A variational principle for the formulation of partitioned structural systems

International Journal for Numerical Methods in Engineering

Volumn 47, Issue 1-3, 2000, Pages 395-418

  Park, K C ^a   Felippa, Carlos A ^a  

^a UCB 450   (United States)

Author keywords

Finite element methods; Hybrid principles; Interface potentials; Lagrange multipliers; Multilevel analysis; Non matching meshes; Parallel computation; Partitioned analysis; Structural dynamics; Variational principles

Indexed keywords

FINITE ELEMENT METHOD; LAGRANGE MULTIPLIERS; PARALLEL PROCESSING SYSTEMS; PARTITIONS (BUILDING); STRUCTURAL ANALYSIS;

INDEPENDENT MESH REFINEMENT;

VARIATIONAL TECHNIQUES;

EID: 0033881844     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0207(20000110/30)47:1/3<395::aid-nme777>3.0.co;2-9     Document Type: Article

References (53)

1. Argyris JH, Kelsey S. Energy Theorems and Structural Analysis. Butterworths: London, 1960: reprinted from Aircraft Engineering 26, Oct-Nov 1954 and 27, April-May 1955.
2. Argyris JH, Kelsey S. Energy Theorems and Structural Analysis. Butterworths: London, 1960: reprinted from Aircraft Engineering 26, Oct-Nov 1954 and 27, April-May 1955.
3. Fraeijs de Veubeke BM. Displacement and equilibrium models. In Stress Analysis, Zienkiewicz OC, Hollister G. (eds). Wiley: London, 1965; 145-197.
4. Washizu K. Variational Methods in Elasticity and Plasticity. Pergamon Press: New York, 1968.
5. Pian THH, Tong P. Basis of finite element methods for solid continua. International Journal for Numerical Methods in Engineering 1969; 1:3-29.
6. Pian THH. Finite element methods by variational principles with relaxed continuity requirements. In Variational Methods in Engineering, vol. 1, Brebbia CA, Tottenham H. (eds). Southampton University Press: Southampton, U.K., 1973.
7. Atluri SN. On 'hybrid' finite-element models in solid mechanics. In Advances in Computer Methods for Partial Differential Equations, Vichnevetsky R (ed.). AICA: Rutgers University, 1975; 346-356.
8. Oden JT, Reddy JN. Variational Methods in Theoretical Mechanics. Springer: Berlin, 1982.
9. Reddy JN. Energy and Variational Methods in Applied Mechanics. Wiley/lnterscience: New York, 1984.
10. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987.
11. Zienkiewicz OC, Taylor RE. The Finite Element Method (4th edn), vol 1. McGraw-Hill: New York; 1989.
12. Felippa CA. A survey of parameterized variational principles and applications to computational mechanics. Computer Methods in Applied Mechanics and Engineering 1994; 113:109-139.
13. Pian THH. Derivation of element stiffness matrices by assumed stress distributions. AIAA Journal 1964; 2: 1333-1336.
14. Hermann LR. A bending analysis for plates, In Proceedings 1st Conference on Matrix Methods in Structural Mechanics, AFFDL-TR-66-80, Air Force Institute of Technology, Dayton, Ohio, 1966; 577-604.
15. Fraeijs de Veubeke BM. A new variational principle for finite elastic displacements. International Journal of Engineering Science 1972; 10:745-763, .
16. Fraeijs de Veubeke BM. Variational principles and the patch test. International Journal for Numerical Methods in Engineering 1974; 8:783-801.
17. Courant R, Hilbert D. Methods of Mathematical Physics, vol I. Interscience: New York, 1953.
18. Sewell MJ. Maximum and Minimum Principles. Cambridge: England, 1987.
19. Lagrange J-L. Mécanique Analytique. 1788 (1965 edn. complète), 2 vols. Blanchard: Paris, 1965.
20. Lanczos C. The Variational Principles of Mechanics (4th edn.), Dover: New York, 1970.
21. Dugas R. A History of Mechanics. Dover: New York, 1988; 332-338.
22. Park KC, Felippa CA. A variational framework for solution method developments in structural mechanics. Journal of Applied Mechanics 1998; 65(1):242-249.
23. Fraeijs de Veubeke BM. Matrix structural analysis: Lecture Notes for the International Research Seminar on the Theory and Application of Finite Element Methods. Calgary, Alberta, Canada, July-August 1973; reprinted in B. M. Fraeijs de Veubeke Memorial Volume of Selected Papers, Geradin M (ed.). Sitthoff & Noordhoff, Alphen aan den Rijn: The Netherlands, 1980; 509-568.
24. Fraeijs de Veubeke BM. Matrix structural analysis: Lecture Notes for the International Research Seminar on the Theory and Application of Finite Element Methods. Calgary, Alberta, Canada, July-August 1973; reprinted in B. M. Fraeijs de Veubeke Memorial Volume of Selected Papers, Geradin M (ed.). Sitthoff & Noordhoff, Alphen aan den Rijn: The Netherlands, 1980; 509-568.
25. Farhat C, Roux F-X. A method of finite element tearing and interconnecting and its parallel solution algorithm International Journal for Numerical Methods in Engineering 1991; 32:1205-1227.
26. Farhat C, Roux F-X. Implicit parallel processing in structural mechanics. Computational Mechanics Advances 1994; 2:1-124.
27. Farhat C, Mandel J. The two-level FETI method for static and dynamic plate problems - Part I: an optimal iterative solver for biharmonic systems. Computer Methods in Applied Mechanics and Engineering 1998; 155:129-151.
28. Farhat C, Chen P-S, Mandel J, Roux F-X. The two-level FETI method for static and dynamic plate problems -Part II: Extension to shell problems, parallel implementation and performance results. Computer Methods in Applied Mechanics and Engineering 1998; 155:153-179.
29. Prager W. Variational principles for linear elastostatics for discontinuous displacements, strains and stresses. In Recent Progress in Applied Mechanics, The Folke-Odgvist Vol. Broger B, Huit J, Niordson F (eds). Almqusit and Wiksell: Stockholm, 1967; 463-474.
30. Tong P. New displacement finite element method for solid continua. International Journal for Numerical Methods in Engineering 1970; 2:73-83.
31. Bergan PG, Nygåard MK. Finite elements with increased freedom in choosing shape functions. International Journal for Numerical Methods in Engineering 1984; 20:643-664.
32. Felippa CA. Parametrized multifield variational principles in elasticity: II. Hybrid functionals and the Free Formulation. Communications in Applied Numerical Methods 1989; 5:89-98.
33. Bernardi C, Maday Y, Patera AT. A new nonconforming approach to domain decomposition: the mortar element method. Technical Report, Université Pierre at Marie Curie, Paris, France, January 1990.
34. Gumaste U, Park KC, Alvin KF. A family of implicit partitioned time integration algorithms for parallel analysis of heterogeneous structural systems. Computational Mechanics, to appear 1999.
35. Felippa CA, Park KC, Justino MR. The construction of free-free flexibility matrices as generalized stiffness inverses. Computers and Structures 1998; 68:411-418.
36. Justino MR, Park KC, Felippa CA. An algebraically partitioned FETI method for parallel structural analysis: implementation and numerical performance evaluation. International Journal for Numerical Methods in Engineering 1997; 40:2739-2758.
37. Park KC, Justino MR, Felippa CA. An algebraically partitioned FETI method for parallel structural analysis: algorithm description. International Journal for Numerical Methods in Engineering 1997; 40:2717-2737.
38. Park KC, Reich GW, Alvin KF. Damage detection using localized flexibilities. In Structural Health Monitoring, Current Status and Perspectives, Chang F-K (ed.). Technomic Pub., 1997; 125-139.
39. Park KC, Felippa CA. A flexibility-based inverse algorithm for identification of structural joint properties. Proceedings of ASME Symposium on Computational Methods on Inverse Problems, Anaheim, CA, 15-20 November 1998.
40. Park KC, Kim N-I. A theory of localized vibration control via partitioned LQR synthesis. Center for Aerospace Structures, Report No. CU-CAS-98-13, University of Colorado, Boulder, CO, July 1998;
41. also Proceedings XXI Congresso Nacional de Matematica Applicada e Computacional, Caxambu, MG, Brazil, September 1998.
42. Pestel EC, Leckie FA. Matrix Methods in Elastomechanics. McGraw-Hill: New York, 1963.
43. Kaveh A. Recent developments in the force method of structural analysis. Applied Mechanics Reviews 1992; 45(9):401-418.
44. Felippa CA. Will the force method come back? Journal of Applied Mechanics 1987; 54:728-729.
45. Felippa CA. Parametric unification of matrix structural analysis: classical formulation and d-connected mixed elements. Finite Elements Analysis Design 1995; 21:45-74.
46. Felippa CA, Park KC. A direct flexibility method. Computer Methods in Applied Mechanics and Engineering 1997; 149:319-337.
47. Gallagher RH. Private communication to Park KC, 1997.
48. Felippa CA. Recent developments in parametrized variational principles for mechanics. Computational Mechanics 1996; 18:159-174.
49. Park KC, Reich GW. A theory for strain-based structural system identification. Proceedings of 9th International Conference on Adaptive Structures and Technologies, 14-16 October 1998, Cambridge, MA.
50. Park KC, Reich GW. A procedure to determine accurate rotations from measured strains and displacements for system identification. Center for Aerospace Structures, Report No. CU-CAS-98-16, University of Colorado, Boulder, CO, July 1998; Proceedings of 17th International Modal Analysis Conference, 8-11 February 1999, Kissimmee, FL.
51. Park KC, Reich GW. A procedure to determine accurate rotations from measured strains and displacements for system identification. Center for Aerospace Structures, Report No. CU-CAS-98-16, University of Colorado, Boulder, CO, July 1998; Proceedings of 17th International Modal Analysis Conference, 8-11 February 1999, Kissimmee, FL.
52. Park KC, Felippa CA, Ohayon R. Partitioned formulation of internal fluid-structure interaction problems via localized Lagrange multipliers. Center for Aerospace Structures, Report No. CU-CAS-98-14, University of Colorado, Boulder, CO, July 1998; Computer Methods in Applied Mechanics and Engineering, 1999, to appear.
53. Park KC, Felippa CA, Ohayon R. Partitioned formulation of internal fluid-structure interaction problems via localized Lagrange multipliers. Center for Aerospace Structures, Report No. CU-CAS-98-14, University of Colorado, Boulder, CO, July 1998; Computer Methods in Applied Mechanics and Engineering, 1999, to appear.