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Research Papers: Numerical Methods

Progress in Lower Bound Direct Methods

[+] Author and Article Information
D. Weichert

Mem. ASME
Institute of General Mechanics,
RWTH-Aachen,
Templergraben 64,
Aachen 52056, Germany
e-mail: weichert@iam.rwth-aachen.de

A. Hachemi

Department of Engineering,
GUtech,
P.O. Box 1816,
Athaibah PC 130, Oman
e-mail: abdelkader.hachemi@gutech.edu.om

J. Simon

Institute of Applied Mechanics
RWTH-Aachen,
Mies-van-der-Rohe-Str. 1,
Aachen 52074, Germany
e-mail: Jaan.Simon@rwth-aachen.de

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received July 31, 2014; final manuscript received January 14, 2015; published online March 23, 2015. Assoc. Editor: Albert E. Segall.

J. Pressure Vessel Technol 137(3), 031005 (Jun 01, 2015) (7 pages) Paper No: PVT-14-1120; doi: 10.1115/1.4029618 History: Received July 31, 2014; Revised January 14, 2015; Online March 23, 2015

The paper reports on recent progress in numerical shakedown and limit analysis based on Melan's lower bound shakedown theorem. After explaining the theoretical foundations of their approach, the authors describe in detail the numerical scheme, in particular the underlying optimization via interior point methods. Numerous examples mostly related to pressure vessel technology are presented, illustrating the potential of the method.

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References

Melan, E., 1938, “Zur Plastizität des räumlichen Kontinuums,” Ing. Arch., 9(2), pp. 116–126. [CrossRef]
Weichert, D., Hachemi, A., and Schwabe, F., 1999, “Shakedown Analysis of Composites,” Mech. Res. Commun., 26(3), pp. 309–318. [CrossRef]
Weichert, D., and Hachemi, A., 2010, “Progress in the Application of Lower Bound Direct Methods in Structural Design,” ASME Int. J. Appl. Mech., 2(1), pp. 145–160. [CrossRef]
Weichert, D., and Gross-Weege, J., 1988, “The Numerical Assessment of Elastic–Plastic Sheets Under Variable Mechanical and Thermal Loads Using a Simplified Two-Surface Yield Condition,” Int. J. Mech. Sci., 30(10), pp. 757–767. [CrossRef]
Halphen, B., and Quoc Son, N., 1975, “Sur les matériaux Standards généralisés,” J. Méc., 14(1), pp. 39–63.
Chen, M., Hachemi, A., and Weichert, D., 2013, “Shakedown and Optimization Analysis of Periodic Composite,” Limit State of Materials and Structures: Direct Methods, Vol. 2, G.de Saxcé, A.Oueslati, E.Charkaluk, and J.-B.Tritsh, eds., Springer, New York, pp. 45–69. [CrossRef]
Akoa, F., Hachemi, A., An, L. T. H., Mouhtamid, S., and Tao, P. D., 2007, “Application of Lower Bound Direct Method to Engineering Structures,” J. Global Optim., 37(4), pp. 609–630. [CrossRef]
Simon, J.-W., and Weichert, D., 2011, “Numerical Lower Bound Shakedown Analysis of Engineering Structures,” Comput. Methods Appl. Mech. Eng., 200(41–44), pp. 2828–2839. [CrossRef]
Simon, J.-W., Kreimeier, M., and Weichert, D., 2013, “A Selective Strategy for Shakedown Analysis of Engineering Structures,” Int. J. Numer. Methods Eng., 94(11), pp. 985–1014. [CrossRef]
Simon, J.-W., and Weichert, D., 2013, “Interior-Point Method for Lower Bound Shakedown Analysis of von Mises-Type Materials,” Limit States of Materials and Structures—Direct Methods, Vol. 2, G.de Saxce, E.Charkaluk, A.Oueslati, and J.-B.Tritsch, eds., Springer, New York, pp. 103–128. [CrossRef]
Simon, J.-W., and Weichert, D., 2012, “Shakedown Analysis of Engineering Structures With Limited Kinematical Hardening,” Int. J. Solids Struct., 49(4), pp. 2177–2186. [CrossRef]
Simon, J.-W., 2013, “Direct Evaluation of the Limit States of Engineering Structures exhibiting Limited, Nonlinear Kinematical Hardening,” Int. J. Plast., 42, pp. 141–167. [CrossRef]
Simon, J.-W., 2014, “Shakedown Analysis of Kinematically Hardening Structures in n-Dimensional Loading Spaces,” Direct Methods for Limit States in Structures and Materials, K. V.Spiliopoulos and D.Weichert, eds., Springer, New York, pp. 57–77. [CrossRef]
Wagner, W., 1991, Festigkeitsberechnungen im Apparate- und Rohrleitungsbau, Vogel Buchverlag, Würzburg, Germany.
Cloud, R. L., and Rodabaugh, E. C., 1968, “Approximate Analysis of the Plastic Limit Pressures of Nozzles in Cylindrical Shells,” J. Eng. Power, 90(2), pp. 171–176.
Mouhtamid, S., 2007, “Anwendung Direkter Methoden zur industriellen Berechnung von Grenzlasten Mechanischer Komponenten,” Ph.D. thesis, RWTH Aachen University, Aachen, Germany.
Fuschi, P., and Polizzotto, C., 1995, “The Shakedown Load Boundary of an Elastic Perfectly Plastic Structure,” Meccanica, 30(2), pp. 155–174. [CrossRef]
Schwabe, F., 2000, “Einspieluntersuchungen von Verbundwerkstoffen mit periodischer Mikrostruktur,” Ph.D. thesis, RWTH Aachen University, Aachen, Germany.
Simon, J.-W., Chen, G., and Weichert, D., 2014, “Shakedown Analysis of Nozzles in the Knuckle Region of Torispherical Heads Under Multiple Thermo-Mechanical Loadings,” Int. J. Pressure Vessels Piping, 116, pp. 47–55. [CrossRef]

Figures

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Fig. 1

Illustration of the two-yield surfaces

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Fig. 2

FE-mesh of pipe-junction

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Fig. 3

Loading and FE mesh of the sheet

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Fig. 4

Admissible loading domains for the elastic-perfectly plastic case

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Fig. 5

Admissible loading domains with limited kinematical hardening

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Fig. 6

System, mechanical loading, and mesh of the flanged pipe

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Fig. 7

Three-dimensional shakedown without hardening

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Fig. 8

Shakedown domain with hardening σU = 1.1 σY

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Fig. 9

Shakedown domain with hardening σU = 1.25 σY

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Fig. 10

Shakedown domain with hardening σU = 1.5 σY

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Fig. 11

Shakedown domain with unlimited hardening

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Fig. 12

Geometry and loading of the Klöpperboden model

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Fig. 13

FEM-model with boundary conditions

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Fig. 14

Elastic domain for the case of proportionally varying P/M/F

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Fig. 15

Elastic domain for the case of independently varying P/M/F

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Fig. 16

Shakedown domain for the case of independently varying P/M/F

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