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Research Papers

Interval Limit Analysis Within a Scaled Boundary Element Framework

[+] Author and Article Information
S. Tangaramvong

Lecturer
Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering,
The University of New South Wales,
Sydney, NSW 2052, Australia,
e-mail: sawekchai@unsw.edu.au

F. Tin-Loi

Emeritus Professor
Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering,
The University of New South Wales,
Sydney, NSW 2052, Australia,
e-mail: f.tinloi@unsw.edu.au

C. M. Song

Professor
Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering,
The University of New South Wales,
Sydney, NSW 2052, Australia,
e-mail: c.song@unsw.edu.au

W. Gao

Associate Professor
Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering,
The University of New South Wales,
Sydney, NSW 2052, Australia,
e-mail: w.gao@unsw.edu.au

1Corresponding author.

Manuscript received November 8, 2014; final manuscript received March 16, 2015; published online October 2, 2015. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 1(4), 041004 (Oct 02, 2015) (9 pages) Paper No: RISK-14-1081; doi: 10.1115/1.4030471 History: Received November 08, 2014; Accepted April 28, 2015; Online October 02, 2015

The paper proposes a novel approach for the interval limit analysis of rigid-perfectly plastic structures with (nonprobabilistic) uncertain but bounded forces and yield capacities that vary within given continuous ranges. The discrete model is constructed within a polygon-scaled boundary finite element framework, which advantageously provides coarse mesh accuracy even in the presence of stress singularities and complex geometry. The interval analysis proposed is based on a so-called convex model for the direct determination of both maximum and minimum collapse load limits of the structures involved. The formulation for this interval limit analysis takes the form of a pair of optimization problems, known as linear programs with interval coefficients (LPICs). This paper proposes a robust and efficient reformulation of the original LPICs into standard nonlinear programming (NLP) problems with bounded constraints that can be solved using any NLP code. The proposed NLP approach can capture, within a single step, the maximum collapse load limit in one case and the minimum collapse load limit in the other, and thus eliminates the need for any combinatorial search schemes.

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References

Kamenjarzh, J. A., 1996, Limit Analysis of Solids and Structures, CRC Press, Boca Raton.
Elishakoff, I., and Soize, C., 2012, Nondeterministic Mechanics, Springer, New York.
Möller, B., and Beer, M., 2008, “Engineering Computation Under Uncertainty—Capabilities of Non-Traditional Models,” Comput. Struct., 86(10), pp. 1024–1041. 10.1016/j.compstruc.2007.05.041
Schuëller, G. I., 2007, “On the Treatment of Uncertainties in Structural Mechanics and Analysis,” Comput. Struct., 85, pp. 235–243. 10.1016/j.compstruc.2006.10.009
Alibrandi, U., and Ricciardi, G., 2005, “Bounds of the Probability of Collapse of Rigid-Plastic Structures by Means of Stochastic Limit Analysis,” Proceedings of the 9th International Conference on Structural Safety and Reliability, Rome, Italy, June 19–23.
Alibrandi, U., and Ricciardi, G., 2008, “The Use of Stochastic Stresses in the Static Approach of Probabilistic Limit Analysis,” Int. J. Numer. Methods Eng., 73(6), pp. 747–782. 10.1002/nme.v73:6
Augusti, G., Baratta, A., and Casciati, F., 1984, Probabilistic Methods in Structural Engineering, Chapman & Hall, London.
Staat, M., and Heitzer, M., 2001, “LISA—A European Project for FEM-Based Limit and Shakedown Analysis,” Nucl. Eng. Des., 206(2–3), pp. 151–166. 10.1016/S0029-5493(00)00415-5
Staat, M., and Heitzer, M., 2003, “Part VII. Probabilistic Limit and Shakedown Problems,” Numerical Methods for Limit and Shakedown Analysis—Deterministic and Probabilistic Problems, M. Staat, and M. Heitzer, eds., (NIC Series, Vol. 15), pp. 217–268.
Ben-Haim, Y., and Elishakoff, I., 1990, Convex Models of Uncertainty in Applied Mechanics, Elsevier Science, Amsterdam.
Song, Ch., and Wolf, J. P., 1997, “The Scaled Boundary Finite-Element Method—Alias Consistent Infinitesimal Finite-Element Cell Method—For Elastodynamics,” Comput. Methods Appl. Mech. Eng., 147(1–2), pp. 329–355. 10.1016/S0045-7825(97)00021-2
Ooi, E. T., Song, Ch., Tin-Loi, F., and Yang, Z., 2012, “Polygon Scaled Boundary Finite Elements for Crack Propagation Modelling,” Int. J. Numer. Methods Eng., 91(3), pp. 319–342. 10.1002/nme.v91.3
Chiong, I., Ooi, E. T., Song, Ch., and Tin-Loi, F., 2014, “Scaled Boundary Polygons With Application to Fracture Analysis of Functionally Graded Materials,” Int. J. Numer. Methods Eng., 98(8), pp. 562–589. 10.1002/nme.v98.8
Maier, G., 1970, “A Matrix Structural Theory of Piecewise Linear Elastoplasticity With Interacting Yield Planes,” Meccanica, 5(1), pp. 54–66. 10.1007/BF02133524
Chinneck, J. W., and Ramadan, K., 2000, “Linear Programming With Interval Coefficients,” J. Oper. Res. Soc., 51(2), pp. 209–220. 10.1057/palgrave.jors.2600891
Deeks, A. J., and Wolf, J. P., 2002, “A Virtual Work Derivation of the Scaled Boundary Finite-Element Method for Elastostatics,” Comput. Mech., 28(6), pp. 489–504. [CrossRef]
Tangaramvong, S., Tin-Loi, F., and Senjuntichai, T., 2011, “An MPEC Approach for the Critical Post-Collapse Behavior of Rigid-Plastic Structures,” Int. J. Solids Struct., 48(19), pp. 2732–2742. 10.1016/j.ijsolstr.2011.05.022
Tangaramvong, S., Tin-Loi, F., Wu, D., and Gao, W., 2013, “Mathematical Programming Approaches for Obtaining Sharp Collapse Load Bounds in Interval Limit Analysis,” Comput. Struct., 125, pp. 114–126. 10.1016/j.compstruc.2013.04.028
Shaocheng, T., 1994, “Interval Number and Fuzzy Number Linear Programmings,” Fuzzy Sets Syst., 66(3), pp. 301–306. 10.1016/0165-0114(94)90097-3
Drud, A. S., 1994, “CONOPT—A Large-Scale GRG Code,” ORSA J. Comput., 6, pp. 207–216. 10.1287/ijoc.6.2.207
Brooke, A., Kendrick, D., Meeraus, A., and Raman, R., 1998, GAMS: A User’s Guide, GAMS Development Corporation, Washington, DC.
Ferris, M. C., 1998, “MATLAB and GAMS: Interfacing Optimization and Visualization Software,” Computer Sciences Department, University of Wisconsin, Madison, WI, Technical Report TR98-19.
Sloan, S. W., and Kleeman, P. W., 1995, “Upper Bound Limit Analysis Using Discontinuous Velocity Fields,” Comput. Methods Appl. Mech. Eng., 127(1–4), pp. 293–314. 10.1016/0045-7825(95)00868-1
Vicente da Silva, M., and Antão, A. N., 2007, “A Non-Linear Programming Method Approach for Upper Bound Limit Analysis,” Int. J. Numer. Methods Eng., 72(10), pp. 1192–1218. 10.1002/(ISSN)1097-0207
Tangaramvong, S., Tin-Loi, F., and Song, C., 2012, “A Direct Complementarity Approach for the Elastoplastic Analysis of Plane Stress and Plane Strain Structures,” Int. J. Numer. Methods Eng., 90(7), pp. 838–866. 10.1002/nme.v90.7
Simo, J. C., and Rifai, M. S., 1990, “A Class of Mixed Assumed Strain Methods and the Method of Incompatible Modes,” Int. J. Numer. Methods Eng., 29(8), pp. 1595–1638. 10.1002/(ISSN)1097-0207

Figures

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Fig. 1

Polygon-scaled boundary finite element: (a) only the boundary is divided into line elements and the domain is described by scaling the boundary; (b) two-node element at boundary; and (c) three-node element at boundary

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Fig. 2

Generic four-node square-scaled boundary finite element (ξ=1 and η=0); × denotes integration points

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Fig. 3

Piecewise linear plane strain von Mises (Tresca) plasticity model in σx−σy−τxy space

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Fig. 4

Example 1: Prandtl’s punch: (a) geometry and nominal loading and (b) scaled boundary finite element model

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Fig. 5

Example 1: plasticity dispositions at (a) αcol, (b) α ¯, and (c) α̲, where • denotes plastic state

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Fig. 6

Example 2: double-edge notched specimen: (a) geometry and nominal loading and (b) scaled boundary finite element model

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Fig. 7

Example 2: plasticity dispositions at (a) αcol, (b) α ¯, and (c) α̲, where • denotes plastic state

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