a two-dimensional(2D)analytical model for estimating the face stability of a rock tunnel in the presence of rock mass stratification.The model uses the kinematical limit analysis approach combined with the block calculation technique.A virtual support force is applied to the tunnel face,and then solved using an optimization method based on the upper limit theorem of limit analysis and the nonlinear Hoek-Brown yield criterion.Several design charts are provided to analyze the effects of rock layer thickness on tunnel face stability,tunnel diameter,the arrangement sequence of weak and strong rock layers,and the variation in rock layer parameters at different positions.The results indicate that the thickness of the rock layer,tunnel diameter,and arrangement sequence of weak and strong rock layers significantly affect the tunnel face stability.Variations in the parameters of the lower layer of the tunnel face have a greater effect on tunnel stability than those of the upper layer.展开更多
To analyze the stability of a shallow square tunnel, a new curved failure mechanism, representing the mechanical characteristics and collapsing form of this type of tunnel, is constructed. Based on the upper bound the...To analyze the stability of a shallow square tunnel, a new curved failure mechanism, representing the mechanical characteristics and collapsing form of this type of tunnel, is constructed. Based on the upper bound theorem of limit analysis and the Hoek-Brown nonlinear failure criterion, the supporting pressure derived from the virtual work rate equation is regarded as an objective function to achieve optimal calculation. By employing variational calculation to optimize the objective function, an upper bound solution for the supporting pressure and the collapsing block shape of a shallow square tunnel are obtained. To evaluate the validity of the failure mechanism proposed in this paper, the solutions computed by the curved failure mechanism are compared with the results calculated by the linear multiple blocks failure mechanism when the Hoek-Brown nonlinear failure criterion is converted into the Mohr-Coulomb linear criterion. The influences of rock mass parameters on the supporting pressure and collapsing block shape are discussed.展开更多
基金supported by the National Foundation for Excellent Doctoral Thesis of China (200025)the Program for New Century Excellent Talents in University (NCET-04-0075)the National Natural Science Foundation of China (19902007)
文摘The natural element method （NEM） is a newly- developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic the- orem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nons- moothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.
文摘The prediction of central bursting defects in the rod extrusion process through conical dies using the upper bound analysisis investigated. A kinematically admissible velocity field, including the radial and angular velocity components, is proposed. A newcriterion is presented to predict the occurrence of the central bursting defects. Parameter bobt, which represents the risk probability ofcracking, is proposed. It is calculated using the shape of the boundary at the entrance by minimizing the total power dissipationduring the extrusion process. When bobt is equal to or greater than bcr, central bursting occurs. Furthermore, the quantitativerelationships between central bursting defects and process parameters （semi die angle, reduction in area and frictional factor） arestudied. The results show that the central bursting defects are affected primarily by the reduction in area and the friction factor. Thepresented criterion is verified by comparing with the FEM simulation data and the results of the published paper.
文摘At present, associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line. It is proved that geotechnical materials do not abide by the associated flow rule. It is impossible for the stress characteristic line to conform to the velocity line. Generalized plastic mechanics theoretically proved that plastic potential surface intersects the Mohr-Coulomb yield surface with an angle, so that the velocity line must be studied by non-associated flow rule. According to limit analysis theory, the theory of slip line field is put forward in this paper, and then the ultimate beating capacity of strip footing is obtained based on the associated flow rule and the non-associated flow nile individually. These two results are identical since the ultimate bearing capacity is independent of flow role. On the contrary, the velocity fields of associated and non-associated flow rules are different which shows the velocity field based on the associat- ed flow rule is incorrect.
基金National Natural Science Foundation of China(No.40927001)
文摘It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based on the lower and upper bounds is presented in this paper, which can obtain the system reliability analytically without concerning the structure of the complex system. The method has been applied to a real system and the reliability results are compared with those acquired by the classical method and the parametric method. The effectiveness and accuracy of the proposed method have been testified.
基金financially supported by the National Natural Science Foundation of China(Grants Nos.41877255,and 52078182).
文摘The tiered geosynthetic-reinforced soil (GRS) walls have been increasingly applied in the high and steep retaining soil structures. However, very little is known about the design method for the tiered GRS wall in practice. This study is aimed at proposing an upper-bound stability analysis method of a tiered GRS wall. The proposed method was firstly validated by the existing results from the centrifuge test and the numerical method, and then a parametric study was performed to investigate the effects of the cohesionless backfill friction angle φ1 and the wall geometric parameters including the offset distance, the total wall height, the batter angle δ, the number of tiers n, and wall height ratio of adjacent tiers on the dimensionless equivalent earth pressure coefficient KT. The analysis results demonstrated that as the φ1 increases, the shear strength of backfill is enhanced and thus the KT or the total reinforcement tensile force decreases, and the KT decreases with the increase of the offset distance at the initial stage and then becomes stable when it reaches a certain critical value. For a fixed offset distance, the KT or the total reinforcement tensile force decreases with the increase of the δ. For the two-tiered GRS walls having the offset distance less than the critical value, the wall with the smaller wall height ratio has a larger KT. Further, the variation of the location of the critical failure surfaces of tiered GRS walls was presented in this study with the variation of the φ1 and the wall geometry.
文摘A more universal and flexible method of constructing the streamlined die surfaces is presented. The streamlined die surfaces are interpolated by the arbitrarily cross sectional shapes of the die entrance and exit. The boundaries of the die entrance and exit are represented by Ferguson curves with tension parameters. By adjusting the tension parameter, the cross sectional shapes of the die entrance and exit with line segments can be accurately constructed. The upper bound method is used to analyze the procedure of extrusion, the pseudo independent parameters in kinematically admissible velocity and die surface are computed by minimizing the extrusion load, so the optimum die surface is obtained. The effects of frictional condition, die length, area reduction and product shaped complexity are discussed in relation to the extrusion load.
文摘The variation principle is discussed and Rayleigh-Ritz method is proposed for construction of veloci ty field. A kinematically admissible velocity field based on polynomials was appIied to the determina tion of forging load and deformed buIge profile during upset forging of blocks. Simulation of upsetforging of rectangular blocks under various friction condjtions was performed. Comparison of the computed results with experiments and FEM shows good agreement. It is shown that this techniquecan be used for 3D simulation of metal forming process.
文摘The focal point of this paper is to present the theoretical aspects of the building blocks of the upper bounds of ISD （integer sub-decomposition） method defined by kP = k11P ＋ k12ψ1 （P） ＋ k21P ＋ k22ψ2 （P） with max {｜k11｜, ｜k12｜} 〈 Ca√n and max{｜k21｜, ｜k22｜}≤C√, where C=I that uses efficiently computable endomorphisms ψj for j=1,2 to compute any multiple kP of a point P of order n lying on an elliptic curve E. The upper bounds of sub-scalars in ISD method are presented and utilized to enhance the rate of successful computation of scalar multiplication kP. Important theorems that establish the upper bounds of the kernel vectors of the ISD reduction map are generalized and proved in this work. The values of C in the upper bounds, that are greater than 1, have been proven in two cases of characteristic polynomials （with degree 1 or 2） of the endomorphisms. The upper bound of ISD method with the case of the endomorphism rings over an integer ring Z results in a higher rate of successful computations kP. Compared to the case of endomorphism rings, which is embedded over an imaginary quadratic field Q = [4-D]. The determination of the upper bounds is considered as a key point in developing the ISD elliptic scalar multiplication technique.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金Project(2014M560652)supported by China Postdoctoral Science FoundationProjects(2011CB013802,2013CB036004)supported by the National Basic Research Program of China
文摘By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle of virtual power, the upper bound solution for surrounding rock pressure of shallow unsymmetrical loading tunnel was derived and verified by an example. The results indicate that the calculated results of the derived upper bound method for surrounding rock pressure of shallow unsymmetrical loading tunnels are relatively close to those of the existing "code method" and test results, which means that the proposed method is feasible. The current code method underestimates the unsymmetrical loading feature of surrounding rock pressure of shallow unsymmetrical loading tunnels, so it is unsafe; when the burial depth is less or greater than two times of the tunnel span and the unsymmetrical loading angle is less than 45°, the upper bound method or the average value of the results calculated by the upper bound method and code method respectively, is comparatively reasonable. When the burial depth is greater than two times of the tunnel span and the unsymmetrical loading angle is greater than 45°, the code method is more suitable.
文摘The extrusion process of hybrid sheet metals through arbitrarily curved dies was analyzed by the method of upper bound. The material under deformation was divided into two deformation regions, bimetal and mono-metal regions, and the flow of the material in each region was assumed as plane strain state. The internal, shearing and frictional power terms were derived and they were used in the upper bound model. The extrusion forces for two types of die shapes, an optimum wedge shaped die and an optimum streamlined die shape for a hybrid sheet composed of copper as sleeve and aluminum as core were determined. The corresponding results for those two die shapes were also determined by using the finite element code, ABAQUS, and compared with the upper bound results. These comparisons show a good agreement.
基金Projects(2013CB0360042011CB013800)supported by the National Basic Research Program of China+1 种基金Project(51178468)supported by the National Natural Science Foundation of ChinaProject(2011G013-B)supported by the Science and Technology Development of Railways Department in China
文摘Based on the nonlinear failure criterion and the upper bound theorem, the modified tangential technique method was proposed to derive the expression of supporting pressure acting on shallow tunnel. Instead of the same stress state, different normal stresses on element boundaries were used. In order to investigate the influence of different factors on supporting pressures, the failure mechanism was established. The solution of supporting pressure, with different parameters, was obtained by optimization theory. The corresponding failure mechanism and numerical results were presented. In comparison with the results using the single tangential technique method, it is found that the proposed method is effective, and the good agreement shows that the present solution of supporting pressure is reliable.
文摘Given the extensive utilization of cantilever retaining walls in construction and development projects,their optimal design and analysis with proper attention to seismic loads is a typical engineering problem.This research presents a new algorithm for pseudo-static analysis of retaining walls employing upper bound method.The algorithm can be utilized to design and check the external and internal stability of the wall based on the proposed mechanism.One of the main features of this algorithm is its ability to determine the critical condition of failure wedges,the minimum safety factor and maximum force acting on the wall,as well as the minimum weight of the wall,simultaneously,by effectively using the multi-objective optimization.The results obtained by the proposed failure mechanisms show that,while using the upper bound limit analysis approach,the active force should be maximized concurrent with optimizing the direction of the plane passing through the back of the heel.The present study also applies the proposed algorithm to determine the critical direction of the earthquake acceleration coefficient.The critical direction of earthquake acceleration coefficient is defined as the direction that maximizes the active force exerted on the wall and minimizes the safety factor for wall stability.The results obtained in this study are in good agreement with those of similar studies carried out based on the limit equilibrium method and finite element analysis.The critical failure mechanisms were determined via optimization with genetic algorithm.
基金Project(2016YFC0800200)supported by the National Key Research Plan of China。
文摘Considering the variation of cohesion along the depth,the upper bound solution of active earth pressure for a rough inclined wall with sloped backfill is formulated based on a log-spiral failure mechanism.For a more accurate prediction,the influence of intermediate principal stress is taken into consideration using the unified strength theory.Converting the search for the active pressure to an optimization problem,the most critical failure surface can be located by a natural selection-based gravitational search algorithm(GSA).The proposed method is validated compared with existing methods for noncohesive and cohesive cases and proved to be more accordance with the limit equilibrium solution.The influences of the variation of soil cohesion and intermediate principal stress on active earth pressure coefficient are then fully studied.It can be concluded that both the variations of soil cohesion and intermediate principal stress have a significant influence on the active earth pressure coefficient.
基金Project(51178468) supported by the National Natural Science Foundation of ChinaProject(2010bsxt07) supported by the Doctoral Dissertation Innovation Fund of Central South University,China
文摘Based on the upper bound theorem of limit analysis,the factor of safety for shallow tunnel in saturated soil is calculated in conjunction with the strength reduction technique.To analyze the influence of the pore pressure on the factor of safety for shallow tunnel,the power of pore pressure is regarded as a power of external force in the energy calculation.Using the rigid multiple-block failure mechanism,the objective function for the factor of safety is constructed and the optimal solutions are derived by employing the sequential quadratic programming.According to the results of optimization calculation,the factor of safety of shallow tunnel for different pore pressure coefficients and variational groundwater tables are obtained.The parameter analysis shows that the pore pressure coefficient and the location of the groundwater table have significant influence on the factor of safety for shallow tunnel.
文摘A recently developed backward extrusion method entitled “modified backward extrusion” was presented using an upper bound analysis. For this purpose deformation area was divided into four distinct zones and a kinematically admissible velocity field for each of them was suggested. Total dissipated power was calculated for the deformation zones and the extrusion power wascomputed. The correlations of important geometrical parameters with extrusion force and dissipated powers were shown. Finding the initial billet size, a challenging area in the modified backward extrusion method, was discussed and the optimum billet radius was obtained, considering the minimum relative extrusion pressure. Finite element analyses were conducted and the results werecompared with the upper bound analysis. Finally, experiments were executed on commercially pure aluminium and a good agreement between upper bound and finite element analyses with experimental values was observed.
基金supported by the Key Innovation Team Program of Innovation Talents Promotion Plan by MOST of China(Grant No.2016RA4059)the Science and Technology Project of Yunnan Provincial Transportation Department(No.25 of 2018)。
文摘An analysis of tunnel face stability generally assumes a single homogeneous rock mass.However,most rock tunnel projects are excavated in stratified rock masses.This paper presents a two-dimensional(2D)analytical model for estimating the face stability of a rock tunnel in the presence of rock mass stratification.The model uses the kinematical limit analysis approach combined with the block calculation technique.A virtual support force is applied to the tunnel face,and then solved using an optimization method based on the upper limit theorem of limit analysis and the nonlinear Hoek-Brown yield criterion.Several design charts are provided to analyze the effects of rock layer thickness on tunnel face stability,tunnel diameter,the arrangement sequence of weak and strong rock layers,and the variation in rock layer parameters at different positions.The results indicate that the thickness of the rock layer,tunnel diameter,and arrangement sequence of weak and strong rock layers significantly affect the tunnel face stability.Variations in the parameters of the lower layer of the tunnel face have a greater effect on tunnel stability than those of the upper layer.
基金supported by the National Natural Science Foundation of China (No. 51178468)the National Basic Research Program (973) of China (No. 2011CB013800)
文摘To analyze the stability of a shallow square tunnel, a new curved failure mechanism, representing the mechanical characteristics and collapsing form of this type of tunnel, is constructed. Based on the upper bound theorem of limit analysis and the Hoek-Brown nonlinear failure criterion, the supporting pressure derived from the virtual work rate equation is regarded as an objective function to achieve optimal calculation. By employing variational calculation to optimize the objective function, an upper bound solution for the supporting pressure and the collapsing block shape of a shallow square tunnel are obtained. To evaluate the validity of the failure mechanism proposed in this paper, the solutions computed by the curved failure mechanism are compared with the results calculated by the linear multiple blocks failure mechanism when the Hoek-Brown nonlinear failure criterion is converted into the Mohr-Coulomb linear criterion. The influences of rock mass parameters on the supporting pressure and collapsing block shape are discussed.
