Uncertainty Multimode Failure and Shakedown Analysis of Shells

  • Thanh Ngọc Trần
  • M. StaatEmail author


This paper presents a numerical procedure for reliability analysis of thin plates and shells with respect to plastic collapse or to inadaptation. The procedure involves a deterministic shakedown analysis for each probabilistic iteration, which is based on the upper bound approach and the use of the exact Ilyushin yield surface. Probabilistic shakedown analysis deals with uncertainties originated from the loads, material strength and thickness of the shell. Based on a direct definition of the limit state function, the calculation of the failure probability may be efficiently solved by using the First and Second Order Reliability Methods (FORM and SORM). The problem of reliability of structural systems (series systems) is handled by the application of a special technique which permits to find all the design points corresponding to all the failure modes. Studies show, in this case, that it improves considerably the FORM and SORM results.


Limit analysis Shakedown analysis Reliability analysis Multimode failure Non-linear optimization 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Chair of Mechanics and RoboticsUniversity of Duisburg-EssenDuisburgGermany
  2. 2.Institute for Bioengineering, Biomechanics LaboratoryAachen University of Applied Sciences, Jülich CampusJülichGermany

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