Novel interval model applied to derived variables in static and structural problems

  • Evgenija D. PopovaEmail author
  • Isaac Elishakoff


In this work, we further develop a newly proposed interval algebraic approach for analysis or design of structures involving uncertain interval-valued parameters. The methodology is based on an algebraic extension of classical interval arithmetic, namely Kaucher arithmetic, and within it the interval equilibrium equations can be completely satisfied by the primary unknown variables (displacements). Here this method is expanded to derived (secondary) variables—forces, strains and stresses which are of particular practical interest in design and strength of materials. Numerical examples are presented to illustrate the proposed methodology and to compare the algebraic interval approach to that based on classical interval arithmetic.


Uncertainty Interval arithmetic Finite element models Forces Strains Stresses 



The first author is supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICTinSES)”, financed by the Bulgarian Ministry of Education and Science.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Department of Ocean and Mechanical EngineeringFlorida Atlantic UniversityBoca RatonUSA

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