Research Papers: Design and Analysis

Limit Load Evaluation Using the mα-Tangent Multiplier in Conjunction With Elastic Modulus Adjustment Procedure

[+] Author and Article Information
S. L. Mahmood

e-mail: slm305@mun.ca

R. Seshadri

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

1Corresponding author. Present address: Babcock and Wilcox Canada Ltd., Cambridge, Ontario.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received September 26, 2012; final manuscript received March 31, 2013; published online August 30, 2013. Assoc. Editor: Wolf Reinhardt.

J. Pressure Vessel Technol 135(5), 051203 (Aug 30, 2013) (9 pages) Paper No: PVT-12-1157; doi: 10.1115/1.4024452 History: Received September 26, 2012; Revised March 31, 2013

In this paper, the mα-tangent multiplier is used in conjunction with the elastic modulus adjustment procedure (EMAP) for limit load determination. This technique is applied to a number of mechanical components possessing different kinematic redundancies. By specifying spatial variations in the elastic modulus, numerous sets of statically admissible and kinematically admissible stress and strain distributions are generated, and limit loads for practical components are then determined using the mα-tangent method. The procedure ensures sufficiently accurate limit loads within a reasonable number of iterations. Results are compared with the inelastic finite element results and are found to be in satisfactory agreement.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Borrvall, T., 2009, “A Heuristic Attempt to Reduce Transverse Shear Locking in Fully Integrated Hexahedra With Poor Aspect Ratio,” 7th European LS-DYNA Conference, May 14–15.
Xia, K., and Zhang Kenn, K. Q., 2009, “A Multiscale Finite Element Formulation for Axisymmetric Elastoplasticity With Volumetric Locking,” Int. J. Numer. Anal. Methods Geomech., 34, pp. 1076–1100.
Jones, G. L., and Dhalla, A. K., 1981, “Classification of Clamp Induced Stresses in Thin Walled Pipe,” Int. J. Pressure Vessels Piping, 81, pp. 17–23.
Seshadri, R., and Fernando, C. P. D., 1992, “Limit Loads of Mechanical Components and Structures Using the GLOSS R-Node Method,” ASME J. Pressure Vessel Technol., 114, pp. 201–208. [CrossRef]
Adibi-Asl, R., Fanous, I. F. Z., and Seshadri, R., 2006, “Elastic Modulus Adjustment Procedures-Improved Convergence Schemes,” Int. J. Pressure Vessels Piping, 83, pp. 154–160. [CrossRef]
Claudia C.Marin-Artieda, and Gary F.Dargush, 2007, “Approximate Limit Load Evaluation of Structural Frames Using Linear Elastic Analysis,” J. Eng. Struct., 29, pp. 296–304. [CrossRef]
Seshadri, R., and Hossain, M. M., 2009, “Simplified Limit Load Determination Using the mα-Tangent Method,” ASME J. Pressure Vessel Technol., 131(2), p. 021213. [CrossRef]
Mendelson, A., 1968, Plasticity: Theory and Applications, MacMillan, New York.
Mura, T., Rimawi, W. H., and Lee, S. L., 1965, “Extended Theorems of Limit Analysis,” Q. Appl. Math., 23, pp. 171–179.
Pan, L., and Seshadri, R., 2002, “Limit Load Estimation Using Plastic Flow Parameter in Repeated Elastic Finite Element Analyses,” ASME J. Pressure Vessel Technology, 124, pp. 433–439. [CrossRef]
Seshadri, R., and Mangalaramanan, S. P., 1997, “Lower Bound Limit Loads Using Variational Concepts: The mα–Method,” Int. J. Pressure Vessels Piping, 71, pp. 93–106. [CrossRef]
Reinhardt, W. D., and Seshadri, R., 2003, “Limit Load Bounds for the mα Multipliers,” ASME J. Pressure Vessel Technol., 125, pp. 11–18. [CrossRef]
Seshadri, R., and Adibi-Asl, R., 2007, “Limit Loads of Pressure Components Using the Reference Two-Bar Structure,” ASME J. Pressure Vessel Technol., 129, pp. 280–286. [CrossRef]
ansys, University Research Version 12.0, SAS IP, Inc.


Grahic Jump Location
Fig. 1

Finite element discretization of a body

Grahic Jump Location
Fig. 2

The mα-tangent construction plot

Grahic Jump Location
Fig. 3

Blunting of Peak Stresses (refer to Fig. 2)

Grahic Jump Location
Fig. 5

Bounds for mαT on the constraint map

Grahic Jump Location
Fig. 4

EMAP flow diagram for estimating limit load

Grahic Jump Location
Fig. 6

Reinforced axisymmetric nozzle model

Grahic Jump Location
Fig. 11

Results for grillage model

Grahic Jump Location
Fig. 7

Results for reinforced axisymmetric nozzle

Grahic Jump Location
Fig. 8

Flat thin head model

Grahic Jump Location
Fig. 9

Results for flat thin head

Grahic Jump Location
Fig. 10

Grillage model (dimensions in millimeter)



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