Robust assessment of collapse resistance of structures under uncertain loads based on Info-Gap model

Abstract The paper proposes a pair of novel mathematical programming based approaches which directly determine the worst collapse load limit in one case, and the best limit in the other case of rigid perfectly-plastic structures subjected to uncertain-but-bounded applied loads using an Info-Gap model. The methods take advantage of the important properties in which the worst collapse load limit defined for an uncertain static formulation is equivalent to the most favourable solution of the uncertain kinematic limit analysis problem, and vice versa for the best collapse load limit. The formulation for capturing the worst collapse load limit (robust worst case solution) takes the form as a mathematical program with equilibrium constraints that is processed using a penalty algorithm, whilst that for the best collapse load limit is a standard linear programming problem. The efficiency and robustness of the proposed schemes are evidenced from a number of successfully solved examples.

[1]  Francis Tin-Loi,et al.  Simultaneous ultimate load and deformation analysis of strain softening frames under combined stresses , 2008 .

[2]  Chen Qiu,et al.  A new approach to fuzzy finite element analysis , 2002 .

[3]  Francis Tin-Loi,et al.  Limit analysis of elastoplastic frames considering 2nd-order geometric nonlinearity and displacement constraints , 2009 .

[4]  Scott W. Sloan,et al.  Lower bound limit analysis using non‐linear programming , 2002 .

[5]  Jirina Vejnarová,et al.  Imprecise probability models and their applications , 2009, Int. J. Approx. Reason..

[6]  Y. Ben-Haim.  Robust reliability in the mechanical sciences , 1996 .

[7]  Hao Zhang,et al.  Interval importance sampling method for finite element-based structural reliability assessment under parameter uncertainties , 2012 .

[8]  Hwan Chung,et al.  Bayesian approaches to the model selection problem in the analysis of latent stage-sequential process , 2012, Comput. Stat. Data Anal..

[9]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[10]  Vaithilingam Jeyakumar,et al.  Characterizing robust set containments and solutions of uncertain linear programs without qualifications , 2010, Oper. Res. Lett..

[11]  Arkadi Nemirovski,et al.  Robust solutions of uncertain linear programs , 1999, Oper. Res. Lett..

[12]  G. Falsone,et al.  A new approach for the stochastic analysis of finite element modelled structures with uncertain parameters , 2002 .

[13]  C. Jiang,et al.  Structural reliability analysis using non-probabilistic convex model , 2013 .

[14]  David Moens,et al.  A survey of non-probabilistic uncertainty treatment in finite element analysis , 2005 .

[15]  Marco Savoia,et al.  Structural reliability analysis through fuzzy number approach, with application to stability , 2002 .

[16]  Giulio Maier,et al.  On structural safety assessment by load factor maximization in piecewise linear plasticity , 2008 .

[17]  K. Marti.  Approximation and derivatives of probabilities of survival in structural analysis and design , 1997 .

[18]  Yakov Ben-Haim,et al.  Info-Gap Economics: An Operational Introduction , 2010 .

[19]  Z. Kang,et al.  Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models , 2009 .

[20]  Vaithilingam Jeyakumar,et al.  Robust duality for generalized convex programming problems under data uncertainty , 2012 .

[21]  M. Ferris,et al.  On the solution of a minimum weight elastoplastic problem involving displacement and complementarity constraints , 1999 .

[22]  K. Marti,et al.  Limit load and shakedown analysis of plastic structures under stochastic uncertainty , 2008 .

[23]  Giulio Maier,et al.  Combined elastoplastic and limit analysis via restricted basis linear programming , 1979 .

[24]  G. Quaranta.  Finite element analysis with uncertain probabilities , 2011 .

[25]  T. Wasfy,et al.  Finite element analysis of flexible multibody systems with fuzzy parameters , 1998 .

[26]  C. Jiang,et al.  Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval , 2007 .

[27]  I. Elishakoff,et al.  Convex models of uncertainty in applied mechanics , 1990 .

[28]  Z. Kang,et al.  On non-probabilistic reliability-based design optimization of structures with uncertain-but-bounded parameters , 2011 .

[29]  Manolis Papadrakakis,et al.  The effect of material and thickness variability on the buckling load of shells with random initial imperfections , 2005 .

[30]  Ying Xiong,et al.  A better understanding of model updating strategies in validating engineering models , 2009 .

[31]  Zhan Kang,et al.  On robust design optimization of truss structures with bounded uncertainties , 2013 .

[32]  M. Beer,et al.  Engineering computation under uncertainty - Capabilities of non-traditional models , 2008 .

[33]  Amir Beck,et al.  Duality in robust optimization: Primal worst equals dual best , 2009, Oper. Res. Lett..

[34]  I. Elishakoff,et al.  Finite Element Methods for Structures with Large Stochastic Variations , 2003 .

[35]  P. Level,et al.  Fuzzy behavior of mechanical systems with uncertain boundary conditions , 2000 .

[36]  Izuru Takewaki,et al.  Worst case plastic limit analysis of trusses under uncertain loads via mixed 0-1 programming , 2007 .

[37]  Michał Kleiber,et al.  The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation , 1993 .

[38]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[39]  Giulio Maier,et al.  Elastic¿plastic and limit-state analyses of frames with softening plastic-hinge models by mathematical programming , 2003 .

[40]  George Stefanou,et al.  Buckling analysis of imperfect shells with stochastic non-Gaussian material and thickness properties , 2009 .

[41]  Francis Tin-Loi,et al.  Performance of the p-version finite element method for limit analysis , 2003 .

[42]  C. Jiang,et al.  Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique , 2011 .

[43]  Arne Stolbjerg Drud,et al.  CONOPT - A Large-Scale GRG Code , 1994, INFORMS J. Comput..

[44]  Y. Ben-Haim.  Information-gap decision theory : decisions under severe uncertainty , 2001 .

[45]  Xu Han,et al.  An uncertain structural optimization method based on nonlinear interval number programming and interval analysis method , 2007 .

[46]  G. Muscolino,et al.  Interval analysis of structures with uncertain-but-bounded axial stiffness , 2011 .

[47]  G. Maier.  A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes , 1970 .