Inverse problems of structural mechanics
https://doi.org/10.31675/1607-1859-2020-22-4-83-101
Abstract
The paper presents a brief review of the main ideas on the extensive class of inverse problems in structural mechanics relating to the identification of design models, technical condition monitoring and finding damages. The numerical implementation of identified incorrectness of inverse problems requires regularization. References include works describing the cases of practical application of reverse problem solutions.
About the Author
A. V. Perelmuter
SCAD Soft
Ukraine
Ukraine
Anatoly V. Perelmuter, DSc
3-а, Prosveshcheniya Str., 03037, Kiev, Ukraine
References
1. Liyakhovich L.S. Osobye svojstva optimalnykh system i osnovnye napravleniya ikh realizacii v metodakh rascheta sooruzhenij [Properties of optimum systems and their implementation in structural analysis]. Tomsk: TSUAB, 2009. 372 p. (rus)
2. Eykhoff P. Osnovy identifikacii system upravleniya [System identification]. Moscow: Mir. 1975. 680 p. (transl. from Dutch)
3. Kozin F., Kozin C.H. A moment technique for system parameter identification. Shock and Vibration Bulletin. 1968. No. 38. Pp. 119−131.
4. Berman A., Flanelly W.G. Theory of incomplete models of dynamic structures. AIAA Journal. 1971. No. 8. Pp. 1481−1487.
5. Baruch M. Optimal correction of mass and stiffness matrices using measured modes. AIAA Journal. 1982. V. 20. No. 11. Pp. 1623−1626.
6. Berman A., Nagy E.J. Improvement of a large analytical model using test data. AIAA Journal. 1983. V. 21. No. 8. Pp. 1168−1173.
7. Emanov A.F., Seleznyov V.S., Bah A.A. Kogerentnoe vosstanovlenie polej stoyachih voln kak osnova detalnogo sejsmologicheskogo obsledovaniya inzhenernyh sooruzhenij [Coherent restoration of standing wave fields as a basis for detailed seismological survey of engineering structures]. Seismostoikoe stroitel'stvo. Bezopasnost' sooruzhenii. 2007. No. 3. Pp. 20−23.
8. Bah A.A., Krasnikov A.A. Ispolzovanie metoda stoyachih voln dlya analiza dinamicheskih harakteristik vysotnyh zdanij na primere 40-etazhnogo kompleksa “Dirizhabl”, g. Moskva [Standing waves method in the analysis of dynamic characteristics of high-rise buildings on the example of 40-storey complex "Dirigible", Moscow]. Seismostoikoe stroitel'stvo. Bezopasnost' sooruzhenii. 2014. No. 1 Pp. 26–30.
9. Belostockij A.M., Kalichava D.K., Aul A.A., Nagibovich A.I. Adaptiruemye konechnoelementnye modeli na osnove dinamicheskogo monitoringa nesushih konstrukcij vysotnyh zdanij. Chast 3. Aprobaciya metodiki na vysotnom komplekse, vozvedennom s vyyavlennymi otstupleniyami ot proekta [Adaptable finite element models based on dynamic monitoring of bearing structures of high-rise buildings. Pt 3. Methodology approbation on a high-rise complex erected with identified deviations from the project]. International Journal for Computational Civil and Structural Engineering. 2012. V. 8. No. 4. Pp. 44−55.
10. Albert A. Regressiya, psevdoinversiya i rekurrentnoe ocenivanie [Regression, and the moor Penrose pseudoinverse]. Moscow: Nauka, 1977. 301 p. (transl. from Engl.)
11. Belostockij A.M., Kalichava D.K. Adaptiruemye konechnoelementnye modeli osnove dinamicheskogo monitoringa nesushih konstrukcij vysotnyh zdanij. Chast 1. Osnovy razrabotannoj raschetno-eksperimentalnoj metodiki [Adaptable finite element models based on dynamic monitoring of bearing structures of high-rise buildings. Pt 1. The developed calculation and experimental methodology]. International Journal for Computational Civil and Structural Engineering. 2012. V. 8. No. 4. Pp. 20−29.
12. Belostockij A.M., Kuhta A.V. Adaptivnye matematicheskie modeli dlya sistem monitoringa stroitelnyh obektov. [Adaptive mathematical models for construction monitoring systems]. Predotvrashenie avarij zdanij i sooruzheni. 2011. Available: www.pamag.ru/pressa/adaptive-math-method
13. Allemang R.J., Brown D.L. A correlation coefficient for modal vector analysis. 1st International Modal Analysis Conference, SEM. Orlando, Florida, 1982. Pp. 110−116.
14. Vatulyan A.O. Obratnye zadachi v mehanike deformiruemogo tverdogo tela [Inverse problems in mechanics of deformable solid]. Moscow: Fizmatgiz, 2007. 224 p. (rus)
15. Tihonov A.N., Arsenin V.Ya. Metody resheniya nekorrektnyh zadach [Methods for solving incorrect problems]. Moscow: Nauka, 1979. 284 p. (rus)
16. Postnov V.A. Ispolzovanie metoda regulyarizacii Tihonova dlya resheniya zadach identifikacii uprugih system [Use of Tikhonov's regularization method to solve problems of elastic system identification]. Izv. RAN MTT. 2010. No. 1. Pp. 64−71. (rus)
17. Tang J.P., Leu K.M. Vibration tests and damage detection of P/C bridge. Journal of the Chinese Institute of Engineers. 1991. V. 14. Рp. 531−536.
18. Hunt D.L., Weiss S.P., West W.M., Dunlap T.A., Freesmeyer S.R. Development and implementation of a shuttle modal inspection system. Sound and Vibration. 1990. V. 24. No. 9. Pp. 34−42.
19. Robinson N.A., Peterson L.D., James G.H., Doebling S.W. Damage detection in aircraft structures using dynamically measured static flexibility matrices. Proc. 14th Int. Conf. on Modal Analysis. 1996. Pp. 857−865.
20. Yu H., Mohammed M.A., Mohammadi M.E., Moaveni B., Barbosa A.R., Richard A.S., Wood L. Structural identification of an 18-story RC building in Nepal using post-earthquake ambient vibration and lidar data. Frontiers in Built Environment. 2017. V. 3. No. 11.
21. Feng M.Q., Kim J.M., Xue H. Identification of a dynamic system using ambient vibration measurements. Journal of Applied Mechanics. 1998. V. 659. Pp. 1010–1021.
22. Cavaleri L., Ferrotto M.F., Di Trapani F., Alessandro A. Vibration tests and structural identification of the Bell Tower of Palermo Cathedral. The Open Construction & Building Technology Journal. 2020. V. 14. Pp. 319−330.
23. Macdonald J., Daniell W. Variation of modal parameters of a cable-stayed bridge identified from ambient vibration measurements and FE modeling. Engineering Structures. 2005. V. 27. Pp. 1916−1930.
24. Plevris V., Papadrakakis M. A hybrid particle swarm-gradient algorithm for global structural optimization. Computer-Aided Civil and Infrastructure Engineering. 2011. V. 26. No. 1. Pp. 48−68.
25. He X., Moaveni B., Conte J., Elgamal A., Masri S. System identification of Alfred Zampa memorial bridge using dynamic field test data. Journal of Structural Engineering. 2009. V. 135. Pp. 54−66.
26. Bazhenov V.G. Matematicheskoe modelirovanie i metody identifikacii deformacionnyh I prochnostnyh harakteristik materialov [Mathematical modeling and methods to identify deformation and strength characteristics of materials]. Fizicheskaya mezomehanika. 2007. V. 10. No. 5. Pp. 91−105. (rus)
27. Kayumov R.A. Rasshirennaya zadacha identifikacii mehanicheskih harakteristik materialov po rezultatam ispytanij konstrukcij [Extended problem of identification of mechanical properties of materials by structural test results]. Izv. AN. Mehanika tverdogo tela. 2004. No. 2. Pp. 94−103. (rus)
28. Guk N.A., Obodan N.I. Identifikaciya mehanicheskih svojstv materiala po rezultatam kosvennyh izmerenij [Identification of mechanical properties of material by indirect measurements]. Mehanika tverdogo tela. 2010. No. 40. Pp. 233−242. (rus)
29. Kuznecov S.F., Semenov A.C. Metod opredeleniya mehanicheskogo sostoyaniya konstrukcij, vzaimodejstvuyushih s neodnorodnym gruntovym osnovaniem [Determination of mechanical state of structures interacting with heterogeneous ground base]. Spravochnik. Inzhenernyj zhurnal. 2012. No. 3. Pp. 23−31. (rus)
30. Guk N.A. Identifikaciya svojstv osnovanij sooruzhenij metodom obratnyh zadach [Identification of properties of foundation structures using inverse problems]. Matematicheskoe i kompyuternoe modelirovanie. Seriya: Fiziko-matematicheskie nauki. 2012. Pp. 65−76.
31. Jang T.S., Sung H.G., Han S.L., Kwon S.H. Inverse determination of the loading source of the infinite beam on elastic foundation. Journal of Mechanical Science and Technology. 2008. V. 22. No. 12. Pp. 2350−2356.
32. Bilotta A., Turco E. A numerical study on the solution of the Cauchy problem in elasticity. International Journal of Solids and Structures. 2009. V. 46. Pp. 4451−4477.
33. Marin L. The minimal error method for the Cauchy problem in linear elasticity. Numerical implementation for two-dimensional homogeneous isotropic linear elasticity. International Journal of Solids and Structures. 2009. V. 46. Pp. 951−974.
34. Wei Liu, Zhichun Yang, Le Wang, Ning Guo. Boundary condition modelling and identification for cantilever-like structures using natural frequencies. Chinese Journal of Aeronautics. 2019, V. 32. No. 6. Pp. 1451−1464.
35. Turco E. A strategy to identify exciting forces acting on structures. International Journal for Numerical Methods in Engineering. 2005. V. 64. Pp. 1483−1508.
36. Turco E. Identification of axial forces on statically indeterminate pin-jointed trusses by a nondestructive mechanical test. The Open Civil Engineering Journal. 2013. V. 7. Pp. 50−57.
37. Ballard P., Constantinescu A. On the inversion of subsurface residual stresses from surface stress measurements. Journal of the Mechanics and Physics of Solids. 1994. V. 42. Pp. 1767−1788.
38. Ring W. Identification of the load of a partially breaking beam from inclination measurements. Inverse Problems. 1999. V. 15. No. 4. Pp. 1003−1020.
39. Jacquelin E., Bennani A., Hamelin P. Force reconstruction: analysis and regularization of a deconvolution problem. Sound and Vibration. 2003. V. 265. Pp. 81–107.
40. Pister K. Mathematical modeling for structural analysis and design. Nuclear Engineering and Design. 1972. V. 8. Pp. 353−375.
41. Reddy A.N., Ananthasuresh G.K. On computing the forces from the noisy displacement data of an elastic body. International Journal for Numerical Methods in Engineering. 2008. V. 76. № 11. Pp. 1645−1677.
42. Yanchevskii I.V. K probleme vosstanovleniya vremennoi zavisimosti nestatsionarnogo vozdeistviya, prilozhennogo k uprugo-deformiruemomu elementu konstruktsii [Restoration of temporary dependence of non-stationary disturbance applied to elastically deformed structural element]. Problemy mashinostroeniya. 2015. V. 18. No. 2. Pp. 43−54.
43. Jang T.S., Han S.L. Numerical experiments on determination of spatially concentrated timevarying loads on a beam: an iterative regularization method. The Journal of Mechanical Science and Technology. 2009. V. 23. No. 10. Pp. 2722−2729.
44. Wang B.T., Chiu C.H. Determination of unknown impact force acting on a simply supported beam. Mechanical System and Signal Processing. 2003. V. 17. No 3. Pp. 683−704.
Review
For citations:
Perelmuter A.V. Inverse problems of structural mechanics. Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture. 2020;22(4):83-101. (In Russ.) https://doi.org/10.31675/1607-1859-2020-22-4-83-101
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