Direct plastic structural design under lognormally distributed strength by chance constrained programming

We propose the so-called chance constrained programming model of stochastic programming theory to analyze limit and shakedown loads of structures under random strength with a lognormal distribution. A dual chance constrained programming algorithm is developed to calculate simultaneously both the upper and lower bounds of the plastic collapse limit and the shakedown limit. The edge-based smoothed finite element method (ES-FEM) is used with three-node linear triangular elements.

[1]  Johannes Groβ-Weege.  On the numerical assessment of the safety factor of elastic-plastic structures under variable loading , 1997 .

[2]  Leone Corradi,et al.  A linear programming approach to shakedown analysis of structures , 1974 .

[3]  Ross B. Corotis,et al.  Stochastic programs for identifying critical structural collapse mechanisms , 1991 .

[4]  H. Nguyen-Dang,et al.  A primal–dual algorithm for shakedown analysis of structures , 2004 .

[5]  Francesco Genna.  A nonlinear inequality, finite element approach to the direct computation of shakedown load safety factors , 1988 .

[6]  FEM Shakedown of uncertain structures by chance constrained programming , 2016 .

[7]  A. Charnes,et al.  Chance-Constrained Programming , 1959 .

[8]  A theoretical investigation of the yield point loading of a square plate with a central circular hole , 1954 .

[9]  L. Fenton.  The Sum of Log-Normal Probability Distributions in Scatter Transmission Systems , 1960 .

[10]  Manfred Staat,et al.  Reliability Analysis of Elasto-Plastic Structures under Variable Loads , 2000 .

[11]  Singiresu S. Rao.  Engineering Optimization : Theory and Practice , 2010 .

[12]  Uncertainty Multimode Failure and Shakedown Analysis of Shells , 2015 .

[13]  N. Zouain.  Shakedown and Safety Assessment , 2004 .

[14]  T. N. Tran,et al.  An edge‐based smoothed finite element method for primal–dual shakedown analysis of structures , 2010 .

[15]  A. Ruszczynski.  Stochastic Programming Models , 2003 .

[16]  Manfred Staat,et al.  Basis Reduction for the Shakedown Problem for Bounded Kinematic Hardening Material , 2000, J. Glob. Optim..

[17]  Ted Belytschko,et al.  Plane stress shakedown analysis by finite elements , 1972 .

[18]  S. Kataoka.  A Stochastic Programming Model , 1963 .

[19]  Manfred Staat.  LIMIT AND SHAKEDOWN ANALYSIS UNDER UNCERTAINTY , 2014 .

[20]  D. Proske.  Bridge Collapse Frequencies versus Failure Probabilities , 2018 .

[21]  Abraham Charnes,et al.  Chance Constraints and Normal Deviates , 1962 .

[22]  F. Tin-Loi,et al.  Elastoplastic analysis of structures under uncertainty: model and solution methods 1 , 1999 .

[23]  G. Garcea,et al.  Finite element shakedown analysis of two‐dimensional structures , 2005 .

[24]  Liqun Qi,et al.  Stochastic ultimate load analysis:models and solution methods 1 , 1996 .

[25]  Hung Nguyen-Xuan,et al.  An edge‐based smoothed finite element method for primal–dual shakedown analysis of structures , 2010 .

[26]  Shakedown Analysis Under Stochastic Uncertainty by Chance Constrained Programming , 2018 .

[27]  Manfred Staat,et al.  Analysis of pressure equipment by application of the primal-dual theory of shakedown , 2006 .

[28]  T. N. Tran,et al.  Reliability Analysis of Inelastic Shell Structures Under Variable Loads , 2009 .

[29]  Manfred Staat,et al.  Probabilistic limit and shakedown analysis of thin plates and shells , 2009 .

[30]  Palle Thoft-Christensen,et al.  Structural Reliability Theory and Its Applications , 1982 .

[31]  Niels C. Lind,et al.  Methods of structural safety , 2006 .

[32]  Vu Duc Khoi.  DUAL LIMIT AND SHAKEDOWN ANALYSIS OF STRUCTURES , 2001 .

[33]  Manfred Staat,et al.  SHAKEDOWN ANALYSIS OF PLATE BENDING UNDER STOCHASTIC UNCERTAINTY BY CHANCE CONSTRAINED PROGRAMMING , 2016, Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016).

[34]  Manfred Staat,et al.  FEM-based shakedown analysis of hardening structures , 2014 .

[35]  Jingxian Wu,et al.  Approximating a Sum of Random Variables with a Lognormal , 2007, IEEE Transactions on Wireless Communications.

[36]  Jaan-Willem Simon,et al.  Shakedown analysis of engineering structures with limited kinematical hardening , 2012 .

[37]  Pu Li,et al.  Chance constrained programming approach to process optimization under uncertainty , 2008, Comput. Chem. Eng..

[38]  V. V Kolbin,et al.  Stochastic Programming , 1977 .

[39]  G. R. Liu,et al.  On Smoothed Finite Element Methods , 2010 .

[40]  A. Borkowski,et al.  Ultimate Load Analysis by Stochastic Programming , 1990 .

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