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柱形域椭圆型偏微分方程的横向本征函数的解法

钟万勰,钟翔翔   

  1. 大连理工大学 ;纽约州立大学
  • 出版日期:1992-02-20 发布日期:1992-02-20

钟万勰,钟翔翔. 柱形域椭圆型偏微分方程的横向本征函数的解法[J]. 数值计算与计算机应用, 1992, 13(2): 107-118.

ON THE TRANSVERSE EIGENVECTOR SOLUTION OF THE ELLIPTIC PARTIAL DIFFERENTIAL EQUATION IN THE PRISMATIC DOMAIN

  1. Zhong Wan-xie;Zhong Xiang-xiang Dalian University of Technology State Univ. of New York at Stony Brook
  • Online:1992-02-20 Published:1992-02-20
一、引 论核柱形结构在工程中是常见的,它的求解方法有很大的实际意义也很有理论价值。例
The algebraic Riccati equations are derived by the limiting process of the semi-analyticalmethod reduced transversely discretized model of the partial differential equation via the va-riational principle. The close relation of that model with the equations in the linear quadraticoptimal control is pointed out. The dual vector is introduced and the physical interpretationfor the positive definite matrix solution of the Riccati equations is given on that basis. Thecanonical transformation matrix is constructed with the solution of the algebraic Riccati equa-tions, then the Hamiltonian matrix is block-diagonalized and the size of the eigenvalue equa-tion is reduced to half of the original one. It is only necessary to solve one of the two equations,the other one can be obtained by some elementary matrix algebraic operations. That gives thefoundation for the eigenvector expansion method in solving differential equations.
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[1] O. C. Zienkiewicz, The Finite Element Method, McGraw-Hill,1977.
[2] ~~1953.
[3] E. Reissner, On Some Problems in Shell Theory, Structural Mechanics, Ed. J. N. Goodier and N. J. Hoff, Pergamon,1960,pp.74-114.
[4] 1962.
[5] 钟万勰:连续时间LQ调节器的二个代数里卡提方程及本征值问题.即将于大连理工大学学报发表.
[6] 钟万勰:离散LQ控制问题的本征解.即将于计算结构力学与应用发表.
[7] R. F. Stengel, Stochastic Optimal Control Theory and Application. John Wiley and Sons,1986.
[8] S. P. Timoshenko, J. N. Goodier, Theory of Elasticity. 2nd ed., McGraw-Hill, 1951.
[9] J. H. Wilkinson, C. Reinsch, Handbook of Automatic Computation. vol. Ⅱ, Linear Algebra.Springer 1971.
[10] 钟万勰、林家浩,不对称实矩阵的本征对共轭子空间迭代法,即将于计算结构力学及应用发表.
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