Solving boundary-value problems using hp-version finite elements in time

International Journal for Numerical Methods in Engineering

Volumn 43, Issue 3, 1998, Pages 425-440

  Warner, Michael S ^a,b   Hodges, Dewey H ^a  

^a Georgia Institute of Technology   (United States)

^b WRIGHT PATTERSON AIR FORCE BASE   (United States)

Author keywords

Boundary value problems; Dynamics; Numerical methods; Optimal control; Time marching

Indexed keywords

FINITE ELEMENT METHOD; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING; TIME DOMAIN ANALYSIS;

HAMILTON'S WEAK PRINCIPLE (HWP); TIME MARCHING METHODS;

BOUNDARY VALUE PROBLEMS;

EID: 0032188598     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19981015)43:3<425::AID-NME422>3.0.CO;2-P     Document Type: Article

References (19)

1. M. Boni et al., 'Dynamic response of mechanical systems by a weak Hamiltonian formulation', Comput. Struct., 20, 495-508 (1985).
2. M. Borri, 'Helicopter rotor dynamics by finite element time approximation', Comput. Math. Appl., 12A, 149-160 (1986).
3. M. Borri, F. Mello and S. N. Atluri, 'Primal and mixed forms of Hamilton's principle for constrained rigid body systems: numerical studies', Comput. Mech., 7, 205-220 (1991).
4. D. H. Hodges and R. R. Bless, 'Weak Hamiltonian finite element method for optimal control problems', J. Guidance, Control, Dyn., 14, 148-156 (1991).
5. R. R. Bless, 'Time-domain finite elements in optimal control with application to launch vehicle guidance', NASA CK 4376, May 1991.
6. R. R. Bless and D. H. Hodges, 'Finite element solution of optimal control problems with state-control inequality constraints', J. Guidance, Control, Dyn., 15, 1029-1032 (1992).
7. R. R. Bless, D. H. Hodges and H. Seywald, 'Finite element method for the solution of state-constrained optimal control problems', J. Guidance, Control, Dyn., 18, 1036-1043 (1995).
8. G. Haskins, M. Johnson and D. Hodges, 'Real time missile guidance system', U.S. Patent 5435503, 1993.
9. G. M. Hulbert, 'A unified set of single-step asymptotic annihilation algorithms for structural dynamics', Comput. Meth. Appl. Mech. Engng., 113, 1-9 (1994).
10. S. C. Fan, T. C. Fung and G. Sheng, 'A comprehensive unified set of single-step algorithms with controllable dissipation for dynamics', Comput. Meth. Appl. Mech. Engng., 145, 87-98 (1997).
11. D. H. Hodges and L.-J. Hou, 'Shape functions for mixed p-version finite elements in the time domain', J. Sound Vib., 145, 169-178 (1991).
12. M. Abramowitz and I. Stegun (eds.), Handbook of Mathematical Functions, National Bureau of Standards, Washington, DC, 1970.
13. U. M. Ascher, R. M. M. Mattheij and R. D. Russell, Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations, SIAM, Philadelphia, Pennsylvania, 1995.
14. I. S. Duff, Harwell Subroutine Library, Computer Science and Systems Division, Harwell Laboratory, Oxfordshire, England, 1988, Chapter M.
15. MACSYMA Reference Manual, Symbolics, Inc., Burlington, MA, 1988.
16. Maple V Mathematics Programming Guide, Waterloo, Springer-Verlag, 1995.
17. W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, Chapter 16, Cambridge University Press, Cambridge, 1986.
18. D. H. Hodges and M. G. Johnson Jr., 'Control variables for finite element solution of missile trajectory optimization', J. Guidance, Control, Dyn., 18, 1208-1211 (1995).
19. D. H. Hodges, 'Finite rotation and nonlinear beam kinematics', Vertica, 11, 297-307 (1987).