To obtain the optimal process parameters of stamping forming, finite element analysis and optimization technique were integrated via transforming multi-objective issue into a single-objective issue. A Pareto-based gen...To obtain the optimal process parameters of stamping forming, finite element analysis and optimization technique were integrated via transforming multi-objective issue into a single-objective issue. A Pareto-based genetic algorithm was applied to optimizing the head stamping forming process. In the proposed optimal model, fracture, wrinkle and thickness varying are a function of several factors, such as fillet radius, draw-bead position, blank size and blank-holding force. Hence, it is necessary to investigate the relationship between the objective functions and the variables in order to make objective functions varying minimized simultaneously. Firstly, the central composite experimental(CCD) with four factors and five levels was applied, and the experimental data based on the central composite experimental were acquired. Then, the response surface model(RSM) was set up and the results of the analysis of variance(ANOVA) show that it is reliable to predict the fracture, wrinkle and thickness varying functions by the response surface model. Finally, a Pareto-based genetic algorithm was used to find out a set of Pareto front, which makes fracture, wrinkle and thickness varying minimized integrally. A head stamping case indicates that the present method has higher precision and practicability compared with the "trial and error" procedure.展开更多
Based on existing algorithms, a newly developed contact search algorithm is proposed. The new algorithm consists of global search, local searching, local tracking and penetration calculation processes. It requires no ...Based on existing algorithms, a newly developed contact search algorithm is proposed. The new algorithm consists of global search, local searching, local tracking and penetration calculation processes. It requires no iteration steps. It can deal with not only general tool surfaces with vertical walls, but also tool surfaces meshed with elements having very poor aspect ratios. It is demonstrated that the FE code employing this new contact search algorithm becomes more reliable, efficient and accurate for sheet metal forming simulation than conventional ones.展开更多
A non-incremental time-space algorithm is proposed for numerical. analysis of forming process with the inclusion of geometrical, material, contact-frictional nonlinearities. Unlike the widely used Newton-Raphso...A non-incremental time-space algorithm is proposed for numerical. analysis of forming process with the inclusion of geometrical, material, contact-frictional nonlinearities. Unlike the widely used Newton-Raphson counterpart, the present scheme features an iterative solution procedure on entire time and space domain. Validity and feasibility of foe present scheme are further justiced by the numerical investigation herewith presented.展开更多
In order to find out the optimal press bend forming path in fabricating aircraft integral panels, this article proposes a new method on the basis of the authors＇ previous work. It is composed of the finite element me...In order to find out the optimal press bend forming path in fabricating aircraft integral panels, this article proposes a new method on the basis of the authors＇ previous work. It is composed of the finite element method （FEM） equivalent model, the surface curvature analysis, the artificial neural network response surface and the genetic algorithm. The method begins with analyzing the objective＇s shape curvature to determine the bending position. Then it optimizes the punch travel at each bending position by the following steps： （1） Establish a multi-step press bend forming FEM equivalent model, with which the FEM ex- periments designed with the Taguchi method are performed. （2） Construct a back-propagation （BP） neural network response surface with the data from the FEM experiments. （3） Use the genetic algorithm to optimize the neural network response surface as the objective function. Finally, this method is verified by press bending a complicated double-curvature grid-type stiffened panel and bears out its effectiveness and intrinsic worth in designing the press bend forming path.展开更多
In the incremental sheet forming （ISF） process, springback is a very important factor that affects the quality of parts. Predicting and controlling springback accurately is essential for the design of the toolpath f...In the incremental sheet forming （ISF） process, springback is a very important factor that affects the quality of parts. Predicting and controlling springback accurately is essential for the design of the toolpath for ISF. A three-dimensional elasto-plastic finite element model （FEM） was developed to simulate the process and the simulated results were compared with those from the experiment. The springback angle was found to be in accordance with the experimental result, proving the FEM to be effective. A coupled artificial neural networks （ANN） and finite element method technique was developed to simulate and predict springback responses to changes in the processing parameters. A particle swarm optimization （PSO） algorithm was used to optimize the weights and thresholds of the neural network model. The neural network was trained using available FEM simulation data. The results showed that a more accurate prediction of s!oringback can be acquired using the FEM-PSONN model.展开更多
The precision forming of thin-walled components has been urgently needed in aviation and aerospace field. However, the wrinkling induced by the compressive instability is one of the major defects in thin-walled part f...The precision forming of thin-walled components has been urgently needed in aviation and aerospace field. However, the wrinkling induced by the compressive instability is one of the major defects in thin-walled part forming. The initiation and growth of the wrinkles are interac- tively affected by many factors such as stress states, mechanical properties of the material, geometry of the workpiece and boundary conditions. Especially when the forming process involves compli- cated boundary conditions such as multi-dies constrains, the perturbation of clearances between workpiece and dies and the contact conditions changing in time and space, etc., the predication of the wrinkling is further complicated. In this paper, the cu.rent prediction methods were summa- rized including the static equilibrium method, the energy method, the initial imperfection method, the eigenvalue buckling analysis method, the static-implicit finite element method and the dynamic- explicit finite element method. Then, a systematical comparison and summary of these methods in terms of their advantages and limitations are presented. By using a combination of explicit FE method, initial imperfection and energy conservation, a hybrid method is recommended to predict plastic wrinkling in thin-walled part forming. Finally, considering the urgent requirements of com- plex thin-walled structures＇ part in aviation and aerospace field, the trends and challenges in wrin- kling prediction under complicated boundary conditions are presented.展开更多
A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularit...A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularity error. The finely-designed GA (FDGA)characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of thenonlinear problem is given. The implementation details in FDGA are described such as the crossoveror recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservationmethod; and the adaptive mutation which used the Gaussian probability distribution to determine thevalues of the offspring produced by mutation mechanism. The examples are provided to verify thedesigned FDGA. The computation results indicate that the FDGA works very well in the field of formerror evaluation such as circularity evaluation.展开更多
Regarding heat forming process of 1Cr18Ni9Ti as typical forming process, this paper presents the study of the effect of various parameters on flow stress, grain size and hardness of formed specimen by means of Gleeble...Regarding heat forming process of 1Cr18Ni9Ti as typical forming process, this paper presents the study of the effect of various parameters on flow stress, grain size and hardness of formed specimen by means of Gleeble-1500 Thermo-simulation machine and metalloscope. On the basis of technical experi- ment this paper, data are proceeded by applying multilayer feedforward back-propagation neural network, a prediction model of technological parameters together with microstructure and property in the heat forming process is established, thus forging property prediction in the heat forming process is realized.展开更多
In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinea...In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.展开更多
The research on numerical simulation for combinative process of SPF/DB is carried out in this paper. The contacting problem of sheets is analyzed by using the penalty method. In order to solve the contact problem of d...The research on numerical simulation for combinative process of SPF/DB is carried out in this paper. The contacting problem of sheets is analyzed by using the penalty method. In order to solve the contact problem of different parts of the sheet, a new algorithm for contacting judgment is proposed. According to the relation of the distance vector and the vector of contacting element area, and the condition of contact, it can be judged whether or not a node on the slave surface and the corresponding master surface are in the state of SPF/DB. The Mindlin shell element is employed to simulate SPF/DB process of an asymmetry double-cell cup of Ti-6Al-4V to examine the efficiency of the new algorithm using ARVIP-3D. The results of the numerical simulation are in good agreement with experimental results.展开更多
Because of the light weight,high stiffness and high structural efficiency,aluminium alloy integral panels are widely used on modern aircrafts.Press bend forming has many advantages,and it becomes a significant techniq...Because of the light weight,high stiffness and high structural efficiency,aluminium alloy integral panels are widely used on modern aircrafts.Press bend forming has many advantages,and it becomes a significant technique in aircraft manufacturing field.In order to design the press bend forming path for aircraft integral panels,we propose a novel optimization method which integrates the finite element method(FEM) equivalent model based on our previous study,the artificial neural network response surface,and the genetic algorithm. First,a multi-step press bend forming FEM equivalent model is established,with which the FEM experiments designed with Taguchi method are performed.Then,the backpropagation(BP) neural network response surface is developed with the sample data from the FEM experiments.Further more,genetic algorithm(GA) is applied with the neural network response surface as the objective function.Finally,experimental and simulation verifications are carried out on a single stiffener specimen.The forming error of the panel formed with the optimal path is only 5.37%and the calculating efficiency has been improved by 90.64%.Therefore,this novel optimization method is quite efficient and indispensable for the press bend forming path designing.展开更多
A method utilizing variable depth increments during incremental forming was proposed and then optimized based on numerical simulation and intelligent algorithm.Initially,a finite element method(FEM) model was set up a...A method utilizing variable depth increments during incremental forming was proposed and then optimized based on numerical simulation and intelligent algorithm.Initially,a finite element method(FEM) model was set up and then experimentally verified.And the relation between depth increment and the minimum thickness tmin as well as its location was analyzed through the FEM model.Afterwards,the variation of depth increments was defined.The designed part was divided into three areas according to the main deformation mechanism,with Di(i=1,2) representing the two dividing locations.And three different values of depth increment,Δzi(i=1,2,3) were utilized for the three areas,respectively.Additionally,an orthogonal test was established to research the relation between the five process parameters(D and Δz) and tmin as well as its location.The result shows that Δz2 has the most significant influence on the thickness distribution for the corresponding area is the largest one.Finally,a single evaluating indicator,taking into account of both tmin and its location,was formatted with a linear weighted model.And the process parameters were optimized through a genetic algorithm integrated with an artificial neural network based on the evaluating index.The result shows that the proposed algorithm is satisfactory for the optimization of variable depth increment.展开更多
In order to design the press bend forming path of aircraft integral panels,a novel optimization method was proposed, which integrates FEM equivalent model based on previous study,the artificial neural network response...In order to design the press bend forming path of aircraft integral panels,a novel optimization method was proposed, which integrates FEM equivalent model based on previous study,the artificial neural network response surface,and the genetic algorithm.First,a multi-step press bend forming FEM equivalent model was established,with which the FEM experiments designed with Taguchi method were performed.Then,the BP neural network response surface was developed with the sample data from the FEM experiments.Furthermore,genetic algorithm was applied with the neural network response surface as the objective function. Finally,verification was carried out on a simple curvature grid-type stiffened panel.The forming error of the panel formed with the optimal path is only 0.098 39 and the calculating efficiency has been improved by 77%.Therefore,this novel optimization method is quite efficient and indispensable for the press bend forming path designing.展开更多
In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a prac...In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a practical algorithm for Jordancanonical form J of a quaternion matrix A, but also provide a practical algorithm forcorresponding nonsingular matrix P with P- 1 AP = J.展开更多
A closed-form numerical algorithm (CFNA) is analyzed in detail. CFNA iswidely used in mechanical dynamics for periodic solution of second-order original differentialequations (SODE) with periodic time-variant coeffici...A closed-form numerical algorithm (CFNA) is analyzed in detail. CFNA iswidely used in mechanical dynamics for periodic solution of second-order original differentialequations (SODE) with periodic time-variant coefficients. The principle of the algorithm is todiscretize the motion period into many short time intervals, so the coefficient matrices of theequation set are regarded as constant in a time interval. Defects are found in the originalalgorithm in treating the modal coordinates at the two end-nodes and important modifications to thedefects is made for the algorithm. The modified algorithm is finally used to solve the dynamicproblem of a three-ring planetary gear transmission.展开更多
This study is concerned with the problems of contact in the process of numerical simulation of sheet metal forming in rigid visco-plastic shell FEM. In respect of analysis of sheet deep drawing process,for the tool m...This study is concerned with the problems of contact in the process of numerical simulation of sheet metal forming in rigid visco-plastic shell FEM. In respect of analysis of sheet deep drawing process,for the tool model described by triangular elements, a kind of contact judging algorithm about the correlation between the node of deformed mesh and the triangular element of a tool is presented. In SPF/DB Lagrangian multiplier method is adopted to solve the contact problem between deformed meshes, and a new reliable practical dynamic contact checking algorithm is presented. As computation examples, the simulation results of metal sheet deep drawing and SPF/DB are introduced in this paper.展开更多
Sheet metal forming is widely applied to automobile, aviation, space flight, ship, instrument, and appliance industries.In this paper, based on analyzing the shortcoming of general finite element analysis (FEA), the c...Sheet metal forming is widely applied to automobile, aviation, space flight, ship, instrument, and appliance industries.In this paper, based on analyzing the shortcoming of general finite element analysis (FEA), the conception of parametric finite element analysis (PFEA) is presented. The parametric finite element analysis, artificial neural networks(ANN) and genetic algorithm (GA) are combined to research thoroughly on the problems of process parametersoptimization of sheet metal forming. The author programs the optimization scheme and applies it in a research ofoptimization problem of inside square hole flanging technological parameters. The optimization result coincides wellwith the result of experiment. The research shows that the optimization scheme offers a good new way in die designand sheet metal forming field.展开更多
Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equa...Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.展开更多
基金Project(2012ZX04010-081) supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China
文摘To obtain the optimal process parameters of stamping forming, finite element analysis and optimization technique were integrated via transforming multi-objective issue into a single-objective issue. A Pareto-based genetic algorithm was applied to optimizing the head stamping forming process. In the proposed optimal model, fracture, wrinkle and thickness varying are a function of several factors, such as fillet radius, draw-bead position, blank size and blank-holding force. Hence, it is necessary to investigate the relationship between the objective functions and the variables in order to make objective functions varying minimized simultaneously. Firstly, the central composite experimental(CCD) with four factors and five levels was applied, and the experimental data based on the central composite experimental were acquired. Then, the response surface model(RSM) was set up and the results of the analysis of variance(ANOVA) show that it is reliable to predict the fracture, wrinkle and thickness varying functions by the response surface model. Finally, a Pareto-based genetic algorithm was used to find out a set of Pareto front, which makes fracture, wrinkle and thickness varying minimized integrally. A head stamping case indicates that the present method has higher precision and practicability compared with the "trial and error" procedure.
基金the National Natural Science F oundation of China (5 9875 0 2 5 ) and Excellent Young Teacher Founda-tion of the Educational Departm ent of China
文摘Based on existing algorithms, a newly developed contact search algorithm is proposed. The new algorithm consists of global search, local searching, local tracking and penetration calculation processes. It requires no iteration steps. It can deal with not only general tool surfaces with vertical walls, but also tool surfaces meshed with elements having very poor aspect ratios. It is demonstrated that the FE code employing this new contact search algorithm becomes more reliable, efficient and accurate for sheet metal forming simulation than conventional ones.
文摘A non-incremental time-space algorithm is proposed for numerical. analysis of forming process with the inclusion of geometrical, material, contact-frictional nonlinearities. Unlike the widely used Newton-Raphson counterpart, the present scheme features an iterative solution procedure on entire time and space domain. Validity and feasibility of foe present scheme are further justiced by the numerical investigation herewith presented.
基金Specialized Research Fund for the Doctoral Program of High Education of China (20091102110021)
文摘In order to find out the optimal press bend forming path in fabricating aircraft integral panels, this article proposes a new method on the basis of the authors＇ previous work. It is composed of the finite element method （FEM） equivalent model, the surface curvature analysis, the artificial neural network response surface and the genetic algorithm. The method begins with analyzing the objective＇s shape curvature to determine the bending position. Then it optimizes the punch travel at each bending position by the following steps： （1） Establish a multi-step press bend forming FEM equivalent model, with which the FEM ex- periments designed with the Taguchi method are performed. （2） Construct a back-propagation （BP） neural network response surface with the data from the FEM experiments. （3） Use the genetic algorithm to optimize the neural network response surface as the objective function. Finally, this method is verified by press bending a complicated double-curvature grid-type stiffened panel and bears out its effectiveness and intrinsic worth in designing the press bend forming path.
基金Project(50175034) supported by the National Natural Science Foundation of China
文摘In the incremental sheet forming （ISF） process, springback is a very important factor that affects the quality of parts. Predicting and controlling springback accurately is essential for the design of the toolpath for ISF. A three-dimensional elasto-plastic finite element model （FEM） was developed to simulate the process and the simulated results were compared with those from the experiment. The springback angle was found to be in accordance with the experimental result, proving the FEM to be effective. A coupled artificial neural networks （ANN） and finite element method technique was developed to simulate and predict springback responses to changes in the processing parameters. A particle swarm optimization （PSO） algorithm was used to optimize the weights and thresholds of the neural network model. The neural network was trained using available FEM simulation data. The results showed that a more accurate prediction of s!oringback can be acquired using the FEM-PSONN model.
基金the National Natural Science Foundation of China(Nos.5090514451275415)National Basic Research Program of China(No.2010CB731701)+2 种基金Program for New Century Excellent Talents in University,Fundamental Research Funds for the Central Universities(3102014KYJD001)of Chinathe EU Marie Curie Actions–Mat Pro Future Project(FP7-PEOPLE-2012-IRSES-318968)of Chinathe‘‘111"Project(B08040)of China for the support to this research
文摘The precision forming of thin-walled components has been urgently needed in aviation and aerospace field. However, the wrinkling induced by the compressive instability is one of the major defects in thin-walled part forming. The initiation and growth of the wrinkles are interac- tively affected by many factors such as stress states, mechanical properties of the material, geometry of the workpiece and boundary conditions. Especially when the forming process involves compli- cated boundary conditions such as multi-dies constrains, the perturbation of clearances between workpiece and dies and the contact conditions changing in time and space, etc., the predication of the wrinkling is further complicated. In this paper, the cu.rent prediction methods were summa- rized including the static equilibrium method, the energy method, the initial imperfection method, the eigenvalue buckling analysis method, the static-implicit finite element method and the dynamic- explicit finite element method. Then, a systematical comparison and summary of these methods in terms of their advantages and limitations are presented. By using a combination of explicit FE method, initial imperfection and energy conservation, a hybrid method is recommended to predict plastic wrinkling in thin-walled part forming. Finally, considering the urgent requirements of com- plex thin-walled structures＇ part in aviation and aerospace field, the trends and challenges in wrin- kling prediction under complicated boundary conditions are presented.
基金The project is supported by National Natural Science Foundation of China(No.59975025).
文摘A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularity error. The finely-designed GA (FDGA)characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of thenonlinear problem is given. The implementation details in FDGA are described such as the crossoveror recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservationmethod; and the adaptive mutation which used the Gaussian probability distribution to determine thevalues of the offspring produced by mutation mechanism. The examples are provided to verify thedesigned FDGA. The computation results indicate that the FDGA works very well in the field of formerror evaluation such as circularity evaluation.
文摘Regarding heat forming process of 1Cr18Ni9Ti as typical forming process, this paper presents the study of the effect of various parameters on flow stress, grain size and hardness of formed specimen by means of Gleeble-1500 Thermo-simulation machine and metalloscope. On the basis of technical experi- ment this paper, data are proceeded by applying multilayer feedforward back-propagation neural network, a prediction model of technological parameters together with microstructure and property in the heat forming process is established, thus forging property prediction in the heat forming process is realized.
基金supported by National Foundation of Natural Science under the Grant 11071216
文摘In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.
文摘The research on numerical simulation for combinative process of SPF/DB is carried out in this paper. The contacting problem of sheets is analyzed by using the penalty method. In order to solve the contact problem of different parts of the sheet, a new algorithm for contacting judgment is proposed. According to the relation of the distance vector and the vector of contacting element area, and the condition of contact, it can be judged whether or not a node on the slave surface and the corresponding master surface are in the state of SPF/DB. The Mindlin shell element is employed to simulate SPF/DB process of an asymmetry double-cell cup of Ti-6Al-4V to examine the efficiency of the new algorithm using ARVIP-3D. The results of the numerical simulation are in good agreement with experimental results.
基金the National Natural Science Foundation of China(Nos.51205004 and 51005010)
文摘Because of the light weight,high stiffness and high structural efficiency,aluminium alloy integral panels are widely used on modern aircrafts.Press bend forming has many advantages,and it becomes a significant technique in aircraft manufacturing field.In order to design the press bend forming path for aircraft integral panels,we propose a novel optimization method which integrates the finite element method(FEM) equivalent model based on our previous study,the artificial neural network response surface,and the genetic algorithm. First,a multi-step press bend forming FEM equivalent model is established,with which the FEM experiments designed with Taguchi method are performed.Then,the backpropagation(BP) neural network response surface is developed with the sample data from the FEM experiments.Further more,genetic algorithm(GA) is applied with the neural network response surface as the objective function.Finally,experimental and simulation verifications are carried out on a single stiffener specimen.The forming error of the panel formed with the optimal path is only 5.37%and the calculating efficiency has been improved by 90.64%.Therefore,this novel optimization method is quite efficient and indispensable for the press bend forming path designing.
文摘A method utilizing variable depth increments during incremental forming was proposed and then optimized based on numerical simulation and intelligent algorithm.Initially,a finite element method(FEM) model was set up and then experimentally verified.And the relation between depth increment and the minimum thickness tmin as well as its location was analyzed through the FEM model.Afterwards,the variation of depth increments was defined.The designed part was divided into three areas according to the main deformation mechanism,with Di(i=1,2) representing the two dividing locations.And three different values of depth increment,Δzi(i=1,2,3) were utilized for the three areas,respectively.Additionally,an orthogonal test was established to research the relation between the five process parameters(D and Δz) and tmin as well as its location.The result shows that Δz2 has the most significant influence on the thickness distribution for the corresponding area is the largest one.Finally,a single evaluating indicator,taking into account of both tmin and its location,was formatted with a linear weighted model.And the process parameters were optimized through a genetic algorithm integrated with an artificial neural network based on the evaluating index.The result shows that the proposed algorithm is satisfactory for the optimization of variable depth increment.
基金Project(20091102110021)supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘In order to design the press bend forming path of aircraft integral panels,a novel optimization method was proposed, which integrates FEM equivalent model based on previous study,the artificial neural network response surface,and the genetic algorithm.First,a multi-step press bend forming FEM equivalent model was established,with which the FEM experiments designed with Taguchi method were performed.Then,the BP neural network response surface was developed with the sample data from the FEM experiments.Furthermore,genetic algorithm was applied with the neural network response surface as the objective function. Finally,verification was carried out on a simple curvature grid-type stiffened panel.The forming error of the panel formed with the optimal path is only 0.098 39 and the calculating efficiency has been improved by 77%.Therefore,this novel optimization method is quite efficient and indispensable for the press bend forming path designing.
基金Supported by the National Natural Science Foudnation of China and Shanghai Priority Academic Discipline Foundation,Shanghai,China.
文摘In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a practical algorithm for Jordancanonical form J of a quaternion matrix A, but also provide a practical algorithm forcorresponding nonsingular matrix P with P- 1 AP = J.
基金This project is supported by National Natural Science Foundation of China (No.50205019) Development Foundation of Shanghai Municipal Commission of Education, China (No.04EB03).
文摘A closed-form numerical algorithm (CFNA) is analyzed in detail. CFNA iswidely used in mechanical dynamics for periodic solution of second-order original differentialequations (SODE) with periodic time-variant coefficients. The principle of the algorithm is todiscretize the motion period into many short time intervals, so the coefficient matrices of theequation set are regarded as constant in a time interval. Defects are found in the originalalgorithm in treating the modal coordinates at the two end-nodes and important modifications to thedefects is made for the algorithm. The modified algorithm is finally used to solve the dynamicproblem of a three-ring planetary gear transmission.
文摘This study is concerned with the problems of contact in the process of numerical simulation of sheet metal forming in rigid visco-plastic shell FEM. In respect of analysis of sheet deep drawing process,for the tool model described by triangular elements, a kind of contact judging algorithm about the correlation between the node of deformed mesh and the triangular element of a tool is presented. In SPF/DB Lagrangian multiplier method is adopted to solve the contact problem between deformed meshes, and a new reliable practical dynamic contact checking algorithm is presented. As computation examples, the simulation results of metal sheet deep drawing and SPF/DB are introduced in this paper.
基金This work was supported by the Natural Science Foundation of the Jiangxi Province of China under grant No.12 and the Committee of Science and Technology of Jiangxi Province, China.
文摘Sheet metal forming is widely applied to automobile, aviation, space flight, ship, instrument, and appliance industries.In this paper, based on analyzing the shortcoming of general finite element analysis (FEA), the conception of parametric finite element analysis (PFEA) is presented. The parametric finite element analysis, artificial neural networks(ANN) and genetic algorithm (GA) are combined to research thoroughly on the problems of process parametersoptimization of sheet metal forming. The author programs the optimization scheme and applies it in a research ofoptimization problem of inside square hole flanging technological parameters. The optimization result coincides wellwith the result of experiment. The research shows that the optimization scheme offers a good new way in die designand sheet metal forming field.
文摘Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.
