Force state maps using reproducing kernel particle method and kriging based functional representations

CMES - Computer Modeling in Engineering and Sciences

Volumn 32, Issue 3, 2008, Pages 123-159

  Namdeo, Vikas ^a   Manohar, C S ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Force state map; Kriging; RKPM; System identification

Indexed keywords

DYNAMICAL SYSTEMS; FLUID STRUCTURE INTERACTION; IDENTIFICATION (CONTROL SYSTEMS); LINEAR SYSTEMS; MAPS; NONLINEAR SYSTEMS; OPTICAL PROJECTORS; SCHRODINGER EQUATION;

DEGREES OF FREEDOMS; DO-MAINS; FIXED POINTS; FORCE STATE MAP; FUNCTIONAL REPRESENTATIONS; ILLUSTRATIVE EXAMPLES; KRIGING; KRIGING TECHNIQUES; LIMIT CYCLES; MAPPING TECHNIQUES; NON LINEARITIES; NONLINEAR DYNAMICAL SYSTEMS; RANDOM FIELDS; REPRODUCING KERNEL PARTICLE METHODS; RKPM; SYSTEM IDENTIFICATION; SYSTEM PARAMETERS; TIME HISTORIES;

SYSTEM STABILITY;

EID: 56849120027     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (61)

1. Al-Hadid, M.A.; Wright, J.R. (1989): Developments in the force state mapping techniques for nonlinear systems and the extension to the location of nonlinear elements in a lumped parameter system, Mechanical Systems and Signal Processing, 3(3), 269-290.
2. Al-Hadid, M.A.; Wright, J.R. (1990): Application of the force-state mapping approach to the identification of nonlinear systems, Mechanical Systems and Signal Processing, 4(6), 463-482.
3. Al-Hadid, M.A.; Wright, J.R. (1992): Estimation of mass and modal mass in the identification of nonlinear single and multi-degree of freedom systems using the force state mapping technique, Mechanical Systems and Signal Processing, 6(4), 383-401.
4. Aluru, N.R. (2000): A point collocation method based on reproducing kernel approximations, International Journal of Numerical Methods in Engineering, 47(6), 1083-1121.
5. Atluri, S.N. (2004): Methods fo computer modeling in engineering and the sciences, Vol 1, Tech Science Press, Forsyth.
6. Atluri, S.N. (2005): The meshless method (MLPG) for domain and BIE discretization, Tech Science Press, Forsyth.
7. Atluri, S.N.; Liu, H.T.; Han, Z.D. (2006a): Meshless local Petrov-Galerkin (MLPG) mixed collocation method for elasticity problems, CMES: Computer Modeling in Engienering & Science, 14(3), 141-152.
8. Atluri, S.N.; Liu, H.T.; Han, Z.D. (2006b): Meshless local Petrov-Galerkin (MLPG) mixed finite difference method for solid mechanics, CMES: Computer Modeling in Engienering & Science, 15(1), 1-16.
9. Belytschko, T.; Krongauz, Y.; Organ, D.; Fleming, M.; Krysl, P. (1996): Meshless methods: An overview and recent developments, Computer Methods in Applied Mechanics and Engineering, 139(1-4), 3-47.
10. Brown, R.G.; Hwang, P.Y.C. (1992): Introduction to random signals and applied Kaiman filtering, 2nd edition, John Wiley and Sons, Inc., New York.
11. Chen, J.; Pan, C.;Wu, C.T.; Liu, W.K. (1996): Reproducing kernel particle methods for large deformation analysis of nonlinear structures, Computer Methods in Applied Mechanics and Engineering, 139(1-4), 195-227.
12. Chen, J. Han, W.; You, Y.; Meng, X. (2003): A reproducing kernel method with nodal interpolation property, International Journal of Numerical Methods in Engineering, 56(7), 935-960.
13. Choi, S.; Marcozzi, M.D. (2004): On the application of MQ-RBF to the valuation of derivative securities, CMES: Computer Modeling in Engineering & Science, 5(3), 201-212.
14. Crawley, E.F.; O'Donnell, K.J. (1986): Identification of nonlinear system parameters in joints using the force-state mapping technique, AIAA Journal, 24, 659-667.
15. Crawley, E.F.; Aubert, A.C. (1986): Identification of nonlinear structural elements by force state mapping, AIAA Journal, 24(1), 155-162.
16. Crawley, E.F.; O'Donnell, K.J. (1987a): A procedure for calculating the damping in multielement space structures, Acta Astronautica, 15(12), 987-996.
17. Crawley, E.F.; O'Donnell, K.J. (1987b): Forcestate mapping identification of nonlinear joints, AIAA Journal, 25(7), 1003-1010.
18. Duym, S.W.R.; Schoukens, J.F.M. (1996): Selection of optimal force-state map, Mechanical Systems and Signal Processing, 10(6), 683-695.
19. Han, Z.D.; Rajendran, A.M.; Atluri, S.N. (2005): Meshless local Petrov-Galerkin (MLPG) approaches for solving nonlinear problems with large deformations and rotations, CMES: Computer Modeling in Engineering & Science, 10(1),1-12.
20. Hon, Y.C.; Ling, L.; Liew, K.M. (2005): Numerical analysis of parameters in a laminated beam model by radial basis functions, CMC-Computers, Materials, & Continua, 2(1), 39-50.
21. Joyot, P.; Trunzler, J.; Chinesta, F. (2006): Meshless and generalized finite element methods: A survey of some major results, in: M Griebel, M.A. Schweitzer (Eds.), Meshfree Methods for Partial Differential II Equations, Lecture Notes in Computational Science and Engineering, 43, Springer-Verlag, Berlin, 93-107.
22. Jun, S.; Liu, W.K.; Belytschko, T. (1998): Explicit reproducing kernel particle methods for large deformation problems, International Journal of Numerical Methods in Engineering, 41(1), 137-166.
23. Kaymaz, I. (2005): Application of kriging method to structural reliability problems, Structural Safety, 27, 133-151.
24. Kerschen, G.; Worden, K.; Vakakis, A.F.; Golinval, J.C. (2006): Past, present and future of nonlinear system identification in structural dynamics, Mechanical Systems and Signal Processing, 20 (3), 505-592.
25. Kim, W.J.; Park, Y.S. (1994): Nonlinear joint parameter identification by applying the forcestate mapping technique in the frequency domain, Mechanical Systems and Signal Processing, 8(5), 519-529.
26. Krongauz, Y. Belytschko, T. (1998): EFG approximation with discontinuous derivatives (Element free Galerkin), International Journal for Numerical Methods in Engineering, 41(7), 1215-1233.
27. La Rocca, A.; Power, H.; La Rocca, V.; Morale, M. (2005): A meshless approach based upon radial basis function Hermite collocation method for predicting the cooling and freezing times of foods, CMC: Computers, Materials, & Continua, 2(4), 239-250.
28. Le, P.; Mai-Duy, N. Tran-Cong, T.; Baker, G. (2008): A meshless modeling of dynamic strain localization in quasi-bnrittle materials using radial basis function networks, CMES: Computer Modeling in Engineering & Science, 125(1), 43-66.
29. Libre, N.A.; Emdadi, A.; Kansa, E.J.; Rahimian, M.; Shekarchi, M. (2008): A stabilized RBF collocation scheme for Neumann type boundary value problems, CMES: Computer Modeling in Engineering & Science, 124(1), 61-80.
30. Li, S.; Liu, W.K. (2002): Meshfree and particle methods and their applications, Applied Mechanics Reviews, ASME, 55(1), 1-34.
31. Liu, G.R. (2003): Meshfree methods, CRC Press, Boca Raton.
32. Liu, W.K.; Jun, S.; Zhang, Y.F. (1995a): Reproducing kernel particle methods, International Journal for Numerical Methods in Fluids, 20, 1081-1106.
33. Liu, W.K.; Jun, S.; Li, S.; Adee, J.; Belytschko, T. (1995b): Reproducing kernel particle methods for structural dynamics, International Journal of Numerical Methods in Engineering, 38(10), 1655-1679.
34. Long, S.Y.; Liu, K.Y.; Li, G.Y. (2008): An analysis of elasto-plastic fracture problem by the meshless local Ptrov-Galerkin method, CMES: Computer Modeling in Engineering & Science, 128(3), 203-216.
35. Lophaven, S.N.; Nielsen, H.B.; Sndergaard, J. (2002): DACE - A Matlab kriging toolbox, Informatics and Mathematical Modelling, Technical University of Denmark, DTU.
36. Lu, H. Kim, D.S.; Liu, W.K. (2005): Treatment of discontinuity in the reproducing kernel element method, International Journal of Numerical Methods in Engineering, 63, 241-255.
37. Ma, Q.W. (2008): A new meshless interpolation scheme for MLPG-R method, CMES: Computer Modeling in Engineering & Science, 123(2), 75-89.
38. Manohar, CS.; Venkatesha, S. (2006): Development of experimental setups for earthquake engineering education, National Program on Earthquake Engineering Education MHRD, Govt, of India.
39. Masri, S.F.; Sassi, H.; Caughey, T.K. (1982): Nonparametric identification of nearly arbitrary nonlinear systems, ASME Journal of Applied Mechanics, 49, 619-628.
40. Masri, S.F.; Caughey, T.K. (1979): A nonparametric identification technique for nonlinear dynamic problems, ASME Journal of Applied Mechanics, 46,433-447.
41. Masri, S.F.; Miller, R.K.; Saud, A.F.; Caughey, T.K. (1987a): Identification of nonlinear vibrating structures: Part I-Formulation, ASME Journal of Applied Mechanics, 54, 918-922.
42. Masri, S.F. Miller, R.K.; Saud, A.F.; Caughey, T.K. (1987b): Identification of nonlinear vibrating structures: Part II Applications, ASME Journal of Applied Mechanics, 54, 923-929.
43. Meskell, C.; Fitzpatrick, J.A. (2002): Errors in parameter estimates from the force state mapping technique for free response due to phase distortion, Journal of Sound and Vibration, 252(5), 967-974.
44. Meskell, C.; Fitzpatrick, J.A.; Rice, H.J. (2001): Application of force state mapping to a nonlinear fluid-elastic system, Mechanical Systems and Signal Processing, 15(1), 75-85.
45. Meskell, C.; Fitzpatrick, J.A. (2003): Investigation of the nonlinear behavior of damping controlled fluid-elastic instability in a normal triangular tube array, Journal of Fluids and Structures, 18(5), 573-593.
46. Namdeo, V. (2007): Novel strategies for identification of nonlinear structures based on particle filtering and force state map construction, MSc(Engg) thesis, Department of Civil Engineering, Indian Institute of Science, Bangalore.
47. Nie, Y.F.; Atluri, S.N.; Zuo, C.W. (2006): The optimal radius of the support oif radial weights used in moving least squares approximation, CMES: Computer Modeling in Engineering & Science, 12(2), 137-147.
48. Orsini, P.; Power, H.; Morvan, H. (2008): Improving volume element methods by meshless radial basis function techniques, CMES: Computer Modeling in Engineering & Science, 123(3), 187-207.
49. Panda, S.S.; Manohar, C.S. (2008): Application of meta-modeling techniques in finite element based reliability analysis of engineering structures, CMES: Computer Modeling in Engineering and Sciences, 128(3), 161-184.
50. Phani, A.S.; Venkatraman, K. (2003): Vibration control of sandwich beams using electrorheological fluids, Mechanical Systems and Signal Processing, 17(5), 1083-1095.
51. Sacks, J.; Welch, W.J.; Mitchell, T.J.; Wynn, H.P. (1989): Design and Analysis of computer experiments, Statistical Science, 4(4), 409-423.
52. Santner, T.J.; Williams, B.H.; Notz, W.I. (2003): The design and analysis of computer experiments, Springer, New York.
53. Shaw, A.; Roy, D. (2007): A novel form of reproducing kernel interpolation method with applications to nonlinear mechanics, CMES: Computer Modeling in Engineering and Sciences, 19(1), 69-98.
54. Shin, K.; Hammond, J.K. (1998a): Force-state mapping method of a chaotic dynamical system, Journal of Sound and Vibration, 218(3), 405-418.
55. Shin, K.; Hammond, J.K. (1998b): Pseudo force state mapping method: incorporation of the embedding and force state mapping methods, Journal of Sound and Vibration, 211(5), 918-922.
56. Simmons, C.F. (1972): Differential equations with applications and historical notes, McGraw-Hill, Inc., New York.
57. Sladek, J.; Sladek, V.; Wen, P.H.; Aliabadi, M.H. (2006): Meshless Local Petrov-Galerkin (MLPG) method for shear deformable shells analysis, CMES: Computer Modeling in Engineering & Science, 13(2), 103-117.
58. Yuan, W.; Chen, P.; Liu, K. (2007): A new quasi-unsymmetric sparse linear systems solver for meshless local Petrov-Galerkin method (MLPG), CMES: Computer Modeling in Engineering & Science, 17(2), 115-134.
59. Worden, K.; Tomlinson, C.R. (2001): Nonlinearity in structural dynamics: detection, identification and modeling, IOP, Bristol and Philadelphia.
60. Worden, K. (1990a): Data processing and experiment design for the restoring force surface method, Part I: integration and differentiation of measured time data, Mechanical Systems and Signal Processing, 4(4), 295-319.
61. Worden, K. (1990b): Data processing and experiment design for the restoring force surface method, Part II: Choice of excitation signal, Mechanical Systems and Signal Processing, 4(4), 321-344.