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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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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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