Keywords: reliability based optimization, limit analysis, residual strain energy, response surface.

Advances in the analysis of elasto-plastic steel (or composite) frames under static loading allow for very efficient and realistic modelling of these structures. In order to assess the probability of failure of the frames subject to uncertain loading conditions and with random material properties in the framework of limit analysis a general reliability analysis approach based on simulation and linear mathematical programming was proposed in [4]. Unfortunately, in the case of reliability-based design optimization the procedure presented in [4] is rather inefficient. The reliability-based design of frames with limited load carrying capacity of the connections and with probabilistically given residual energy condition, described by Logo et al. in [1], which is the foundation of the proposed fast reliability-based design optimization procedure, appears more promising.

The residual energy condition originates from the assumption, that the complementary strain energy of the residual forces can be considered as an overall measure of the plastic performance of the structure [2], and that this measure is an uncertain quantity. In other words, all design uncertainties such as material properties, manufacturing inaccuracy, etc. responsible for the resistance of the structure can be substituted by a single random variable. The probability of the occurrence of a failure event should be rare, therefore, a suitably low admissible level of the failure probability is assumed.

An introduction of yet another condition for the optimization procedure of finding the limit load multiplier results in two important consequences. It yields a nonlinear optimization problem that can be solved by using a sequential quadratic programming algorithm and the outcome of the optimization procedure is the limit load multiplier corresponding to the assumed admissible level of failure probability. The entire limit load envelope can be easily determined in this way. This envelope determines a region in the load space guaranteeing resistance of the structure for all combinations of loads. In practice, a response surface technique is used to reduce computational cost [3]. Failure probability with respect to the scatter of external loads is estimated in a classical fashion with the limit load envelope taken as the limit state function.

Product of these two failure probabilities determines global failure probability. Moreover, by changing cross section areas of the structural members we can obtain required global reliability level. Simple portal frame is optimized to illustrate the research results.

1

J. Lógó, M. Movahedi Rad, J. Knabel, Z. Hortobágyi, "Reliability Based Limit Analysis and Shakedown of Framed Structures with Limited Residual Strain Energy Capacity", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 161, 2008. doi:10.4203/ccp.88.161

2

S. Kaliszky, J. Lógó, "Optimal Plastic Limit and Shakedown Design of Bar Structures with Constraints on Plastic Deformation", Engineering Structures, 19(1), 19-27, 1997. doi:10.1016/S0141-0296(96)00066-1

3

K. Dolinski, J. Knabel, "Reliability-oriented Shakedown Formulation", in G. Augusti, G.I. Schueller, M. Ciampoli, (Editors), "ICOSSAR 2005", Millpress, Rotterdam, 2323-2330, 2005.

4

R.B. Corotis, A.M. Nafday, "Structural system reliability using linear programming and simulation", J. Struct. Eng., ASCE 115(10), 2435-2447, 1989. doi:10.1061/(ASCE)0733-9445(1989)115:10(2435)

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