Abstract
A general formulation of an inverse problem of structural mechanics as an optimization problem is presented. The following features of a typical problem are accentuated: a large computational effort needed to evaluate the function values multiplied by the number of calls for the numerical simulation of the process under consideration, and that the function values often present some level of numerical noise. The main features of the Multipoint Approximation technique based on the Response Surface methodology (MARS) are presented with the emphasis on the choice of approximation functions. As a promising way of selection of the structure of approximations, the Genetic Programming methodology is presented. The use of optimization techniques for the solution of inverse problems of structural mechanics is illustrated by examples of damage recognition in steel structures and identification of parameters in various constitutive models.
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References
Armstrong, P. J. and Frederick, C. O. (1966) A mathematical representation of the multiaxial Bauschinger effect., GEGB report RD/B/N731, Berkeley Nuclear Laboratories.
Audze, P. and Eglais, V. (1977). New approach for planing out of experiments, Problems of Dynamics and Strengths, 35, pp. 104–107, Riga, Zinatne Publishing House (in Russian).
Baruch, M. (1982). 15 Optimal correction of mass and stiffness matrices using measured modes. AIAA J. 20, 441.
Bates, S.J., Sienz, J. and Toropov, V.V. (2004) Formulation of the optimal Latin Hypercube design of experiments using a permutation genetic algorithm. Paper AIAA-2 004-2011, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA, April 19–22
Britanti, S., Maier, G. and Nappi, A. (1984) Inverse problems in structural elastoplasticity: a Kalman filter approach, A. Sawczuk and G. Bianchi, (eds.). Plasticity today. Modelling, methods and applications, 311–329. Elsevier.
Box, G.E.P. and Draper, N.R. (1987). Empirical model-building and response surfaces, Wiley.
Cawley, P. and Adams, R. D. (1979). The location of defects in structures from measurements of natural frequencies. J. Strain Analysis 14, 49.
Chaboche, J. L. and Rousselier, G. (1983) On the plastic and viscoplastic constitutive equations-Part I: Rules developed with internal variable concept. Trans AS ME, J. Press. Vessel Technol., 105, 153–158
Chun, B. K., Jinn, J. T. and Lee, J. K. (2002a) Modeling the Bauschinger effect for sheet metals, part I: theory, Int. J. Plasticity, 18, 571–595.
Chun, B. K., Jinn, J. T. and Lee, J. K. (2002b) Modeling the Bauschinger effect for sheet metals, part II: applications, Int. J. Plasticity, 18, 597–616.
Distefano, N. (1970) On the identification problem in linear viscoelasticity, ZAMM, 50, 683–690.
Geng, L., Shen, Y. and Wagoner, R. H. (2002) Anisotropic hardening equations derived from reverse-bending testing, Int. J. Plasticity, 18, 743–767.
Gioda, G. and Maier, G. (1980) Direct search solution of an inverse problem in elastoplasticity: identification of cohesion, friction angle and in situ stress by pressure tunnel tests, Int. J. Num. Meth. Engng., 15, 1823–1848.
Gioda, G. and Sakurai, S. (1987) Back analysis procedures for the interpretation of field measurements in geomechanics. Int. J. for Numerical and Analytical Methods in Geomechanics, 11, 555–583.
Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Company, Inc.
Guccione, J. M., McCulloch, A. D. and Waldman, L. K. (1991) Passive material properties of intact ventricular myocardium determined from a cylindrical model. Transact. of the ASME, J. of Biomechanical Engng., 113-51, 42–45.
Hajela, P. and Soeiro, F. J. (1990a) Structural damage detection based on static and modal analysis. AIAA J. 28, 1110.
Hajela, P. and Soeiro, F. J. (1990b) Recent Developments in Damage Detection Based on System Identification Methods. Structural Optimization 2, 1.
Hassiotis, S. and Jeong, G. D. (1993) Assessment of structural damage from natural frequency measurements. J. Computers & Structures 49, 679.
Hamasaki, H., Yoshida, F., Shinbata, K., Toropov, V. V. (2003) Identification of material properties for lead-free solder using micro-indentation experiments, FE simulation and optimization. In Short Paper of 5th World Congress of Structural and Multidisciplinary Optimization, Lido di Jesolo, Italy, May 2003, 101–102
Hawkins, R., Wright, J.C. (1971) Mechanical properties and press-formability of copper/mild steel sandwich sheet materials, J. Inst. Metal. 99, 357–371.
Hendriks, M. A. N. (1991) Identification of the mechanical behaviour of solid materials, Ph.D. Thesis, Eindhoven University of Technology, The Netherlands.
Iding, R. H., Pister, K. S. and Taylor, R. L. (1974) Identification of nonlinear elastic solids, Comput. Meth. Appl. Mech. Engng, 5, 121–142.
Kabe, A. M. (1985) Stiffness matrix adjustment using mode data. AIAA J. 23, 1431.
Kanetake, K., Tozawa, Y, Kato, T. and Aiba, S. (1981) Effect of texture on deformation behavior of aluminum sheets, J. Jpn Inst. Light Metals, 31, 307–312
Kavanagh, K. T. and Clough, R. W. (1971) Finite element applications in the characterization of elastic solids, Int. J. Solids & Structures, 7, 11–23.
Kavanagh, K. T. (1972) Extension of classical experimental techniques for characterizing composite-material behavior, Experimental mechanics, 12, 50–56.
Kim, J.-K., Yu, T.-X. (1997) Forming and failure behaviour of coated, laminated and sandwiched sheet metals: a review, J. Materials Processing Technology 63, 33–42.
Koza, J.R. (1992) Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press.
Kristen, H. A. D. (1976) Determination of rock mass elastic moduli by back analysis of deformation measurements, Proc. Symp. on Exploration for Rock Engineering, Johannesburg, 165–172.
Lapierre, H. and Ostiguy, G. (1990) Structural model verification with linear quadratic optimization theory. AIAA J. 28, 1497.
Lead-Free Solder Project. (1997) NCMS Report 0401 RE96.
Lin, E. I.-H. and Sackman, J. L. (1975) Identification of dynamic properties of nonlinear viscoelastic materials and the associated wave propagation problem, Int. J. Solids & Structures, 11, 1145–1159.
Ma, X. and Yoshida, F. (2003) Rate-dependent indentation hardness of a power-law creep solder alloy, Appl. Phys. Lett. 82, 188–190.
Madsen, K. and Hegelund, P. (1991) Non-gradient Subroutines for Non-linear Optimization. Institute for Numerical Analysis, Technical University of Denmark, Report NI-91-05.
Maier, G. (1981) Inverse problem in engineering plasticity: a quadratic programming approach. Rendiconti dell’ Accademia Nazionale dei Lincei, Serie VIII, LXX-4, 203–209.
Maier, G., Giannessi, F. and Nappi, (1982) A. Indirect identification of yield limits by mathematical programming. Eng. Struct., 4, 86–98
Majlessi, S. A., Dadras, P. (1983) Pure plastic bending of sheet laminates under plane strain condition, Int. J. Mech. Sciences. 25, 1–14.
Mackay, M. D., Beckman, R. J., and Conover, W. J. (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239–245.
Marti, K. (1991) Stochastic programming: Numerical solution techniques by semi-stochastic approximation methods, in Slowinski, R. and Teghem, J. (eds.), Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty, Kluwer, 23–43.
Oomens, C. W. J., van Ratingen, M. R., Janssen, J. D., Kok, J. J. and Hendriks, M. A. N. (1993) A numerical-experimental method for a mechanical characterization of biological materials, J. Biomechanics, 26-4/5, 617–621.
Pedersen, P. (1989) Optimization methods applied to identification of material parameters. Proc. of the GAMM seminar on Discretization methods and structural optimization, Lecture Notes in Engineering, 42. Springer.
Pedersen, P. and Frederiksen, P. S. (1990) Sensitivity analysis for identification of material parameters, Proc. 9th Int. Conf. on Experimental Mechanics, Copenhagen, 545–551.
Pedersen, P. and Frederiksen, P. S. (1992) Identification of orthotropic material moduli by a combined experimental/numerical approach, Measurement, 10, 113–118.
Pharr, G. M. and Oliver, W. C. (1989) Nanoindentation of silver-relations between hardness and dislocation structure, J. Mater. Res., Vol. 4, No. 1, 94–101.
Prager, W. (1956) A new method of analyzing stresses and strains in work-hardening plastic solids, Appl. Mech., 23, 493–496.
Ravaii, H., Toropov, V.V. and Horoshenkov, K.V. (1997) Structural damage recognition based on optimization techniques. In Gutkowski, W., Mroz, Z., eds., Proc. of 2nd World Congress of Structural and Multidisciplinary Optimization, Zakopane, Poland, May 1997, vol. 1, pp. 299–304, Polish Academy of Sciences, 1997.
Ravaii, H., Toropov, V.V. and Horoshenkov, K.V. (1998a) Mixed numerical-experimental damage recognition in steel structures. In Allison, I.M. (ed.), Experimental Mechanics. Advances in Design, Testing and Analysis-Proc. 11th Int. Conf. on Experimental Mechanics, Oxford, August 24–28, 1998, vol. 1, A.A. Balkema, Rotterdam, 77–82.
Ravaii, H., Toropov, V.V. and Mahfouz, S.Y. (1998b) Application of a genetic algorithm and derivative-based techniques to identification of damage in steel structures. In: M. Tanaka, G.S. Dulikravich, eds., Inverse Problems in Engineering Mechanics-Proc. Int. Symposium, Nagano City, Japan, March 24–27, 1998, Elsevier, 571–580.
Rikards, R. (1993) Elaboration of optimal design models for objects from data of experiments. In Pedersen, P., ed., Optimal design with advanced materials, The Frithiof Niordson volume. Proceedings of the IUTAM Symposium, Lyngby, Denmark, Elsevier, 149–162.
Semiatin, N. L. and Piehler, H. R. (1979a) Deformation of sandwich sheet materials in uniaxial tension, Metal. Trans. 10A, 85–96.
Semiatin, N. L. and Piehler, H. R. (1979b) Formability of sandwich sheet materials in plane strain compression and rolling, Metal. Trans. 10A, 97–107.
Semiatin, N. L. and Piehler, H. R. (1979c) Forming limits of sandwich sheet materials, Metal. Trans. 10A, 1107–1118.
Shiratori, E., Ikegami, K. and Yoshida, F. (1976a) The subsequent yield Surfaces after proportional preloading of the Tresca-type material, Bulletin of the JSME, 19, 1122–1128.
Shiratori, E., Ikegami, K., Yoshida, F., Kaneko, K. and Koike, S., (1976b) The subsequent yield surfaces after preloading under combined axial load and torsion, Bulletin of the JSME, 19–134, 877–883.
Sol, H., De Visscher, J. and De Wilde, W. P. (1993) Identification of the viscoelastic material properties of orthotropic plates using a mixed numerical/experimental technique, C. A. Brebbia and G. M. Carlomagno, eds., Computational methods and Experimental Measurements VI, vol. 2, Comp. Mech. Publications, 131–142.
Sol, H. and Oomens, C. W. J., Eds. (1997) Material Identification using Mixed Numerical — Experimental Methods. Proc. Euromech 357 Colloquium, Kerkrade, The Netherlands, April 1997, Kluwer.
Tanaka, K. (1986) A thermomechanical sketch of shape memory effect: One-dimensional tensile behavior, Res. Mech., 18, 251.
Tanaka, K., Kobayashi, S. and Sato, Y. (1986) Thermomechanics of transformation pseudoelasticity and shape memory effect in alloys, Int. J. Plasticity, 2, 59.
Tanaka, K., Tobushi, H. and Miyazaki, S. (1993) Mechanical Properties of Shape Memory Alloys. Yokendo Ltd.
Tanaka, M. and Dulikravich, G.S., Eds. (1998) Inverse Problems in Engineering Mechanics. Proc. Int. Symposium, Nagano City, Japan, March 1998, Elsevier.
Toropov, V. V. and Van der Giessen, E. (1993) Parameter identification for nonlinear constitutive models: Finite Element simulation-Optimization-Nontrivial experiments, In: Pedersen, P., ed., Optimal Design with Advanced Materials, Elsevier, 113–130.
Toropov, V.V., van der Giessen, E. and Yoshida, F. (1996) Material parameter identification based on nontrivial experiments, numerical simulation and optimization. In: Friswell, M.I.; Mottershead, J.E., eds., Proceedings of 1st International Conf. on Identification in Engineering Systems, Swansea, March 1996, The Cromwell Press Ltd., 328–337.
Toropov, V.V. and Markine, V.L. (1996) The use of simplified numerical models as mid-range approximations. 6th AIAA/NASA/ISSMO Symp. on Multidisciplinary Analysis and Optimization, Bellevue WA, Part 2, 952–958, AIAA
Toropov, V. V. and Alvarez, L.F. (1998a) Application of genetic programming and response surface methodology to optimization and inverse problems. In: M. Tanaka, G.S. Dulikravich, eds., Inverse Problems in Engineering Mechanics-Proc. Int. Symp., Nagano City, March 1998, Elsevier, 551–560.
Toropov, V. V. and Alvarez, L.F. (1998b) Approximation model building for design optimization using genetic programming methodology, Paper AIAA-98-4769, 7th AIAA/USAF/NASA/ISSMO Symp. on Multidisciplinary Analysis and Optimization, St. Louis, USA, September 1998, 1, AIAA, 490–498.
Toropov, V. V., Alvarez, L.F. and Ravaii, H. (1999a) Structural damage recognition using optimization techniques and genetic programming methodology, 3rd ISSMO/UBCAD/UB/AIAA World Congress of Structural and Multidisciplinary Optimization, Buffalo, NY, USA, May 17–21, 1999 (CD Proceedings).
Toropov, V. V., Alvarez, L.F. and Ravaii, H. (1999b) Recognition of damage in steel structures using genetic programming methodology. In: M.I. Friswell, J.E. Mottershead, A.W. Lees (eds.), Proc. 2nd International Conf. on Identification in Engineering Systems, Swansea, March 29–31, 1999, The Cromwell Press Ltd., 382–391.
Toropov, V. V. (2001) Modelling and approximation strategies in optimization-global and mid-range approximations, response surface methods, genetic programming, low / high fidelity models. In: Blachut, J.; Eschenauer, H. A., eds., Emerging Methods for Multidisciplinary Optimization, CISM Courses and Lectures, No. 425, International Centre for Mechanical Sciences, 205–256, Springer-Verlag, 2001.
Venkataraman, S., Haftka, R. and Johnson, T. (1998) Design of shell structures for buckling using correction response surface approximations. Paper AIAA-98-4855, Proceedings of 7th AIAA/USAF/ NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis: AIAA. 1131–1144.
Verguts, H., Sowerby, R. (1975) The pure plastic bending of laminated sheet metals, Int. J. Mech. Sciences, 17, 31–51.
Vestergaard, B. (1990) Experimentation and identification for models of visco-elastic materials, Proc. 9th Int. Conf on Experimental Mechanics, Copenhagen, 601–608.
Wagoner, R. H., Geng, L. and Balakrishnan, V. (2000) Role of hardening law in springback, In Khan, A. S., Zhan, H. and Yuen Y., eds., Proceedings of 8th Int. Symp. on Plasticity and Its Current Applications, NEAT Press, 609–611
Wu, P. D. and Van der Giessen, E. (1991) Analysis of elastic-plastic torsion of circular bars at large strains, Arch. Appl Mech., 61, 89–103.
Yoshida, F., Hino, R. and Okada, T. (1990) Deformation and fracture of stainless-steel/aluminium sheet metal laminates in stretch bending. Proceedings of 5th Int. Symp. on Plasticity and Its Current Applications, Elsevier, 869–872.
Yoshida, F., Hino, R. and Okada, T. (1995) Deformation and fracture of stainless-steel/aluminium sheet metal laminates in stretch bending/unbending. In Tanimura, S. and Khan, A. S. eds., Proceedings of the 5th International Symposium on Plasticity and Its Current Applications, Gordon and Breach Publ., 869–872.
Yoshida, F. (1995) Ratchetting behaviour of 304 stainless steel at 650°C under multiaxially strain-controlled and uniaxially/multiaxially stress-controlled conditions, European J. Mechanics, A/Solids, 14, 97–117.
Yoshida, F. (1997) Deformation and fracture of sheet metal laminates in plastic forming, In Hui, D., ed., Proceedings of 4th International Conference on Composite Engineering, 61–64.
Yoshida, F., Urabe, M. and Toropov, V. V. (1998) Identification of material parameters in constitutive model for sheet metals from cyclic bending tests, Int. J. Mechanical Sciences, 40–2, 237–249.
Yoshida, F. and Hino, R. (1997) Forming limit of stainless steel-clad aluminium sheets under plane stress condition, J. Materials Processing Technology, 63, 66–71.
Yoshida, F. and Urabe, M. (1999) Computer-aided process design for the tension levelling of metallic strips, J. Materials Processing Technology, 89/90, 218–223.
Yoshida, F., Toropov, V.V., Kyogoku, H. and Sakuma, T. (1999) Identification of material parameters of Ti-Ni shape memory alloy. In: M.I. Friswell, J.E. Mottershead, A.W. Lees, eds., Proceedings of 2nd International Conf. on Identification in Engineering Systems, Swansea, March 29–31, 1999, The Cromwell Press Ltd., 150–159.
Yoshida, F. and Urabe, M. (2000) Computer-aided process design for tension levelling of clad sheet metal, Key Engineering Materials, 177–180, 503–508.
Yoshida, F. (2000) A constitutive model of cyclic plasticity, Int. J. Plasticity, 16, 359–380.
Yoshida, F., Uemori, T. and Fujiwara, K. (2002) Elastic-plastic behavior of steel sheets under in-plane cyclic tension-compression at large strain, Int. J. Plasticity 18, 633–659.
Yoshida, F. and Uemori, T. (2002) A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation, Int. J. Plasticity 18, 661–689.
Zhao, K. M., Lee, J. K. (2001) Generation of cyclic stress-strain curves for sheet metals, ASME, J. Eng. Mater. Technology, 123, 391–397.
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Toropov, V., Yoshida, F. (2005). Application of Advanced Optimization Techniques to Parameter and Damage Identification Problems. In: Mróz, Z., Stavroulakis, G.E. (eds) Parameter Identification of Materials and Structures. CISM International Centre for Mechanical Sciences, vol 469. Springer, Vienna. https://doi.org/10.1007/3-211-38134-1_6
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