Research Papers: Numerical Methods

Progress in Lower Bound Direct Methods

[+] Author and Article Information
D. Weichert

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

A. Hachemi

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

J. Simon

Institute of Applied Mechanics
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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


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]


Grahic Jump Location
Fig. 1

Illustration of the two-yield surfaces

Grahic Jump Location
Fig. 2

FE-mesh of pipe-junction

Grahic Jump Location
Fig. 3

Loading and FE mesh of the sheet

Grahic Jump Location
Fig. 4

Admissible loading domains for the elastic-perfectly plastic case

Grahic Jump Location
Fig. 5

Admissible loading domains with limited kinematical hardening

Grahic Jump Location
Fig. 6

System, mechanical loading, and mesh of the flanged pipe

Grahic Jump Location
Fig. 12

Geometry and loading of the Klöpperboden model

Grahic Jump Location
Fig. 14

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

Grahic Jump Location
Fig. 15

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

Grahic Jump Location
Fig. 16

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

Grahic Jump Location
Fig. 7

Three-dimensional shakedown without hardening

Grahic Jump Location
Fig. 8

Shakedown domain with hardening σU = 1.1 σY

Grahic Jump Location
Fig. 9

Shakedown domain with hardening σU = 1.25 σY

Grahic Jump Location
Fig. 13

FEM-model with boundary conditions

Grahic Jump Location
Fig. 10

Shakedown domain with hardening σU = 1.5 σY

Grahic Jump Location
Fig. 11

Shakedown domain with unlimited hardening



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In