SHAKEDOWN ANALYSIS OF PLATE BENDING UNDER STOCHASTIC UNCERTAINTY BY CHANCE CONSTRAINED PROGRAMMING

1 Aachen University of Applied Sciences, Jülich Campus, Institute for Bioengineering, Biomechanics Lab., Heinrich-Mußmann-Str. 1, 52428 Jülich, Germany, trinhdhkt@gmail.com, m.staat@fhaachen.de, http://www.fh-aachen.de/forschung/institut-fuer-bioengineering/ 2 University of Duisburg-Essen, Chair of Mechanics and Robotics, Lotharstr. 1, 47057 Duisburg, Germany, thanh.tran@uni-due.de 3 TU Braunschweig, Institute of Scientific Computing, Hans-Sommer-Str. 65, 38092 Braunschweig, Germany, wire@tu-bs.de 4 Technical University of Crete, 73100 Chania, Greece, gestavr@dpem.tuc.gr

[1]  T. N. Tran.  A dual algorithm for shakedown analysis of plate bending , 2011 .

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

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

[4]  Manfred Staat,et al.  Numerical methods for limit and shakedown analysis : deterministic and probabilistic problems , 2003 .

[5]  Michael L. Overton,et al.  An Efficient Primal-Dual Interior-Point Method for Minimizing a Sum of Euclidean Norms , 2000, SIAM J. Sci. Comput..

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

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

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

[9]  Antonio Capsoni,et al.  Limit analysis of plates-a finite element formulation , 1999 .

[11]  D. Vu,et al.  Shakedown analysis of structures made of materials with temperature-dependent yield stress , 2007 .

[12]  Matthew Gilbert,et al.  Limit analysis of plates using the EFG method and second‐order cone programming , 2009 .

[13]  David Lloyd Smith,et al.  Mathematical programming methods in structural plasticity , 1990 .

[14]  D. Weichert,et al.  Direct Methods for Limit and Shakedown Analysis of Structures: Advanced Computational Algorithms and Material Modelling , 2015 .

[15]  Ted Belytschko,et al.  Numerical Methods for the Limit Analysis of Plates , 1968 .

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

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

[18]  Manfred Staat,et al.  FEM-computation of load carrying capacity of highly loaded passive components by direct methods , 1999 .

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

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

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