A numerical-analytical method is applied for the two-dimensional magnetic field computation in rotational electric machines in this paper. The analytical expressions for air gap magnetic field are derived. The pole pa...A numerical-analytical method is applied for the two-dimensional magnetic field computation in rotational electric machines in this paper. The analytical expressions for air gap magnetic field are derived. The pole pairs in the expressions are taken into account so that the solution region can be reduced within one periodic range. The numerical and analytical magnetic field equations are linked with equal vector magnetic potential boundary conditions. The magnetic field of a brushless permanent magnet machine is computed by the proposed method. The result is compared to that obtained by finite element method so as to validate the correction of the method.展开更多
It is not convenient to solve those engineering problems defined in an infinite field by using FEM. An infinite area can be divided into a regular infinite external area and a finite internal area. The finite internal...It is not convenient to solve those engineering problems defined in an infinite field by using FEM. An infinite area can be divided into a regular infinite external area and a finite internal area. The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate. All governing equations were transformed into the Hamiltonian system. The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element.This new element, like a super finite element, can be combined with commonly used finite elements. The proposed method was verified by numerical case studies. The results show that the preparation work is very simple, the infinite analytical element has a high precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.展开更多
Owing to the complexity of geo-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering appl...Owing to the complexity of geo-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering applications. A three-dimensional anisotropic heterogeneous steady random seepage model was developed on the basis of the finite element method. A statistical analysis of the distribution characteristics of soil parameters sampled from the main embankment of the Yangtze River in the Southern Jingzhou zone of China was conducted. The Kolomogorov-Smirnov test verified the statistical hypothesis that the permeability coefficient tensor has a Gaussian distribution. With the help of numerical analysis of the stochastic seepage field using the developed model, various statistical and random characteristics of the stochastic seepage field of the main embankment of the Yangtze River in the Southern Jingzhou zone of China were investigated. The model was also examined with statistical testing. Through the introduction of random variation of the upstream and downstream water levels into the model, the effects of the boundary randomness due to variation of the downstream and upstream water levels on the variation of simulated results presented with a vector series of the random seepage field were analyzed. Furthermore, the combined influence of the variation of the soil permeability coefficient and such seepage resistance measures as the cut-off wall and relief ditch on the hydraulic head distribution was analyzed and compared with the results obtained by determinate analysis. Meanwhile, sensitivities of the hydraulic gradient and downstream exit height to the variation of boundary water level were studied. The validity of the simulated results was verified by stochastic testing and measured data. The developed model provides more detail and a full stochastic algorithm to characterize and analyze three-dimensional stochastic seepage field problems.展开更多
文摘A numerical-analytical method is applied for the two-dimensional magnetic field computation in rotational electric machines in this paper. The analytical expressions for air gap magnetic field are derived. The pole pairs in the expressions are taken into account so that the solution region can be reduced within one periodic range. The numerical and analytical magnetic field equations are linked with equal vector magnetic potential boundary conditions. The magnetic field of a brushless permanent magnet machine is computed by the proposed method. The result is compared to that obtained by finite element method so as to validate the correction of the method.
文摘It is not convenient to solve those engineering problems defined in an infinite field by using FEM. An infinite area can be divided into a regular infinite external area and a finite internal area. The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate. All governing equations were transformed into the Hamiltonian system. The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element.This new element, like a super finite element, can be combined with commonly used finite elements. The proposed method was verified by numerical case studies. The results show that the preparation work is very simple, the infinite analytical element has a high precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.
基金supported by the National Natural Science Foundation of China (Grant No. 50379046)the Doctoral Fund of the Ministry of Education of China (Grant No. A50221)
文摘Owing to the complexity of geo-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering applications. A three-dimensional anisotropic heterogeneous steady random seepage model was developed on the basis of the finite element method. A statistical analysis of the distribution characteristics of soil parameters sampled from the main embankment of the Yangtze River in the Southern Jingzhou zone of China was conducted. The Kolomogorov-Smirnov test verified the statistical hypothesis that the permeability coefficient tensor has a Gaussian distribution. With the help of numerical analysis of the stochastic seepage field using the developed model, various statistical and random characteristics of the stochastic seepage field of the main embankment of the Yangtze River in the Southern Jingzhou zone of China were investigated. The model was also examined with statistical testing. Through the introduction of random variation of the upstream and downstream water levels into the model, the effects of the boundary randomness due to variation of the downstream and upstream water levels on the variation of simulated results presented with a vector series of the random seepage field were analyzed. Furthermore, the combined influence of the variation of the soil permeability coefficient and such seepage resistance measures as the cut-off wall and relief ditch on the hydraulic head distribution was analyzed and compared with the results obtained by determinate analysis. Meanwhile, sensitivities of the hydraulic gradient and downstream exit height to the variation of boundary water level were studied. The validity of the simulated results was verified by stochastic testing and measured data. The developed model provides more detail and a full stochastic algorithm to characterize and analyze three-dimensional stochastic seepage field problems.
