Improvement of reduction method combined with sub-domain scheme in large-scale problem

International Journal for Numerical Methods in Engineering

Volumn 70, Issue 2, 2007, Pages 206-251

  Kim, Hyungi ^a   Cho, Maenghyo ^a  

^a Seoul National University   (South Korea)

Author keywords

Reduction method; Sub domain method; Two level condensation scheme

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; DEGREES OF FREEDOM (MECHANICS); EIGENVALUES AND EIGENFUNCTIONS; NUMERICAL METHODS;

REDUCTION METHOD; SUB-DOMAIN SCHEME; TWO-LEVEL CONDENSATION SCHEME;

LARGE SCALE SYSTEMS;

ALGORITHMS; APPROXIMATION THEORY; DEGREES OF FREEDOM (MECHANICS); EIGENVALUES AND EIGENFUNCTIONS; LARGE SCALE SYSTEMS; NUMERICAL METHODS;

EID: 34147116765     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1868     Document Type: Article

References (46)

1. Noor AK. Recent advances and applications of reduction method. AIAA Journal 1994; 47(5):125-146.
2. Guyan RJ. Reduction of stiffness and mass matrices. AIAA Journal 1965; 3(2):380.
3. Leung YT. An accurate method of dynamic condensation in structural analysis. International Journal for Numerical Methods in Engineering 1978; 12:1705-1715.
4. Suarez LE. Dynamic condensation method for structural eigenvalue analysis. AIAA Journal 1992; 30(4): 1046-1054.
5. Paz M. Dynamic condensation. AIAA Journal 1984; 22(5):724-727.
6. O'Callahan J. A procedure for an improved reduced system (IRS) model. Proceedings of the Seventh International Modal Analysis Conference, Union College, Schenectady, NY, 1989; 17-21.
7. Zhang D, Li WS. Succession-level approximate reduction (SAR) technique for structural dynamic model. Analysis Conference, Nashville, TN. Union College Press: Schenectady, NY, 1995; 435-441.
8. Kim KO, Kang MK. Convergence acceleration of iterative modal reduction methods. AIAA Journal 2001; 39(1):134-140.
9. Bauchau OA, Nikishkov YG. Aeroelastic stability using reduced order aerodynamic models. AIAA 99-1264-CP, AIAA/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, St. Louis, Missouri, 12-15 April 1999.
10. Kim T. An efficient response-based model analysis for dynamic systems with multiple inputs. AIAA-2001-1380, AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 42nd, Seattle, WA, 16-19 April 2001.
11. Kim T, Bussoletti JE. An optimal reduced-order aeroelastic modeling based on a response-based modal analysis of unsteady CFD model. AIAA-2001-1525, AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 42nd, Seattle, WA, 16-19 April 2001.
12. Juang J-N, Pappa RS. An eigensystem realization algorithm for modal parameter identification an model reduction. Journal of Guidance, Control, and Dynamics 1985; 8:620-627.
13. Kim T. Frequency-domain Karhunen-Loeve method and its application to linear dynamic systems. AIAA Journal 1998; 36(11):2117-2123.
14. Roger Ohayon. Reduced models for fluid-structure interaction problems. International Journal for Numerical Methods in Engineering 2004; 60:139-152.
15. Gaitonde AL, Jones DP. Reduced order state-space models from the pulse response of a linearized CFD scheme. International Journal for Numerical Methods in Engineering 2003; 42:581-606.
16. Epureanu BI, Hall KC, Dowell EH. Reduced order models of unsteady transonic viscous flows in turbomachinery. Journal of Fluids and Structures 2000; 14(8):1215-1235.
17. Ohayon R. Symmetric formulations for modal analysis of internal fluid structure systems. In Fluid-structure interactions, aeroelasticity, flow-induced vibration and noise, Paiussis MP (ed.). Proceedings of the Fourth International Symposium, IMECE-1997, vol. AD 53-1, ASME, Fairfield, NJ, 67-74.
18. Matta KW. Selection of degrees of freedom for dynamic analysis. Journal of Pressure Vessel Technology 1987; 109(1):65-69.
19. Kidder RL. Reduction of structural frequency evaluations. AIAA Journal 1973; 11(6):892.
20. Henshell RD, Ong JH. Automatic masters from eigenvalues economization. Journal of Earthquake Engineering and Structural Dynamics 1975; 3:375-383.
21. Shah VN, Raymund M. Analytical selection of masters for the reduced eigenvalue problem. International Journal for Numerical Methods in Engineering 1982; 18(1):89-98.
22. Kim KO, Choi YJ. Energy method for selection of degrees of freedom in condensation. AIAA Journal 2000; 38(7):1253-1259.
23. Cho M, Kim H. Element-based node selection method for reduction of eigenvalue problems. AIAA Journal 2004; 42(8):1677-1684.
24. Kim H, Cho M. Construction of reduced system by two-level condensation scheme and refined sensitivity analysis. 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs, California, 19-22 April 2004.
25. Kim H, Cho M. Two-level scheme for selection of degrees of freedom by energy estimation combined with sequential elimination, ICAS 2004.5.11.1, 24th Congress of the International Council of the Aeronautical Sciences, Yokohama, Japan, 29 August-3 September 2004.
26. Kim H, Cho M. Two-level scheme for selection of primary degrees of freedom and semi-analytic sensitivity based on the reduced system. Computer Methods in Applied Mechanics and Engineering 2006; 195(33-36): 4244-4268.
27. Craig Jr, Bampton C. Coupling of substructures for dynamic analyses. AIAA Journal 1968; 6(7):1313-1319.
28. Maday Y, Mavriplis C, Patera A. Nonconforming mortar element methods: application to spectral discretizations, NASA CR-181729, ICASE Report No. 88-59, 1988.
29. Aminpour MA, Bansom JB, Mccleary SL. A coupled analysis method for structures with independently modeled finite element subdomains. International Journal for Numerical Methods in Engineering 1995; 38:3695-3718.
30. Farhat C, Roux FX. A method of finite element tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering 1991; 32:1205-1228.
31. Quiroz L, Beckers P. Non-conforming mesh gluing in the finite elements method. International Journal for Numerical Methods in Engineering 1995; 38:2165-2184.
32. Dohrmann CR, Key SW, Heinstein MW. A method for connecting dissimilar finite element meshes in two dimensions. International Journal for Numerical Methods in Engineering 2000; 48:655-678.
33. Dohrmann CR, Key SW, Heinstein MW. Methods for connecting dissimilar three-dimensional finite element meshes. International Journal for Numerical Methods in Engineering 2000; 47(5):1057-1080.
34. Craig Jr, RR, Chang C-J. On the use of attachment modes in substructure coupling for dynamic analysis, Paper 77-405, AIAA/ASME 18th Structures, Structural Dynamics and Materials Conference, San Diego, CA, 1977.
35. Hintz RM. Analytical methods in component modal synthesis. AIAA Journal 1975; 13:1007-1016.
36. Hurty WC. Dynamic analysis of structural systems using component modes. AIAA Journal 1965; 3:678-685.
37. Gravouil A, Combescure A. Multi-time step explicit-implicit method for non-linear structural dynamics. International Journal for Numerical Methods in Engineering 2001; 50:199-225.
38. Faucher V, Combescure A. A time and space mortar method for coupling linear modal subdomains and non-linear subdomains inexplicit structural dynamics. Computational Methods and Applied Mechanical Engineering 2003; 192:509-533.
39. Faucher V, Combescure A. Local modal reduction in explicit dynamics with domain decomposition. Part 1: extension to subdomains undergoing finite rigid rotations. International Journal for Numerical Methods in Engineering 2004; 60(5):2531-2560.
40. Faucher V, Combescure A. Local modal reduction in explicit dynamics with domain decomposition. Part 2: specific interface treatment when modal subdomains are involved. International Journal for Numerical Methods in Engineering 2004; 61(1):69-95.
41. Bouhaddi N, Fillod R. A method for selecting master DOF in dynamic substructuring using the Guyan condensation method. Computers and Structures 1992; 45(5):941-946.
42. Bouhaddi N, Fillod R. Substructuring by a two level dynamic condensation method. Computers and Structures 1996; 60(3):403-409.
43. Cho M, Kim WB. A coupled finite element analysis of independently modeled substructures by penalty frame method. KSME International Journal 2002; 16(10):1201-1210.
44. Pantano A, Averill RC. A penalty-based finite element interface technology. Computers and Structures 2002; 80:1725-1748.
45. Pantano A, Averill RC. A mesh-independent interface technology for simulation of mixed-mode delamination growth. International Journal of Solids and Structures 2004; 41:3809-3831.
46. Aminpour MA. An assumed stress hybrid 4 node shell element with drilling degrees of freedom. International Journal for Numerical Methods in Engineering 1992; 33:19-38.