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Review Article

Variational Method in Limit Load Analysis—A Review

[+] Author and Article Information
Reza Adibi-Asl

Kinectrics NSS,
393 University Avenue,
Toronto, ON M5G 1E6, Canada

R. Seshadri

Faculty of Engineering and Applied Science,
Memorial University,
St. John's, NL A1B 3X5, Canada

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received November 26, 2017; final manuscript received July 26, 2018; published online August 22, 2018. Assoc. Editor: Kiminobu Hojo.

J. Pressure Vessel Technol 140(5), 050804 (Aug 22, 2018) (13 pages) Paper No: PVT-17-1240; doi: 10.1115/1.4041058 History: Received November 26, 2017; Revised July 26, 2018

This paper reviews the literature on variational method in limit load analysis and presents both analytical and numerical approaches. One of the most successful applications of variational method in theory of plasticity is limit load analysis. The main objective of the limit load analysis is to estimate the load at the impending plastic limit state of a body. However, for complicated problems it may be very difficult to find the exact limit load. Therefore, based on the extremum principles of limit load analysis, the lower-bound theorem or the upper bound theorem is employed to estimate the limit load directly without considering the entire loading history. In general, limit load analysis plays an important role in design and fitness-for-service assessment of pressurized vessels and piping.

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Topics: Stress
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Figures

Grahic Jump Location
Fig. 1

A body with elastic-perfectly plastic material-fixed boundary conditions

Grahic Jump Location
Fig. 2

Regions of lower and upper bounds of mα

Grahic Jump Location
Fig. 3

Concept of lower-bound solution

Grahic Jump Location
Fig. 4

Concept of upper-bound solution

Grahic Jump Location
Fig. 7

Programming method, lower-bound solution

Grahic Jump Location
Fig. 8

Programming method, upper-bound solution

Grahic Jump Location
Fig. 9

Variation of limit load multipliers with iterations, q = 0.5

Grahic Jump Location
Fig. 10

Reference volume concept

Grahic Jump Location
Fig. 11

Schematic representation of plasticity spread at collapse for an indeterminate beam

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