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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.

Copyright © 2015 by ASME
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References

Figures

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Fig. 2

FE-mesh of pipe-junction

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Fig. 1

Illustration of the two-yield surfaces

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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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