Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub&...Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is展开更多
In this paper, Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduce...In this paper, Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition of high Eigen values of the iteration matrix to enable convergence. While extrapolation of a convergent fixed point iteration using a geometric series sum is a known form of Aitken acceleration, it is shown that in this paper, the same formula can be used to estimate the solution of sets of linear equations from diverging Gauss-Seidel iterations. In both convergent and divergent iterations, the ratios of differences among the consecutive values of iteration eventually form a convergent (divergent) series with a factor equal to the largest Eigen value of the iteration matrix. Higher order Aitken extrapolation is shown to eliminate the influence of dominant Eigen values of the iteration matrix in successive order until the iteration is determined by the lowest possible Eigen values. For the convergent part of the Gauss-Seidel iteration, further acceleration is made possible by coupling of the extrapolation technique with the successive over relaxation (SOR) method. Application examples from both convergent and divergent iterations have been provided. Coupling of the extrapolation with the SOR technique is also illustrated for a steady state two dimensional heat flow problem which was solved using MATLAB programming.展开更多
The research on multiple launch rocket system(MLRS)is now even more demanding in terms of reducing the time for dynamic calculations and improving the firing accuracy,keeping the cost as low as possible.This study emp...The research on multiple launch rocket system(MLRS)is now even more demanding in terms of reducing the time for dynamic calculations and improving the firing accuracy,keeping the cost as low as possible.This study employs multibody system transfer matrix method(MSTMM),to model MLRS.The use of this method provides effective and fast calculations of dynamic characteristics,initial disturbance and firing accuracy.Further,a new method of rapid extrapolation of ballistic trajectory of MLRS is proposed by using the position information of radar tests.That extrapolation point is then simulated and compared with the actual results,which demonstrates a good agreement.The closed?loop fire correction method is used to improve the firing accuracy of MLRS at low cost.展开更多
Rapid alternating stress is formed in structure subjected to harsh thermal-acoustic loads,which will affect fatigue performance and reduce fatigue life seriously.First,fatigue experiment of superalloy thin-walled stru...Rapid alternating stress is formed in structure subjected to harsh thermal-acoustic loads,which will affect fatigue performance and reduce fatigue life seriously.First,fatigue experiment of superalloy thin-walled structure was carried out to obtain fatigue damage location and failure time of the experiment specimen,and S-iN curves of superalloy thin-walled structure at 723 K were fitted.Then,dynamic response simulation of superalloy thin-walled structure under the same load as experiment was implemented,and fatigue life was estimated based on the fatigue life prediction model which mainly included:improved rain-flow counting method,Morrow average stress model and Miner linear cumulative damage theory.Further,comparisons between simulation solutions and experimental results achieved a consistency,which verified the validity of the Fatigue Life Prediction Model(FLPM).Moreover,taking a rectangle plate as the analysis object,the distributions of Fain-low circulation blocks and damage levels of the structure were discussed respectively.Finally,current research indicates that in pre-buckling the structure is in softened area and fatigue life decreases with the increase of temperature;in post-buckling the structure is in hardened area and fatigue life increases with the increase of temperature within a certain range.展开更多
基金The works is supported by the National Natural Science Foundation of China(19871054)
文摘Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is
文摘In this paper, Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition of high Eigen values of the iteration matrix to enable convergence. While extrapolation of a convergent fixed point iteration using a geometric series sum is a known form of Aitken acceleration, it is shown that in this paper, the same formula can be used to estimate the solution of sets of linear equations from diverging Gauss-Seidel iterations. In both convergent and divergent iterations, the ratios of differences among the consecutive values of iteration eventually form a convergent (divergent) series with a factor equal to the largest Eigen value of the iteration matrix. Higher order Aitken extrapolation is shown to eliminate the influence of dominant Eigen values of the iteration matrix in successive order until the iteration is determined by the lowest possible Eigen values. For the convergent part of the Gauss-Seidel iteration, further acceleration is made possible by coupling of the extrapolation technique with the successive over relaxation (SOR) method. Application examples from both convergent and divergent iterations have been provided. Coupling of the extrapolation with the SOR technique is also illustrated for a steady state two dimensional heat flow problem which was solved using MATLAB programming.
基金supported by the Na- tional Natural Science Foundation of China (No. 11472135)the Science Challenge Project (No. JCKY2016212A506- 0104)
文摘The research on multiple launch rocket system(MLRS)is now even more demanding in terms of reducing the time for dynamic calculations and improving the firing accuracy,keeping the cost as low as possible.This study employs multibody system transfer matrix method(MSTMM),to model MLRS.The use of this method provides effective and fast calculations of dynamic characteristics,initial disturbance and firing accuracy.Further,a new method of rapid extrapolation of ballistic trajectory of MLRS is proposed by using the position information of radar tests.That extrapolation point is then simulated and compared with the actual results,which demonstrates a good agreement.The closed?loop fire correction method is used to improve the firing accuracy of MLRS at low cost.
基金co-supported by Aviation Basic Science Fund Project of China(No.20151554002)Natural Sciences Key Project of Chengdu Aeronautic Polytechnic in China(No.061754)Natural Sciences General Project of Sichuan Province Education Department in China(No.18ZB0057).
文摘Rapid alternating stress is formed in structure subjected to harsh thermal-acoustic loads,which will affect fatigue performance and reduce fatigue life seriously.First,fatigue experiment of superalloy thin-walled structure was carried out to obtain fatigue damage location and failure time of the experiment specimen,and S-iN curves of superalloy thin-walled structure at 723 K were fitted.Then,dynamic response simulation of superalloy thin-walled structure under the same load as experiment was implemented,and fatigue life was estimated based on the fatigue life prediction model which mainly included:improved rain-flow counting method,Morrow average stress model and Miner linear cumulative damage theory.Further,comparisons between simulation solutions and experimental results achieved a consistency,which verified the validity of the Fatigue Life Prediction Model(FLPM).Moreover,taking a rectangle plate as the analysis object,the distributions of Fain-low circulation blocks and damage levels of the structure were discussed respectively.Finally,current research indicates that in pre-buckling the structure is in softened area and fatigue life decreases with the increase of temperature;in post-buckling the structure is in hardened area and fatigue life increases with the increase of temperature within a certain range.
