Partitioned analysis of coupled mechanical systems. (English) Zbl 0985.76075

Summary: This tutorial article reviews the use of partitioned analysis of coupled dynamical systems. Attention is focused on the computational simulation of systems in which a structure is a major component. Important applications in that class are provided by thermomechanics, fluid-structure interaction and control-structure interaction. In the partitioned solution approach, systems are spatially decomposed into partitions. This decomposition is driven by physical or computational considerations. The solution is separately advanced in time over each partition. Interaction effects are accounted for by transmission and synchronization of coupled state variables. We also discuss recent developments in the use of this approach for multilevel decomposition aimed at massively parallel computation.


76M99 Basic methods in fluid mechanics
74S99 Numerical and other methods in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74F05 Thermal effects in solid mechanics
Full Text: DOI


[1] K.C. Park, C.A. Felippa, Partitioned analysis of coupled systems, in: T. Belytschko, T.J.R. Hughes (Eds.), Computational Methods for Transient Analysis, North-Holland, Amsterdam, 1983, pp. 157-219 (Chapter 3)
[2] Park, K.C.; Felippa, C.A., A variational principle for the formulation of partitioned structural systems, Int. J. numer. methods engrg., 47, 395-418, (2000) · Zbl 0988.74032
[3] Park, K.C.; Felippa, C.A.; Ohayon, R., Partitioned formulation of internal fluid – structure interaction problems via localized Lagrange multipliers, Comput. methods appl. mech. engrg., 190, 2989-3007, (2001) · Zbl 0983.74022
[4] Peaceman, D.W.; Rachford, H.H., The numerical solution of parabolic and elliptic differential equations, SIAM j., 3, 28-41, (1955) · Zbl 0067.35801
[5] Douglas, J.; Rachford, H.H., On the numerical solution of the heat equation in two and three space variables, Trans. amer. math. soc., 82, 421-439, (1956) · Zbl 0070.35401
[6] Yanenko, N.N., The method of fractional steps, (1991), Springer Berlin · Zbl 0099.33502
[7] Richtmyer, R.L.; Morton, K.W., Difference methods for initial value problems, (1967), Interscience New York · Zbl 0155.47502
[8] K.C. Park, C.A. Felippa, J.A. DeRuntz, Stabilization of staggered solution procedures for fluid – structure interaction analysis, in: T. Belytschko, T.L. Geers (Eds.), Computational Methods for Fluid-Structure Interaction Problems, AMD vol. 26, American Society of Mechanical Engineers, New York, 1977, pp. 95-124 · Zbl 0389.76002
[9] Belytschko, T.; Mullen, R., Mesh partitions of explicit – implicit time integration, (), 673-690
[10] Belytschko, T.; Mullen, R., Stability of explicit – implicit mesh partitions in time integration, Int. J. numer. methods engrg., 12, 1575-1586, (1978) · Zbl 0398.65059
[11] Belytschko, T.; Yen, T.; Mullen, R., Mixed methods for time integration, Comput. methods appl. mech. engrg., 17/18, 259-275, (1979) · Zbl 0403.73002
[12] Hughes, T.J.R.; Liu, W.-K., Implicit – explicit finite elements in transient analysis: I. stability theory; II. implementation and numerical examples, J. appl. mech., 45, 371-378, (1978) · Zbl 0392.73077
[13] Hughes, T.J.R.; Pister, K.S.; Taylor, R.L., Implicit – explicit finite elements in nonlinear transient analysis, Comput. methods appl. mech. engrg., 17/18, 159-182, (1979) · Zbl 0413.73074
[14] Hughes, T.J.R.; Stephenson, R.S., Stability of implicit – explicit finite elements in nonlinear transient analysis, Int. J. engrg. sci., 19, 295-302, (1981) · Zbl 0445.73074
[15] Hughes, T.J.R., The finite element method – linear static and dynamic finite element analysis, (1987), Prentice-Hall Englewood Cliffs, NJ
[16] Geers, T.L., Residual potential and approximate methods for three-dimensional fluid – structure interaction, J. acoust. soc. am., 45, 1505-1510, (1971)
[17] Geers, T.L., Doubly asymptotic approximations for transient motions of general structures, J. acoust. soc. am., 45, 1500-1508, (1980) · Zbl 0385.76081
[18] Geers, T.L.; Felippa, C.A., Doubly asymptotic approximations for vibration analysis of submerged structures, J. acoust. soc. am., 73, 1152-1159, (1980)
[19] T.L. Geers, Boundary element methods for transient response analysis, in: T. Belytschko, T.J.R. Hughes (Eds.), Computational Methods for Transient Analysis, North-Holland, Amsterdam, 1983, pp. 221-244 (Chapter 4) · Zbl 0599.76096
[20] Felippa, C.A.; Park, K.C., Staggered transient analysis procedures for coupled-field mechanical systems: formulation, Comput. methods appl. mech. engrg., 24, 61-111, (1980) · Zbl 0453.73091
[21] Felippa, C.A.; DeRuntz, J.A., Finite element analysis of shock-induced hull cavitation, Comput. methods appl. mech. engrg., 44, 297-337, (1984) · Zbl 0526.76069
[22] Park, K.C., Partitioned transient analysis procedures for coupled-field problems: stability analysis, J. appl. mech., 47, 370-376, (1980) · Zbl 0437.73072
[23] Park, K.C.; Felippa, C.A., Partitioned transient analysis procedures for coupled-field problems: accuracy analysis, J. appl. mech., 47, 919-926, (1980) · Zbl 0462.73066
[24] K.C. Park, C.A. Felippa, Recent advances in partitioned analysis procedures, in: R. Lewis, P. Bettess, E. Hinton (Eds.), Numerical Methods in Coupled Problems, Wiley, London, 1984, pp. 327-352 (Chapter 11)
[25] Felippa, C.A.; Geers, T.L., Partitioned analysis of coupled mechanical systems, Eng. comput., 5, 123-133, (1988)
[26] Belvin, W.K.; Park, K.C., Structural tailoring and feedback control synthesis: an interdisciplinary approach, J. guidance, control & dynamics, 13, 3, 424-429, (1990) · Zbl 0704.93025
[27] Park, K.C.; Belvin, W., A partitioned solution procedure for control – structure interaction simulations, J. guidance, control & dynamics, 14, 59-67, (1991) · Zbl 0751.93046
[28] Schuler, J.J.; Felippa, C.A., Superconducting finite elements based on a gauged potential variational principle, I. formulation, II. computational results, J. comput. syst. engrg., 5, 215-237, (1994)
[29] Farhat, C.; Park, K.C.; Pelerin, Y.D., An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems, Comput. methods appl. mech. engrg., 85, 349-365, (1991) · Zbl 0764.73081
[30] C. Farhat, T.Y. Lin, Transient aeroelastic computations using multiple moving frames of reference, in: AIAA Eighth Applied Aerodynamics Conference, Portland, OR, August 1990, AIAA Paper No. 90-3053
[31] Farhat, C.; Roux, F.-X., Implicit parallel processing in structural mechanics, Comput. mech. adv., 2, 1-124, (1994) · Zbl 0805.73062
[32] Farhat, C.; Chen, P.S.; Mandel, J., A scalable Lagrange multiplier based domain decomposition method for implicit time-dependent problems, Int. J. numer. methods engrg., 38, 3831-3854, (1995) · Zbl 0844.73077
[33] M. Lesoinne, C. Farhat, Stability analysis of dynamic meshes for transient aeroelastic computations, in: 11th AIAA Computational Fluid Dynamics Conference, Orlando, FL, July 1993, AIAA Paper No. 93-3325
[34] Farhat, C.; LantĂ©ri, S., Simulation of compressible viscous flows on a variety of MPPs: computational algorithms for unstructured dynamic meshes and performance results, Comput. methods appl. mech. engrg., 119, 35-60, (1994) · Zbl 0847.76065
[35] Maman, N.; Farhat, C., Matching fluid and structure meshes for aeroelastic computations: a parallel approach, Comput. struct., 54, 779-785, (1995)
[36] Piperno, S.; Farhat, C.; Larrouturou, B., Partitioned procedures for the transient solution of coupled aeroelastic problems, Comput. methods appl. mech. engrg., 124, 11-79, (1995) · Zbl 1067.74521
[37] Lesoinne, M.; Farhat, C., Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations, Comput. methods appl. mech. engrg., 134, 71-90, (1996) · Zbl 0896.76044
[38] Farhat, C.; Lesoinne, M.; LeTallec, P., Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity, Comput. methods appl. mech. engrg., 157, 95-114, (1998) · Zbl 0951.74015
[39] Lesoinne, M.; Farhat, C., A higher order subiteration free staggered algorithm for nonlinear transient aeroelastic problems, Aiaa j., 36, 8, 1754-1756, (1998)
[40] J.T. Batina, Unsteady Euler airfoil solutions using unstructured dynamic meshes, in: AIAA 27th Aerospace Sciences Meeting, Reno, NV, January 1989, AIAA Paper No. 89-0115
[41] R.G. Menon, K.C. Park, Parallel solution of control structure interaction for massively actuated structures, in: T. Kawai, et al. (Eds.), Proceedings of the Third World Congress on Computational Mechanics, Chiba, Japan, August 1994, pp. 562-563
[42] Alvin, K.F.; Park, K.C., A second-order structural identification procedure via system theory-based realization, Aiaa j., 32, 397-406, (1994) · Zbl 0810.93021
[43] W.K. Wilkie, K.C. Park, W.K. Belvin, Helicopter dynamic stall suppression using piezoelectric active fiber composite rotor blades, in: Proceedings of the 1998 AIAA SDM Conference, 20-24 April, Long Beach, CA, 1998, Paper No. AIAA-98-2002
[44] Wilkie, W.K.; Belvin, W.K.; Park, K.C., Torsional stiffness optimization of piezoelectric active twist helicopter rotor blades, ()
[45] Carmichael, D.G., Structural modeling and optimization, (1981), Ellis Horwood London
[46] Pister, K.S., Mathematical modeling for structural analysis and design, Nucl. eng. des., 18, 353-375, (1972)
[47] ()
[48] ()
[49] ()
[50] Schrefler, B.A., A partitioned solution procedure for geothermal reservoir analysis, Comm. appl. numer. methods, 1, 47-59, (1985) · Zbl 0587.76150
[51] B.A. Schrefler, Partitioned solution procedure and infinite elements in the mechanics of porous media, in: Proceedings of the VIII Conference on Computational Methods in Structural Mechanics, Iadwisin, Poland, 1987
[52] Lewis, R.W.; Schrefler, B., The finite element method in the static and dynamics of deformation and consolidation of porous media, (1998), Wiley Chichester · Zbl 0935.74004
[53] O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, fourth ed., vol. 2, McGraw-Hill, London, 1991 · Zbl 0991.74002
[54] F. Armero, Numerical analysis of dissipative dynamical systems in solid and fluid mechanics, with a special emphasis on coupled problems, Ph.D. Dissertation, Department of Mechanical Engineering, Stanford University, 1993
[55] Piperno, S.; Farhat, C., Partitioned procedures for the trasnsient solultion of coupled aeroelastic problems – part II: energy transfer analysis and three-dimensional applications, Comput. methods appl. mech. engrg., 190, 3147-3160, (2001) · Zbl 1015.74009
[56] Felippa, C.A.; Park, K.C., Computational aspects of time integration procedures in structural dynamics: I. implementation, J. appl. mech., 45, 595-602, (1978) · Zbl 0393.73090
[57] Stuart, A.M.; Humphries, A.R., Dynamic systems and numerical analysis, (1996), Cambridge University Press Cambridge · Zbl 0869.65043
[58] Warming, R.F.; Hyett, B.J., The modified equation approach to the stability and accuracy of finite difference methods, J. comput. phys., 14, 159-169, (1974) · Zbl 0291.65023
[59] ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.