Ross, Michael R.; Felippa, Carlos A.; Park, K. C.; Sprague, Michael A. Treatment of acoustic fluid-structure interaction by localized Lagrange multipliers: formulation. (English) Zbl 1194.74471 Comput. Methods Appl. Mech. Eng. 197, No. 33-40, 3057-3079 (2008). Summary: A new concept is presented for modeling the dynamic interaction between an acoustic fluid and an elastic structure. The coupling of this multiphysics system is done by inserting a kinematic interface frame between the fluid and the structure, and using node-collocated Lagrange multipliers to connect the frame to each subsystem. The time-domain response analysis is performed by a partitioned analysis procedure. The main advantages of this localized Lagrange multiplier (LLM) primal-dual coupling method are: complete localization of the structure and fluid subsystems, elimination of the conventional predictor in the partitioned time integration method, and the ability to accommodate non-matching meshes. The standard Newmark time integrator is used on both the fluid and structure models. It is shown that if the integrator is A-stable and second-order accurate for a monolithic treatment, it retains those properties for both Mortar and LLM partitioned solution procedures. Infinite and finite piston problems are used to explain and verify the methodology. A sequel paper under preparation presents and discusses a set of benchmark and application examples that involve the response of existing dams to seismic excitation. Cited in 22 Documents MSC: 74S05 Finite element methods applied to problems in solid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76M10 Finite element methods applied to problems in fluid mechanics Keywords:coupled systems; fluid-structure interaction; earthquake dynamics; partitioned analysis; non-matching meshes; Lagrange multipliers PDFBibTeX XMLCite \textit{M. R. Ross} et al., Comput. Methods Appl. Mech. Eng. 197, No. 33--40, 3057--3079 (2008; Zbl 1194.74471) Full Text: DOI References: [1] Berenger, J. P., A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114, 185-200 (1990) · Zbl 0814.65129 [2] C. Bernardi, Y. Maday, A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method. Technical Report, Université Pierre at Marie Curie, Paris, France, 1990.; C. Bernardi, Y. Maday, A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method. Technical Report, Université Pierre at Marie Curie, Paris, France, 1990. · Zbl 0797.65094 [3] Bleich, H. H.; Sandler, I. S., Interaction between structures and bilinear fluids, Int. J. Solids Struct., 6, 617-639 (1970) · Zbl 0195.27202 [4] Blom, F., A monolithical fluid-structure interaction algorithm applied to the piston problem, Comput. Methods Appl. Mech. Engrg., 167, 369-391 (1998) · Zbl 0948.76046 [5] Brenan, H. H.; Campbell, S. L.; Petzold, L. R., Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (1989), North Holland: North Holland New York · Zbl 0699.65057 [6] Chen, H.; Taylor, R. L., Vibration analysis of fluid-solid systems using a finite element displacement formulation, Int. J. Numer. Methods Engrg., 29, 683-698 (1990) · Zbl 0724.73173 [7] Chopra, A. K., Dynamics of Structures: Theory and Applications to Earthquake Engineering (1995), Prentice Hall, Inc.: Prentice Hall, Inc. New Jersey · Zbl 0842.73001 [8] Clough, R. W.; Penzien, J., Dynamics of Structures (1975), McGraw-Hill: McGraw-Hill New York · Zbl 0357.73068 [9] Cook, R. D.; Malkus, D. S.; Plesha, M. E.; Witt, R. J., Concepts and Applications of Finite Element Analysis (2002), John Wiley and Sons: John Wiley and Sons New York [10] B. El-Aidi, Nonlinear Earthquake Response of Concrete Gravity Dam Systems. Ph.D. Thesis, California Institute of Technology, Pasadena, 1989.; B. El-Aidi, Nonlinear Earthquake Response of Concrete Gravity Dam Systems. Ph.D. Thesis, California Institute of Technology, Pasadena, 1989. [11] Farhat, C.; Lesoinne, M.; Maman, N., Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution, Int. J. Numer. Methods Engrg., 21, 807-835 (1995) · Zbl 0865.76038 [12] Farhat, C.; Piperno, S.; Larrouturu, B., Partitioned procedures for the transient solution of coupled aeroelastic problems; Part I: model problem, theory and two-dimensional application, Comput. Methods Appl. Mech. Engrg., 124, 79-112 (1995) · Zbl 1067.74521 [13] 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 [14] Felippa, C. A., A family of early-time approximations for fluid-structure interaction, J. Appl. Mech., 47, 4, 703-708 (1980) · Zbl 0453.73056 [15] Felippa, C. A.; DeRuntz, J. A., Finite element analysis of shock-induced hull cavitiation, Comput. Methods Appl. Mech. Engrg., 44, 297-337 (1984) · Zbl 0526.76069 [16] Felippa, C. A.; Ohayon, R., Mixed variational formulation of finite element analysis of acoustoelastic/slosh fluid-structure interaction, J. Fluids Struct., 4, 35-57 (1990) · Zbl 0732.73069 [17] Felippa, C. A.; Park, K. C.; Farhat, C., Partitioned analysis of coupled mechanical systems, Comput. Methods Appl. Mech. Engrg., 190, 3247-3270 (2001) · Zbl 0985.76075 [18] Felippa, C. A., Construction of customized mass-stiffness pairs using templates, ASCE J. Aerospace, 19, 241-258 (2006) [19] Graff, K. F., Wave Motion in Elastic Solids (1975), Oxford University Press: Oxford University Press New York · Zbl 0314.73022 [20] Hamdi, M. A.; Ousset, Y., A displacement method for the analysis of vibrations of coupled fluid-structure systems, Int. J. Numer. Methods Engrg., 13, 139-150 (1978) · Zbl 0384.76060 [21] Hughes, T. J.R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (1987), Prentice Hall: Prentice Hall Englewood Cliffs, NJ, Reprinted by Dover, New York, 2000 · Zbl 0634.73056 [22] L.A. Jakobsen, A finite element approach to analysis and sensitivity analysis of time dependent fluid-structure interaction systems. Ph.D. Thesis, Aalborg University, Denmark, 2002.; L.A. Jakobsen, A finite element approach to analysis and sensitivity analysis of time dependent fluid-structure interaction systems. Ph.D. Thesis, Aalborg University, Denmark, 2002. [23] Kim, Y.; Yun, C., A spurious free four-node displacement-based fluid element for fluid-structure interaction analysis, Engrg. Struct., 19, 8, 665-678 (1997) [24] Kreyszig, E., Advanced Engineering Mathematics (1999), John Wiley and Sons, Inc.: John Wiley and Sons, Inc. New York [25] Lighthill, J., Waves in Fluids (1978), Cambridge Univ. Press: Cambridge Univ. Press Cambridge, UK · Zbl 0375.76001 [26] Lysmer, J.; Kuhlemeyer, R. L., Finite dynamic model for infinite media, J. Engrg. Mech. Division, 95, EM4, 859-876 (1969), Proc. ASCE [27] Michler, C.; Hulshoff, S. J.; van Brummelen, E. H.; de Borst, R., A monolithic approach to fluid-structure interaction, Comput. Fluids, 33, 839-848 (2004) · Zbl 1053.76042 [28] Mindlin, R. D.; Bleich, H. H., Response of an elastic cylindrical shell to a transverse step shock wave, J. Appl. Mech., 20, 180-195 (1953) · Zbl 0050.18807 [29] Morand, C.; Ohayon, R., Fluid-Structure Interaction (1995), Wiley: Wiley Chichester, UK [30] R.E. Newton, Effects of cavitation on underwater shock loading - Part 1. Technical Report NPS-69-78-013, Naval Postgraduate School, Monterey, CA, 1978.; R.E. Newton, Effects of cavitation on underwater shock loading - Part 1. Technical Report NPS-69-78-013, Naval Postgraduate School, Monterey, CA, 1978. [31] R.E. Newton, Effects of cavitation on underwater shock loading – axisymmetric geometry. Technical Report NPS-69-78-017PR, Naval Postgraduate School, Monterey, CA, 1978.; R.E. Newton, Effects of cavitation on underwater shock loading – axisymmetric geometry. Technical Report NPS-69-78-017PR, Naval Postgraduate School, Monterey, CA, 1978. [32] R.E. Newton, Finite element analysis of shock-induced cavitation. ASCE, Spring Convention, 1980, Preprint 80-110.; R.E. Newton, Finite element analysis of shock-induced cavitation. ASCE, Spring Convention, 1980, Preprint 80-110. [33] R.E. Newton, Effects of cavitation on underwater shock loading – plane problem. Technical Report NPS-69-81-001, Naval Postgraduate School, Monterey, CA, 1981.; R.E. Newton, Effects of cavitation on underwater shock loading – plane problem. Technical Report NPS-69-81-001, Naval Postgraduate School, Monterey, CA, 1981. [34] Park, K. C.; Felippa, C. A.; DeRuntz, J. A., Stabilization of staggered solution procedures for fluid-structure interaction analysis, (Belytschko, T.; Geers, T. L., Computational Methods for Fluid-Structure Interaction Problems. Computational Methods for Fluid-Structure Interaction Problems, AMD, vol. 26 (1977), American Society of Mechanical Engineers, ASME: American Society of Mechanical Engineers, ASME New York), 95-124 · Zbl 0389.76002 [35] Park, K. C.; Felippa, C. A., Partitioned analysis of coupled systems, (Belytschko, T.; Hughes, T. J.R., Computational Methods for Transient Analysis (1983), North-Holland: North-Holland Amsterdam-New York), (Chapter 3) · Zbl 0546.73063 [36] 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 [37] Park, K. C.; Felippa, C. A.; Ohayon, R., Partitioned formulation of internal fluid-structure interaction problems by localized Lagrange multipliers, Comput. Methods Appl. Mech. Engrg., 190, 2989-3007 (2001) · Zbl 0983.74022 [38] Park, K. C.; Felippa, C. A.; Rebel, G., A simple algorithm for localized construction of nonmatching structural interfaces, Int. J. Numer. Methods Engrg., 53, 2117-2142 (2002) · Zbl 1169.74653 [39] Park, K. C.; Felippa, C. A.; Rebel, G., Interfacing nonmatching finite element discretizations: the zero moment rule, (Wall, W. A.; Bleitzinger, K.-U.; Schweizerhof, K., Trends in Computational Mechanics (2001), CIMNE: CIMNE Barcelona, Spain), 355-367 [40] Park, K. C.; Felippa, C. A.; Ohayon, R., Reduced order modeling in coupled systems: formulations and computational algorithms, (Ibrahimbegovic, A.; Brank, B., Engineering Structures Under Extreme Conditions (2006), IOS Press: IOS Press Amsterdam), 267-289 [41] Piperno, S.; Farhat, C., Partitioned procedures for the transient solution of coupled aeroelastic problems - Part II energy transfer analysis and three-dimensional applications, Comput. Methods Appl. Mech. Engrg., 190, 3147-3170 (2001) · Zbl 1015.74009 [42] Prager, W., Variational principles for linear elastostatics for discontinuous displacements, strains and stresses, (Broger, B.; Hult, J.; Niordson, F., Recent Progress in Applied Mechanics, The Folke-Odgvist Volume (1967), Almqusit and Wiksell: Almqusit and Wiksell Stockholm), 463-474 [43] Qi, Q.; Geers, T. L., Evaluation of perfectly matched layers for computational acoustics, J. Comput. Phys., 139, 166-183 (1997) · Zbl 0903.76073 [44] Rebel, G.; Park, K. C.; Felippa, C. A., A contact formulation based on localized Lagrange multipliers: formulation and applications to two-dimensional problems, Int. J. Numer. Methods Engrg., 54, 263-297 (2002) · Zbl 1022.74031 [45] M.R. Ross, Coupling and simulation of acoustic fluid-structure interaction systems using localized Lagrange multipliers. Ph.D. Thesis, University of Colorado at Boulder, 2006. <http://caswww.colorado.edu/courses/FSI.d>; M.R. Ross, Coupling and simulation of acoustic fluid-structure interaction systems using localized Lagrange multipliers. Ph.D. Thesis, University of Colorado at Boulder, 2006. <http://caswww.colorado.edu/courses/FSI.d> [46] M.R. Ross, M.A. Sprague, C.A. Felippa, K.C. Park, Treatment of acoustic fluid structure interaction by localized Lagrange multipliers applications, Technical Report CU-CAS-TR-02, College of Engineering, University of Colorado, Boulder, CO, 2008, Comput. Methods Appl. Mech. Engrg., to be submitted for publication.; M.R. Ross, M.A. Sprague, C.A. Felippa, K.C. Park, Treatment of acoustic fluid structure interaction by localized Lagrange multipliers applications, Technical Report CU-CAS-TR-02, College of Engineering, University of Colorado, Boulder, CO, 2008, Comput. Methods Appl. Mech. Engrg., to be submitted for publication. · Zbl 1194.74471 [47] Sprague, M. A.; Geers, T. L., A spectral-element method for modeling cavitation in transient fluid-structure interaction, Int. J. Numer. Methods Engrg., 60, 2467-2499 (2004) · Zbl 1075.74696 [48] Wilson, E. L.; Khalvati, M., Finite elements for the dynamic analysis of fluid-solid systems, Int. J. Numer. Methods Engrg., 19, 1657-1668 (1983) · Zbl 0519.76094 [49] X. Yue, Development of joint elements and solution algorithms for dynamic analysis of jointed structures. Ph.D. Thesis, University of Colorado at Boulder, 2002.; X. Yue, Development of joint elements and solution algorithms for dynamic analysis of jointed structures. Ph.D. Thesis, University of Colorado at Boulder, 2002. [50] Zienkiewicz, O. C.; Paul, D. K.; Hinton, E., Cavitation in fluid-structure response (with particular reference to dams under earthquake loading), Earthquake Engrg. Struct. Dyn., 11, 463-481 (1983) 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.