×

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.

MSC:

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
PDFBibTeX XMLCite
Full Text: DOI

References:

[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: Springer Berlin · Zbl 0099.33502
[7] Richtmyer, R. L.; Morton, K. W., Difference Methods for Initial Value Problems (1967), Interscience: Interscience New York · Zbl 0155.47502
[9] Belytschko, T.; Mullen, R., Mesh partitions of explicit-implicit time integration, (Bathe, K.-J.; Oden, J. T.; Wunderlich, W., Formulations and Computational Algorithms in Finite Element Analysis (1976), MIT Press: MIT Press Cambridge), 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: Prentice-Hall Englewood Cliffs, NJ · Zbl 0634.73056
[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)
[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
[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
[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
[34] Farhat, C.; Lantéri, 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)
[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
[44] Wilkie, W. K.; Belvin, W. K.; Park, K. C., Torsional stiffness optimization of piezoelectric active twist helicopter rotor blades, (Hagood, N., Adaptive Structures and Technologies (1999), Technomic: Technomic Lancaster, PA)
[45] Carmichael, D. G., Structural Modeling and Optimization (1981), Ellis Horwood: Ellis Horwood London
[46] Pister, K. S., Mathematical modeling for structural analysis and design, Nucl. Eng. Des., 18, 353-375 (1972)
[47] (Hinton, E.; Bettess, P.; Lewis, R. W., Numerical Methods in Coupled Problems (1981), Pineridge Press: Pineridge Press Swansea, UK) · Zbl 0473.00013
[48] (Lewis, R. W., Numerical Methods in Coupled Problems (1984), Wiley: Wiley London)
[49] (Lewis, R. W., Numerical Methods for Transient and Coupled Problems (1987), Wiley: Wiley London)
[50] Schrefler, B. A., A partitioned solution procedure for geothermal reservoir analysis, Comm. Appl. Numer. Methods, 1, 47-59 (1985) · Zbl 0587.76150
[52] Lewis, R. W.; Schrefler, B., The Finite Element Method in the Static and Dynamics of Deformation and Consolidation of Porous Media (1998), Wiley: Wiley Chichester · Zbl 0935.74004
[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 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] (Kloeden, P. E.; Palmer, K. J., Chaotic Numerics (1994), American Mathematical Society: American Mathematical Society Providence, RI)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.