The riccati transfer matrix method

Journal of Mechanical Design, Transactions of the ASME

Volumn 100, Issue 2, 1978, Pages 297-302

  Horner, G C ^a,c   Pilkey, W D ^b  

^a Mechanical Technology Inc   (United States)

^b UNIVERSITY OF VIRGINIA   (United States)

^c NASA LANGLEY RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84991851128     PISSN: 10500472     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.3453915     Document Type: Article

References (18)

1. Pestel, E. C., and F. A. Leckie, Matrix Methods in Elaslo-mechanics, McGraw-Hill, New York, 1963, pp. 130-408.
2. Uhrig, R., “The Transfer Matrix Method Seen ¡is One Method of Structural Analysis Among Others,” Journal of Sound and Vibration, Vol. 4, No. 2, Sept. 1966, pp. 136-148.
3. Acton, F. S., Numerical Methods That Work, Harper and Row, New York, 1970, pp. 148-150.
4. Horner, G. C., “The Riccati Transfer Matrix Method,” PhD Dissertation, University of Virginia, Charlottesville, May 1975.
5. Cohen, G. A., “Computer Analysis of Asymmetrical Deformation of Orthotropic Shells of Revolution,” AIAA Journal, Vol. 2, No. 5, May 1964, pp. 932-934.
6. Kalnins, A., "Analysis of Shells of Revolution Subjected to Symmetrical and Nonsymmetrical Loads,” Journal of Applied Mechanics, Trans. ASME, Series E, Vol. 31, Sept. 1964, pp. 467-476.
7. Hurty, W. D., and Rubinstein, M. F., Dynamics of Structures, Prentice-Hall, New Jersey, 1965, pp. 219-225.
8. Pestel, E., “Dynamics of Structures by Transfer Matrices,” EOARDC under contract AF 61(052) - 302, 1960.
9. Scott, M. R., “Invariant Imbedding of Linear Partial Differential Equations via Generalized Riccati Transformation," Journal of Mathematical Analysis and Application, Vol. 36, No. 2, Nov. 1971, pp. 432-459.
10. Bellman, R. R., Kalaba, R. E., and Wing, G. M., “Invariant Imbedding and the Reduction of Two-Point Boundary Value Problems to Initial Value Problems,” Proceedings of the National Academy of Science U. S. A., Vol. 46, 1960, pp. 1646-1649.
11. Miller, R. E., “Use of the Field Method for Numerical Integration of Two-Point Boundary Value Problems,” AIAA Journal, Vol. 5, No. 4, Apr. 1967, pp. 811-813.
12. Rybicki, G. B., and Usher, P. D., “The Generalized Riccati Transformation as a Simple Alternative to Invariant Imbedding,” Astrophysical Journal, Vol. 146, No. 3, Mar. 1966, pp. 871-879.
13. Alspaugh, D., Kagiwada, H., and Kalaba, R., “Dynamic Programming, Invariant Imbedding and Thin Beam Theory," International Journal of Engineering Science, Vol. 7, 1969, pp. 1117-1126.
14. Bellman, R. E., Kagiwada, H. H., and Kalaba, R. E., “Invariant Imbedding and the Numerical Integration of Bound-ary-Value Problems for Unstable Linear Systems of Ordinary Differential Equations,” Communications of the ACM, Vol. 10, No. 2, Feb. 1967, pp. 100-102.
15. Jordan, P. F., and Shelley, P. E., “Stabilization of Unstable Two-Point Boundary Value Problems,” AIAA Journal, Vol. 4, No. 5, May 1966, pp. 923-924.
16. Distefano, N., and Schujman, J., “Solutions of Elastic Plates by Invariant Imbedding,” ASCE, Vol. 97, No. EMo, Oct. 1971, pp. 1349-1361.
17. Cohen, G. A., “Numerical Integration of Shell Equations Using the Field Method,” Journal of Applied Mechanics, Thans. ASME, Series E, Vol. 41, Mar. 1974, pp. 261-266.
18. Pilkey, W. D., Manual for the Response of Structural Members, Vol. 1, 2, 1969, AD 693 141-142.