nach oben

Computational Mechanics

Erschienen in:

15.05.2018 | Original Paper

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

verfasst von: Heng Peng, Yinghua Liu, Haofeng Chen

Erschienen in: Computational Mechanics | Ausgabe 1/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.

Nächster Artikel A mortar formulation including viscoelastic layers for vibration analysis

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

König JA, Maier G (1981) Shakedown analysis of elastoplastic structures: a review of recent developments. Nucl Eng Des 66(1):81–95CrossRef

Maier G (2001) On some issues in shakedown analysis. J Appl Mech-T ASME 68(5):799–807. https://doi.org/10.1115/1.1379368 MATHCrossRef

Melan E (1938) Ingenieur-Archiv. Zur Plastizität des räumlichen Kontinuums 9(2):116–126

Koiter WT (1960) General theorems for elastic-plastic solids. In: Sneddon JN, Hill R (eds) Progress in solid mechanics, vol 1. North-Holland, Amsterdam, pp 167–221

König JA (1987) Shakedown of elastic-plastic structures. Elsevier, Amsterdam

Peigney M (2014) Shakedown of elastic-perfectly plastic materials with temperature-dependent elastic moduli. J Mech Phys Solids 71:112–131. https://doi.org/10.1016/j.jmps.2014.06.008 MathSciNetMATHCrossRef

Zarka J, Casier J (1979) Cyclic loading on an elastoplastic structure. In: Nemet-Nasser S (ed) Practical rule, mechanics today, vol 6. Pergamon Press, OxfordMATH

Zarka J (1980) Direct analysis of elastic-plastic structures with ‘overlay’ materials during cyclic loading. Int J Numer Meth Eng 15(2):225–235. https://doi.org/10.1002/nme.1620150206 MATHCrossRef

Stein E, Zhang GB, Konig JA (1992) Shakedown with nonlinear strain-hardening including structural computation using finite-element method. Int J Plast 8(1):1–31MATHCrossRef

10.

Pycko S, Maier G (1995) Shakedown theorems for some classes of nonassociative hardening elastic-plastic material models. Int J Plast 11(4):367–395. https://doi.org/10.1016/S0749-6419(95)00004-6 MATHCrossRef

11.

Chinh PD (2007) Shakedown theory for elastic plastic kinematic hardening bodies. Int J Plast 23(7):1240–1259. https://doi.org/10.1016/j.ijplas.2006.11.003 MATHCrossRef

12.

Polizzotto C (2010) Shakedown analysis for a class of strengthening materials within the framework of gradient plasticity. Int J Plast 26(7):1050–1069. https://doi.org/10.1016/j.ijplas.2010.01.006 MATHCrossRef

13.

Weichert D (1986) On the influence of geometrical nonlinearities on the shakedown of elastic-plastic structures. Int J Plast 2(2):135–148. https://doi.org/10.1016/0749-6419(86)90009-4 MATHCrossRef

14.

Gross-Weege J (1990) A unified formulation of statical shakedown criteria for geometrically nonlinear problems. Int J Plast 6(4):433–447. https://doi.org/10.1016/0749-6419(90)90012-4 CrossRef

15.

Corradi L, Maier G (1974) Dynamic non-shakedown theorem for elastic perfectly-plastic continua. J Mech Phys Solids 22(5):401–413. https://doi.org/10.1016/0022-5096(74)90005-2 MATHCrossRef

16.

Borino G, Polizzotto C (1996) Dynamic shakedown of structures with variable appended masses and subjected to repeated excitations. Int J Plast 12(2):215–228. https://doi.org/10.1016/S0749-6419(96)00004-6 MATHCrossRef

17.

Chen HF, Ponter ARS (2004) A simplified creep-reverse plasticity solution method for bodies subjected to cyclic loading. Eur J Mech a-Solid 23(4):561–577. https://doi.org/10.1016/j.euromechsol.2004.04.003 MATHCrossRef

18.

Klebanov JM, Boyle JT (1998) Shakedown of creeping structures. Int J Solids Struct 35(23):3121–3133. https://doi.org/10.1016/S0020-7683(97)00359-4 MATHCrossRef

19.

Ponter ARS (2016) Shakedown limit theorems for frictional contact on a linear elastic body. Eur J Mech A/Solids 60:17–27. https://doi.org/10.1016/j.euromechsol.2016.05.003 MathSciNetMATHCrossRef

20.

Borkowski A, Kleiber M (1980) On a numerical approach to shakedown analysis of structures. Comput Methods Appl Mech Eng 22(1):101–119. https://doi.org/10.1016/0045-7825(80)90053-5 MATHCrossRef

21.

Zhang Y (1995) An iteration algorithm for kinematic shakedown analysis. Comput Methods Appl Mech Eng 127(1–4):217–226. https://doi.org/10.1016/0045-7825(95)00121-6 MATHCrossRef

22.

Ponter ARS, Carter KF (1997) Limit state solutions, based upon linear elastic solutions with a spatially varying elastic modulus. Comput Methods Appl Mech Eng 140(3–4):237–258. https://doi.org/10.1016/S0045-7825(96)01104-8 MATHCrossRef

23.

Ponter ARS, Carter KF (1997) Shakedown state simulation techniques based on linear elastic solutions. Comput Methods Appl Mech Eng 140(3–4):259–279. https://doi.org/10.1016/S0045-7825(96)01105-X MathSciNetMATHCrossRef

24.

Chen HF, Ponter ARS (2001) Shakedown and limit analyses for 3-D structures using the linear matching method. Int J Press Vessels Piping 78(6):443–451. https://doi.org/10.1016/S0308-0161(01)00052-7 CrossRef

25.

Casciaro R, Garcea G (2002) An iterative method for shakedown analysis. Comput Methods Appl Mech Eng 191(49–50):5761–5792. https://doi.org/10.1016/S0045-7825(02)00496-6 MATHCrossRef

26.

Garcea G, Armentano G, Petrolo S, Casciaro R (2005) Finite element shakedown analysis of two-dimensional structures. Int J Numer Methods Eng 63(8):1174–1202. https://doi.org/10.1002/nme.1316 MATHCrossRef

27.

Spiliopoulos KV, Panagiotou KD (2012) A direct method to predict cyclic steady states of elastoplastic structures. Comput Methods Appl Mech Eng 223:186–198. https://doi.org/10.1016/j.cma.2012.03.004 MathSciNetMATHCrossRef

28.

Spiliopoulos KV, Panagiotou KD (2014) A residual stress decomposition based method for the shakedown analysis of structures. Comput Methods Appl Mech Eng 276:410–430. https://doi.org/10.1016/j.cma.2014.03.019 MATHCrossRef

29.

Vu DK, Yan AM, Nguyen-Dang H (2004) A primal-dual algorithm for shakedown analysis of structures. Comput Methods Appl Mech Eng 193(42–44):4663–4674. https://doi.org/10.1016/j.cma.2004.03.011 MATHCrossRef

30.

Simon JW, Weichert D (2011) Numerical lower bound shakedown analysis of engineering structures. Comput Methods Appl Mech Eng 200(41–44):2828–2839. https://doi.org/10.1016/j.cma.2011.05.006 MathSciNetMATHCrossRef

31.

Zouain N, Borges L, Silveira JL (2002) An algorithm for shakedown analysis with nonlinear yield functions. Comput Methods Appl Mech Eng 191(23–24):2463–2481. https://doi.org/10.1016/S0045-7825(01)00374-7 MathSciNetMATHCrossRef

32.

Christiansen E, Andersen KD (1999) Computation of collapse states with von Mises type yield condition. Int J Numer Methods Eng 46(8):1185–1202MathSciNetMATHCrossRef

33.

Makrodimopoulos A, Martin CM (2006) Lower bound limit analysis of cohesive-frictional materials using second-order cone programming. Int J Numer Methods Eng 66(4):604–634. https://doi.org/10.1002/nme.1567 MATHCrossRef

34.

Krabbenhoft K, Lyamin AV, Sloan SW (2007) Shakedown of a cohesive-frictional half-space subjected to rolling and sliding contact. Int J Solids Struct 44(11–12):3998–4008. https://doi.org/10.1016/j.ijsolstr.2006.11.001 MATHCrossRef

35.

Nguyen AD, Hachemi A, Weichert D (2008) Application of the interior-point method to shakedown analysis of pavements. Int J Numer Methods Eng 75(4):414–439. https://doi.org/10.1002/nme.2256 MATHCrossRef

36.

Garcea G, Leonetti L (2011) A unified mathematical programming formulation of strain driven and interior point algorithms for shakedown and limit analysis. Int J Numer Methods Eng 88(11):1085–1111. https://doi.org/10.1002/nme.3188 MathSciNetMATHCrossRef

37.

Simon JW, Weichert D (2012) Shakedown analysis with multidimensional loading spaces. Comput Mech 49(4):477–485. https://doi.org/10.1007/s00466-011-0656-8 MathSciNetMATHCrossRef

38.

Liu YH, Zhang XF, Cen ZZ (2005) Lower bound shakedown analysis by the symmetric Galerkin boundary element method. Int J Plast 21(1):21–42. https://doi.org/10.1016/j.ijplas.2004.01.003 MATHCrossRef

39.

Ribeiro TSA, Beer G, Duenser C (2008) Efficient elastoplastic analysis with the boundary element method. Comput Mech 41(5):715–732. https://doi.org/10.1007/s00466-007-0227-1 MATHCrossRef

40.

Le CV, Nguyen-Xuan H, Askes H, Bordas SPA, Rabczuk T, Nguyen-Vinh H (2010) A cell-based smoothed finite element method for kinematic limit analysis. Int J Numer Methods Eng 83(12):1651–1674. https://doi.org/10.1002/nme.2897 MathSciNetMATHCrossRef

41.

Tran TN, Liu GR, Nguyen-Xuan H, Nguyen-Thoi T (2010) An edge-based smoothed finite element method for primal-dual shakedown analysis of structures. Int J Numer Methods Eng 82(7):917–938. https://doi.org/10.1002/nme.2804 MathSciNetMATHCrossRef

42.

Nguyen-Xuan H, Rabczuk T, Nguyen-Thoi T, Tran TN, Nguyen-Thanh N (2012) Computation of limit and shakedown loads using a node-based smoothed finite element method. Int J Numer Methods Eng 90(3):287–310. https://doi.org/10.1002/nme.3317 MathSciNetMATHCrossRef

43.

Nguyen-Xuan H, Liu GR (2015) An edge-based finite element method (ES-FEM) with adaptive scaled-bubble functions for plane strain limit analysis. Comput Methods Appl Mech Eng 285:877–905. https://doi.org/10.1016/j.cma.2014.12.014 MathSciNetMATHCrossRef

44.

Chen S, Liu Y, Cen Z (2008) Lower bound shakedown analysis by using the element free Galerkin method and non-linear programming. Comput Methods Appl Mech Eng 197(45–48):3911–3921. https://doi.org/10.1016/j.cma.2008.03.009 MATHCrossRef

45.

Yu S, Zhang X, Sloan SW (2016) A 3D upper bound limit analysis using radial point interpolation meshless method and second-order cone programming. Int J Numer Methods Eng. https://doi.org/10.1002/nme.5273 MathSciNetCrossRef

46.

Zhou S, Liu Y, Wang D, Wang K, Yu S (2014) Upper bound shakedown analysis with the nodal natural element method. Comput Mech 54(5):1111–1128. https://doi.org/10.1007/s00466-014-1043-z MathSciNetMATHCrossRef

47.

Zhou S, Liu Y, Chen S (2012) Upper bound limit analysis of plates utilizing the C1 natural element method. Comput Mech 50(5):543–561. https://doi.org/10.1007/s00466-012-0688-8 MathSciNetMATHCrossRef

48.

Do HV, Nguyen-Xuan H (2017) Limit and shakedown isogeometric analysis of structures based on Bézier extraction. Eur J Mech A/Solids 63:149–164. https://doi.org/10.1016/j.euromechsol.2017.01.004 MathSciNetMATHCrossRef

49.

Heitzer M, Pop G, Staat M (2000) Basis reduction for the shakedown problem for bounded kinematic hardening material. J Global Optim 17(1–4):185–200MathSciNetMATHCrossRef

50.

Seshadri R (1995) Inelastic evaluation of mechanical and structural components using the generalized local stress strain method of analysis. Nucl Eng Des 153(2–3):287–303. https://doi.org/10.1016/0029-5493(95)90020-9 CrossRef

51.

Seshadri R, Mangalaramanan SP (1997) Lower bound limit loads using variational concepts: the m(alpha)-method. Int J Press Vessels Pip 71(2):93–106CrossRef

52.

Mackenzie D, Shi J, Boyle JT (1994) Finite-element modeling for limit analysis by the elastic compensation method. Comput Struct 51(4):403–410MATHCrossRef

53.

Ponter ARS, Engelhardt M (2000) Shakedown limits for a general yield condition: implementation and application for a Von Mises yield condition. Eur J Mech a-Solid 19(3):423–445. https://doi.org/10.1016/S0997-7538(00)00171-6 MATHCrossRef

54.

Boulbibane M, Ponter ARS (2005) Extension of the linear matching method to geotechnical problems. Comput Methods Appl Mech Eng 194(45–47):4633–4650. https://doi.org/10.1016/j.cma.2004.11.009 MATHCrossRef

55.

Chen HF, Ponter ARS (2001) A method for the evaluation of a ratchet limit and the amplitude of plastic strain for bodies subjected to cyclic loading. Eur J Mech a-Solid 20(4):555–571. https://doi.org/10.1016/S0997-7538(01)01162-7 MathSciNetMATHCrossRef

56.

Chen HF (2010) Lower and upper bound shakedown analysis of structures with temperature-dependent yield stress. J Press Vess-T ASME 132(1):273–281. https://doi.org/10.1115/1.4000369 CrossRef

57.

Lytwyn M, Chen HF, Ponter ARS (2015) A generalised method for ratchet analysis of structures undergoing arbitrary thermo-mechanical load histories. Int J Numer Methods Eng 104(2):104–124. https://doi.org/10.1002/nme.4924 MathSciNetMATHCrossRef

58.

Barbera D, Chen H, Liu Y, Xuan F (2017) Recent developments of the linear matching method framework for structural integrity assessment. J Press Vessel Technol 139(5):051101–051109. https://doi.org/10.1115/1.4036919 CrossRef

59.

Gokhfeld DA, Charniavsky OF (1980) Limit analysis of structures at thermal cycling, vol 4. Sijthoff & Noordhoff edn, Alphen aan den Rijn, The Netherlands

60.

Leonetti L, Casciaro R, Garcea G (2015) Effective treatment of complex statical and dynamical load combinations within shakedown analysis of 3D frames. Comput Struct 158:124–139. https://doi.org/10.1016/j.compstruc.2015.06.002 CrossRef

61.

Frederick C, Armstrong P (1966) Convergent internal stresses and steady cyclic states of stress. J Strain Anal Eng Des 1(2):154–159CrossRef

62.

Polizzotto C (2003) Variational methods for the steady state response of elastic-plastic solids subjected to cyclic loads. Int J Solids Struct 40(11):2673–2697. https://doi.org/10.1016/S0020-7683(03)00093-3 MathSciNetMATHCrossRef

63.

ABAQUS (Dassault Systems, Version 6.14, 2014)

64.

Carvelli V, Cen ZZ, Liu Y, Maier G (1999) Shakedown analysis of defective pressure vessels by a kinematic approach. Arch Appl Mech 69(9–10):751–764MATHCrossRef

65.

Zhang T, Raad L (2002) An eigen-mode method in kinematic shakedown analysis. Int J Plast 18(1):71–90. https://doi.org/10.1016/S0749-6419(00)00055-3 MATHCrossRef

66.

Francois A, Abdelkader H, An LTH, Said M, Tao PD (2007) Application of lower bound direct method to engineering structures. J Global Optim 37(4):609–630MathSciNetMATHCrossRef

67.

Belytsch T (1972) Plane stress shakedown analysis by finite elements. Int J Mech Sci 14(9):619–625CrossRef

68.

Zhang G (1992) Einspielen und dessen numerische Behandlung von Flächentragwerken aus ideal plastischem bzw. kinematisch verfestigendem Material. Ph.D. thesis, University Hanover, Germany

69.

Groß-Weege J (1997) On the numerical assessment of the safety factor of elastic-plastic structures under variable loading. Int J Mech Sci 39(4):417–433. https://doi.org/10.1016/S0020-7403(96)00039-2 MATHCrossRef

70.

Krabbenhoft K, Lyamin AV, Sloan SW (2007) Bounds to shakedown loads for a class of deviatoric plasticity models. Comput Mech 39(6):879–888. https://doi.org/10.1007/s00466-006-0076-3 MathSciNetMATHCrossRef

Titel: A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures
verfasst von: Heng Peng
Yinghua Liu
Haofeng Chen
Publikationsdatum: 15.05.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Computational Mechanics / Ausgabe 1/2019
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI: https://doi.org/10.1007/s00466-018-1581-x

Neuer Inhalt

Bildnachweise

VDI-Icon, Profil Icon, inhalt2, Springer Professional Modul/© Springer Fachmedien Wiesbaden GmbH, Nachhaltigkeitsaward Key Visual/© Cometis AG/Global ESG Monitor | Daniel Rupp | Generiert mit KI, Search Icon, Banner Hanser, Beijing Auto Show 2024: Deutsche Hersteller wollen angreifen./© EKH-Pictures / Generated with AI / Stock.adobe.com, Buchstaben, die aus einem Megaphon kommen/© MicroStockHub/Getty Images/iStock, Digitale Lieferkette/© zapp2photo / stock.adobe.com, Zeitschrift Wissensmanagement Cover, PatentFit-Logo/© Springer Fachmedien Wiesbaden GmbH, Sustainibility Finance/© Robert Kneschke / stock.adobe.com / Springer Fachmedien Wiesbaden GmbH, Zukunftswerkstatt Sales Excellence 2024/© AndreyPopov / Getty Images / iStock, 2023_Antrieb/© supervisuell

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1/2019

A beam formulation based on RKPM for the dynamic analysis of stiffened shell structures

Numerical procedure to couple shell to solid elements by using Nitsche’s method

Identification of viscoelastic properties from numerical model reduction of pressure diffusion in fluid-saturated porous rock with fractures

A challenging dam structural analysis: large-scale implicit thermo-mechanical coupled contact simulation on Tianhe-II

Computational and experimental investigation of free vibration and flutter of bridge decks

A mortar formulation including viscoelastic layers for vibration analysis

Neuer Inhalt

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.