Metal injection moulding (MIM) is a new technology to manufacture small intricate parts in large quantity. Numerical simulation plays an important role in its development. To predict the specific segregation effect in...Metal injection moulding (MIM) is a new technology to manufacture small intricate parts in large quantity. Numerical simulation plays an important role in its development. To predict the specific segregation effect in MIM injection, mixture theory is adopted to model the injection flow by a bi-phasic model. This model conducts to the solution of two-coupled Stokes equations. It is an extremely computational consuming solution in the scope of the traditional algorithms, which induce a serious challenge to cost-effectivity of the MIM simulation. Referred to some methods proposed by Lewis in mono-phasic simulation and the implicit algorithms in MIM simulation, a new explicit algorithm is proposed and realized to perform efficiently this type of bi-phasic flow. Numerically this algorithm is devised to perform the simulation in a fully uncoupled manner except for a global solution of the pressure field in each time step. The physical coupling is taken into account in a sequential pattern by fractional steps.展开更多
Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing. Their numerical properties in the solution of a linear elastic sy...Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing. Their numerical properties in the solution of a linear elastic system have been well explored and their applications to the pseudodynamic testing of a nonlinear system have been shown to be feasible. However, their numerical properties in the solution of a nonlinear system are not apparent. Therefore, the performance of both algorithms for use in the solution of a nonlinear system has been analytically evaluated after introducing an instantaneous degree of nonlinearity. The two algorithms have roughly the same accuracy for a small value of the product of the natural frequency and step size. Meanwhile, the first algorithm is unconditionally stable when the instantaneous degree of nonlinearity is less than or equal to 1, and it becomes conditionally stable when it is greater than 1. The second algorithm is conditionally stable as the instantaneous degree of nonlinearity is less than 1/9, and becomes unstable when it is greater than 1. It can have unconditional stability for the range between 1/9 and 1. Based on these evaluations, it was concluded that the first algorithm is superior to the second one. Also, both algorithms were found to require commensurate computational efforts, which are much less than needed for the Newmark explicit method in general structural dynamic problems.展开更多
An explicit unconditionally stable algorithm for hybrid tests,which is developed from the traditional HHT-α algorithm,is proposed.The unconditional stability is first proven by the spectral radius method for a linear...An explicit unconditionally stable algorithm for hybrid tests,which is developed from the traditional HHT-α algorithm,is proposed.The unconditional stability is first proven by the spectral radius method for a linear system.If the value of α is selected within [-0.5,0],then the algorithm is shown to be unconditionally stable.Next,the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system.The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening.To improve the stability of the proposed method,the structure stiffness is then identified and updated.Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability.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
Research reports show that the accuracies of many explicit friction factor models, having different levels of accuracies and complexities, have been improved using genetic algorithm (GA), a global optimization approac...Research reports show that the accuracies of many explicit friction factor models, having different levels of accuracies and complexities, have been improved using genetic algorithm (GA), a global optimization approach. However, the computational cost associated with the use of GA has yet to be discussed. In this study, the parameters of sixteen explicit models for the estimation of friction factor in the turbulent flow regime were optimized using two popular global search methods namely genetic algorithm (GA) and simulated annealing (SA). Based on 1000 interval values of Reynolds number (Re) in the range of and 100 interval values of relative roughness () in the range of , corresponding friction factor (f) data were obtained by solving Colebrook-White equation using Microsoft Excel spreadsheet. These data were then used to modify the parameters of the selected explicit models. Although both GA and SA led to either moderate or significant improvements in the accuracies of the existing friction factor models, SA outperforms the GA. Moreover, the SA requires far less computational time than the GA to complete the corresponding optimization process. It can therefore be concluded that SA is a better global optimizer than GA in the process of finding an improved explicit friction factor model as an alternative to the implicit Colebrook-White equation in the turbulent flow regime.展开更多
A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying dom...A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function (RBF) coupled with a polynomial basis function,in which the shape function possesses the kronecker delta function property.So,additional treatment is not required for imposing essential boundary conditions.Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain,which is very similar to that of the collocation method except that numerical integration can be implemented over local domain in the present method.Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.展开更多
A corrected explicit method of double time steps(CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the g...A corrected explicit method of double time steps(CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the generalized-a method and the precise integration method were implemented in typical nonlinear examples for the purpose of comparison. Both conservative and non-conservative systems were examined. The results show that it isn't unconditionally stable for the precise integration method, the Newmark method and the generalized-a method in nonlinear systems. The stable interval of the three methods is less than that of the CEMDTS. When a small time step(?t≤Tmin/20) is employed, the precise integration method is endowed with the highest accuracy while the CEMDTS possesses the smallest computation effort. However, the CEMDTS becomes the most accurate one when the time step is large(?t≥0.3Tmin) or the system is strongly nonlinear. Therefore, the CEMDTS is more applicable to the nonlinear vibration systems.展开更多
In the simulation of the metal injection moulding (MIM), the behaviours of feedstock are much di?erent from which of the polymer injection. It is a mixture of the metallic powder in high concentration and some plastic...In the simulation of the metal injection moulding (MIM), the behaviours of feedstock are much di?erent from which of the polymer injection. It is a mixture of the metallic powder in high concentration and some plastic binder. The advance in simulation of the mould ?lling with such high viscous feedstock is featured by the development of a fully explicit vectorial algorithm. On the basis of previous explicit software realized by the authors, the new algorithm avoids the global solution for pressure ?elds and the use of MINI elements to improve its e?ciency. Except for the operations at element level, neither global solution nor the construction of global matrix is required in simulation. A special strategy is used to regulate the incompressibility condition in ?lled domain at each time step. In case of the MIM problems, this method provides a fast way to simulate the ?lling processes. The computational cost is about linearly proportional to the degree of freedom number. Moreover, this vectorial algorithm can be easily parallelized for high performance computation with multi-clusters. The comparison of numerical results with previous simulations on 3D cases proves the validity and e?ciency of new algorithm.展开更多
Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm (Chang, 2003) are presented. One extends the stability study from a given time step t...Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm (Chang, 2003) are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom (SDOF) system, can be applied to a nonlinear multiple degree of freedom (MDOF) system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.展开更多
基金Supported by the Invited Professor Program of French Ministry of Education (No. 9808588) , the French-Chinese Advanced Research Program (M98-04)the Foundation for University Key Teacher by the Chinese Ministry of Education (GG-460-10613-2770).
摘要Metal injection moulding (MIM) is a new technology to manufacture small intricate parts in large quantity. Numerical simulation plays an important role in its development. To predict the specific segregation effect in MIM injection, mixture theory is adopted to model the injection flow by a bi-phasic model. This model conducts to the solution of two-coupled Stokes equations. It is an extremely computational consuming solution in the scope of the traditional algorithms, which induce a serious challenge to cost-effectivity of the MIM simulation. Referred to some methods proposed by Lewis in mono-phasic simulation and the implicit algorithms in MIM simulation, a new explicit algorithm is proposed and realized to perform efficiently this type of bi-phasic flow. Numerically this algorithm is devised to perform the simulation in a fully uncoupled manner except for a global solution of the pressure field in each time step. The physical coupling is taken into account in a sequential pattern by fractional steps.
基金Science Council,Chinese Taipei,Under Grant No. NSC-96-2211-E-027-030
摘要Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing. Their numerical properties in the solution of a linear elastic system have been well explored and their applications to the pseudodynamic testing of a nonlinear system have been shown to be feasible. However, their numerical properties in the solution of a nonlinear system are not apparent. Therefore, the performance of both algorithms for use in the solution of a nonlinear system has been analytically evaluated after introducing an instantaneous degree of nonlinearity. The two algorithms have roughly the same accuracy for a small value of the product of the natural frequency and step size. Meanwhile, the first algorithm is unconditionally stable when the instantaneous degree of nonlinearity is less than or equal to 1, and it becomes conditionally stable when it is greater than 1. The second algorithm is conditionally stable as the instantaneous degree of nonlinearity is less than 1/9, and becomes unstable when it is greater than 1. It can have unconditional stability for the range between 1/9 and 1. Based on these evaluations, it was concluded that the first algorithm is superior to the second one. Also, both algorithms were found to require commensurate computational efforts, which are much less than needed for the Newmark explicit method in general structural dynamic problems.
基金Scientific Research Fund of the Institute of Engineering Mechanics,CEA under Grant Nos.2017A02,2016B09 and 2016A06the National Science-technology Support Plan Projects under Grant No.2015BAK17B02the National Natural Science Foundation of China under Grant Nos.51378478,51408565,51678538 and 51161120360
摘要An explicit unconditionally stable algorithm for hybrid tests,which is developed from the traditional HHT-α algorithm,is proposed.The unconditional stability is first proven by the spectral radius method for a linear system.If the value of α is selected within [-0.5,0],then the algorithm is shown to be unconditionally stable.Next,the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system.The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening.To improve the stability of the proposed method,the structure stiffness is then identified and updated.Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability.
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
摘要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.
摘要Research reports show that the accuracies of many explicit friction factor models, having different levels of accuracies and complexities, have been improved using genetic algorithm (GA), a global optimization approach. However, the computational cost associated with the use of GA has yet to be discussed. In this study, the parameters of sixteen explicit models for the estimation of friction factor in the turbulent flow regime were optimized using two popular global search methods namely genetic algorithm (GA) and simulated annealing (SA). Based on 1000 interval values of Reynolds number (Re) in the range of and 100 interval values of relative roughness () in the range of , corresponding friction factor (f) data were obtained by solving Colebrook-White equation using Microsoft Excel spreadsheet. These data were then used to modify the parameters of the selected explicit models. Although both GA and SA led to either moderate or significant improvements in the accuracies of the existing friction factor models, SA outperforms the GA. Moreover, the SA requires far less computational time than the GA to complete the corresponding optimization process. It can therefore be concluded that SA is a better global optimizer than GA in the process of finding an improved explicit friction factor model as an alternative to the implicit Colebrook-White equation in the turbulent flow regime.
基金supported by the National Natural Science Foundation of China(No.10902038)
摘要A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function (RBF) coupled with a polynomial basis function,in which the shape function possesses the kronecker delta function property.So,additional treatment is not required for imposing essential boundary conditions.Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain,which is very similar to that of the collocation method except that numerical integration can be implemented over local domain in the present method.Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.
基金Projects(51405402,51505390)supported by the National Natural Science Foundation of ChinaProjects(2016YFB1200404,2016YFB1200505)supported by the National Key Research and Development Program of China
摘要A corrected explicit method of double time steps(CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the generalized-a method and the precise integration method were implemented in typical nonlinear examples for the purpose of comparison. Both conservative and non-conservative systems were examined. The results show that it isn't unconditionally stable for the precise integration method, the Newmark method and the generalized-a method in nonlinear systems. The stable interval of the three methods is less than that of the CEMDTS. When a small time step(?t≤Tmin/20) is employed, the precise integration method is endowed with the highest accuracy while the CEMDTS possesses the smallest computation effort. However, the CEMDTS becomes the most accurate one when the time step is large(?t≥0.3Tmin) or the system is strongly nonlinear. Therefore, the CEMDTS is more applicable to the nonlinear vibration systems.
基金Project supported by the Research Fund for the Doctoral Program of Higher Education of China (No. 20020613005)and the French Programme of Alternant Doctoral Training.
摘要In the simulation of the metal injection moulding (MIM), the behaviours of feedstock are much di?erent from which of the polymer injection. It is a mixture of the metallic powder in high concentration and some plastic binder. The advance in simulation of the mould ?lling with such high viscous feedstock is featured by the development of a fully explicit vectorial algorithm. On the basis of previous explicit software realized by the authors, the new algorithm avoids the global solution for pressure ?elds and the use of MINI elements to improve its e?ciency. Except for the operations at element level, neither global solution nor the construction of global matrix is required in simulation. A special strategy is used to regulate the incompressibility condition in ?lled domain at each time step. In case of the MIM problems, this method provides a fast way to simulate the ?lling processes. The computational cost is about linearly proportional to the degree of freedom number. Moreover, this vectorial algorithm can be easily parallelized for high performance computation with multi-clusters. The comparison of numerical results with previous simulations on 3D cases proves the validity and e?ciency of new algorithm.
基金NSC, Chinese Taipei Under Grant No. NSC-97-2221-E-027-036-MY2
摘要Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm (Chang, 2003) are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom (SDOF) system, can be applied to a nonlinear multiple degree of freedom (MDOF) system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.