Acta Mechanica

, Volume 219, Issue 1–2, pp 45–64 | Cite as

Probability and convexity concepts are not antagonistic

  • Xiaojun Wang
  • Lei Wang
  • Isaac Elishakoff
  • Zhiping Qiu


This study is devoted to two objectives to illustrate that the probability and convexity concepts are not antagonistic and to introduce a new non-probabilistic convex model for structural reliability analysis. It is shown that the new measure of safety is easier to evaluate than the corresponding measure utilizing the interval analysis. Moreover, interrelation between the classical probabilistic method and convex modeling method is demonstrated. The purpose of this study is not to replace the probabilistic approach by the convex modeling method, but to illustrate that the probability and convexity concepts are compatible. Some numerical examples are presented to illustrate the feasibility of the proposed methodology.


Uncertain Parameter Interval Analysis Safe Region Uncertain Variable Limit State Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Xiaojun Wang
    • 1
  • Lei Wang
    • 1
  • Isaac Elishakoff
    • 2
  • Zhiping Qiu
    • 1
  1. 1.Institute of Solid MechanicsBeijing University of Aeronautics and AstronauticsBeijingChina
  2. 2.Department of Mechanical EngineeringFlorida Atlantic UniversityBoca RatonUSA

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