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Research Papers: Design and Analysis

Estimating Lower Bound Limit Loads for Structures Subjected to Multiple Loads

[+] Author and Article Information
C. Hari Manoj Simha

CanmetMATERIALS,
183 Longwood Road South,
Hamilton, ON L8P 0A5, Canada
e-mail: hari.simha@nrcan.gc.ca

Reza Adibi-Asl

AMEC NSS,
393 University Avenue,
4th Floor,
Toronto, ON M5G 1E6, Canada
e-mail: reza.adibiasl@amec.com

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received January 15, 2014; final manuscript received February 6, 2015; published online February 23, 2015. Assoc. Editor: Albert E. Segall.

J. Pressure Vessel Technol 137(4), 041205 (Aug 01, 2015) (10 pages) Paper No: PVT-14-1004; doi: 10.1115/1.4029793 History: Received January 15, 2014; Revised February 06, 2015; Online February 23, 2015

It is shown that the extended variational theorem of Mura et al. (1965, “Extended Theorems of Limit Analysis,” Q. Appl. Math., 23(2), pp. 171–179) can be applied to structures subjected to more than one load and be used to compute lower bound limit load multipliers. In particular, the multiplier proposed by Simha and Adibi-Asl (2011, “Lower Bound Limit Load Estimation Using a Linear Elastic Analysis,” ASME J. Pressure Vessel Technol., 134(2), p. 021207), which can be computed using an elastic stress field, is shown to be a lower bound. Furthermore, it is demonstrated that lower bound limit load for cracked structures may also be computed using a subvolume selection method. No iterations or elastic modulus adjustment are required. Several analytical and numerical examples that illustrate the procedure are presented.

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Copyright © 2015 by ASME
Topics: Stress , Pressure
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References

American Society of Mechanical Engineers, 2007, Boiler and Pressure Vessel Code, Section III, Rules for Construction of Nuclear Facility Components.
American Petroleum Institute, 2007, ASME—API 579-1/ASME FFS-1 Fitness for Service, Washington, DC.
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(2), pp. 201–208. [CrossRef]
Mackenzie, D., Boyle, J. T., and Hamilton, R., 2000, “The Elastic Compensation Method for Limit and Shakedown Analysis: A Review,” J. Strain Anal. Eng. Des., 35(3), pp. 171–188. [CrossRef]
Belytschko, T., Liu, W. K., Moran, B., and Elkhodary, K., 2013, Nonlinear Finite Elements for Continua and Structures, John Wiley and Sons, New York.
Fraldi, M., Nunziante, L., Gesualdo, A., and Guarracino, F., 2010, “On the Bounding of Limit Load Multipliers for Combined Loading,” Proc. R. Soc. A, 466(2175), pp. 493–514. [CrossRef]
Seshadri, R., and Mangalaramanan, S. P., 1997, “Lower Bound Limit Loads Using Variational Concepts: The M(Alpha) Method,” Int. J. Pressure Vessels Piping, 71(2), pp. 93–106. [CrossRef]
Mura, T., Rimawi, W. H., and Lee, S. L., 1965, “Extended Theorems of Limit Analysis,” Q. Appl. Math., 23(2), pp. 171–179.
Reinhardt, W. D., and Seshadri, R., 2003, “Limit Load Bounds for the M(Alpha) Multiplier,” ASME J. Pressure Vessel Technol., 125(1), pp. 11–18. [CrossRef]
Seshadri, R., and Indermohan, H., 2004, “Lower Bound Limit Load Determination: The Mβ-Multiplier Method,” ASME J. Pressure Vessel Technol., 126(2), pp. 237–240. [CrossRef]
Seshadri, R., and Hossain, M. M., 2009, “Simplified Limit Load Determination Using the Mα-Tangent Method,” ASME J. Pressure Vessel Technol., 131(2), pp. 287–294. [CrossRef]
Adibi-Asl, R., and Seshadri, R., 2009, “Simplified Limit Load Estimation of Components With Cracks Using the Reference Two-Bar Structure,” ASME J. Pressure Vessel Technol., 131(1), p. 011204. [CrossRef]
Simha, C. H. M., and Adibi-Asl, R., 2011, “Lower Bound Limit Load Estimation Using a Linear Elastic Analysis,” ASME J. Pressure Vessel Technol., 134(2), p. 021207. [CrossRef]
Pan, L., and Seshadri, R. R., 2002, “Limit Load Estimation Using Plastic Flow Parameter in Repeated Elastic Finite Analyses,” ASME J. Pressure Vessel Technol., 124(4), pp. 433–439. [CrossRef]
Seshadri, R., 1991, “The Generalized Local Stress Strain (Gloss) Analysis—Theory and Applications,” ASME J. Pressure Vessel Technol., 113(2), pp. 219–227. [CrossRef]
Larson, L. D., Stokey, W. F., and Panarell, J. E., 1974, “Limit Analysis of a Thin-Walled Tube Under Internal-Pressure, Bending Moment, Axial Force, and Torsion,” ASME J. Appl. Mech., 41(3), pp. 831–832. [CrossRef]

Figures

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Fig. 1

Solid continuum with multiple loads and zero displacement regions. Extension of the variational formulation due to Mura et al. [8]. Dark gray is used for applied tractions, and a lighter gray is used for fixed displacement.

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Fig. 2

Subvolumes that participate in the collapse for a single load case. Gray-scale coloring is similar to what was used in Fig. 1. For clarity, only one traction and reaction are shown. Lightest gray is used to denote localized regions.

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Fig. 3

Analytical examples. Top: beam under axial load and moment. Bottom: pipe under internal pressure and moment loading.

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Fig. 4

Normalized multipliers versus nondimensional parameter λ for plate under bending and axial load. Asymptotic values of multipliers for pure bending are indicated.

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Fig. 5

Pressure moment interaction diagram and cross section of the pipe showing regions under compression and tension; β is the location of the neutral axis. The moment acts as shown in Fig. 3.

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Fig. 6

Normalized multipliers for pipe under bending and internal pressure

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Fig. 7

Through-wall cracked plate under axial loading and bending moment

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Fig. 8

Multipliers for cracked plate subjected to axial load and bending. Top: Closed symbols—Eq. (44) was used to compute m for normalization. Bottom: Open symbols—elastic–plastic finite element analysis was used to compute m. Lines are a guide for the eye.

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Fig. 9

Schematic of circumferentially cracked pipe with bending and pressure loads. Geometry of pipe and crack is also depicted.

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Fig. 10

Multipliers for circumferentially cracked pipe under internal pressure and in-plane bending. Elastic–plastic finite element analysis was used to compute m. Lines are a guide for the eye.

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Fig. 11

Convergence study for cracked plate under tension and bending. Loading is for λ = 0.8.

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Fig. 12

Contour plots of cracked plate and pipe. Left: elastic results; regions where (1/2)((σeɛe)(k)/ρ)≥0.15 are identified. Right: elastic–plastic results; regions where σe ≥ σy are identified.

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