A Complementarity Approach for Elastoplastic Analysis of Frames with Uncertainties

Abstract:

Traditional elastoplastic analysis presumes that all structural data are known exactly. However, these values often cannot be predicted precisely: they are influenced by such factors as manufacturing errors, material defects, and environmental changes. Ignoring these may lead to inaccurate (overly conservative or nonconservative) results. It is thus important that the effects of uncertain data be quantified in a reliable assessment of structural safety. This paper presents the elastoplastic analysis of skeletal frames with uncertaintiesassumed to be interval quantities (i.e. with known upper and lower bounds). Starting from the well-known mixed complementarity program (MCP) statement of the state problem without uncertainties, we extend this to an optimisation problem formulation involving complementarity constraints (that represent the plastic nature of the ductile material). Calculations for both upper and lower bounds of displacements corresponding to monotonically increasing loads are computed. The final results are checked through a comparison with interval limit analyses and Monte Carlo simulations.

• Periodical: Applied Mechanics and Materials (Volume 553)
• Pages: 594-599
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.553.594
• Online since: May 2014
• Authors: Cheng Wei Yang*, Francis Tin-Loi, Sawekchai Tangaramvong, Wei Gao
• Keywords: Complementarity, Elastoplastic Analysis, Interval Data, Stepwise Holonomic, Uncertainty

References

[1] A. Der Kiureghian, Measures of structural safety under imperfect states of knowledge, Journal of Structural Engineering New York, N.Y. 115 (1989) 1119–1140.

DOI: 10.1061/(asce)0733-9445(1989)115:5(1119)

[2] B. Möller, M. Beer, Engineering computation under uncertainty - Capabilities of non-traditional models, Computers and Structures. 86 (2008) 1024–1041.

DOI: 10.1016/j.compstruc.2007.05.041

[3] Z.Q. Luo, J.S. Pang, D. Ralph, Mathematical Programs with Equilibrium Constraints, Cambridge University Press, Cambridge, (1996).

[4] G. Maier, A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes, Meccanica. 5 (1966) 54–66.

DOI: 10.1007/bf02133524

[5] O. De Donato, A. Franchi, A modified gradient method for finite element elastoplastic analysis by quadratic programming, Computer Methods in Applied Mechanics and Engineering. 2 (1973) 107–131.

DOI: 10.1016/0045-7825(73)90010-8

[6] S. Tangaramvong, F. Tin-Loi, D. Wu, W. Gao, Mathematical programming approaches for obtaining sharp collapse load bounds in interval limit analysis, Computers and Structures. 125 (2013) 114–126.

DOI: 10.1016/j.compstruc.2013.04.028

[7] P.T. Harker, J.S. Pang, Existence of optimal solutions to mathematical programs with equilibrium constraints, Operations Research Letters. 7 (1988) 61–64.

DOI: 10.1016/0167-6377(88)90066-1

[8] S. Tangaramvong, F. Tin-Loi, Simultaneous ultimate load and deformation analysis of strain softening frames under combined stresses, Engineering Structures. 30 (2008) 664–674.

DOI: 10.1016/j.engstruct.2007.05.014