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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., block 8, 1113, Sofia, Bulgaria

    Evgenija D. Popova

  2. Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL, USA

    Isaac Elishakoff

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  1. Evgenija D. Popova
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  2. Isaac Elishakoff
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Correspondence to Evgenija D. Popova.

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Popova, E.D., Elishakoff, I. Novel interval model applied to derived variables in static and structural problems. Arch Appl Mech 90, 869–881 (2020). https://doi.org/10.1007/s00419-019-01644-8

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