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Improved solution to the generalized Galilei’s problem with interval loads

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Abstract

Model of a bar subjected to multiple axial external loads, where load magnitudes are considered as uncertain and represented by intervals, is recently considered by Elishakoff, Gabriele and Wang in this journal. Beside a high complexity of the proposed procedure for computing the intervals of the reaction and of the axial force distribution its assumptions are not always fulfilled and in these cases the obtained interval enclosures are far from the optimal (narrowest) ones. In this work we present a simple and efficient computational model for the reaction and for the axial force distribution which is based on the algebraic extension of classical interval arithmetic. It is proved that this model always yields the narrowest interval enclosure. The new interval model can be generalized and applied to other linear equilibrium equations in mechanics.

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Notes

  1. For the sake of better understanding, we denote intervals from \(\mathbb {KR}\) by [a]. Of course, \(\mathbf {a}\in \mathbb {IR}\subset \mathbb {KR}\), and thus, \([a]=\mathbf {a}\in \mathbb {KR}\) is a correct assignment.

  2. In the text of this work forces (and other vector quantities) are denoted by drawing a short arrow above the letter used to represent it. This is necessary in order to distinguish vectors from the interval-valued scalars, which are denoted by bold-faced letters, and other real-valued scalars. The magnitude of a vector will be denoted by the corresponding italic-faced letter.

  3. The IEEE interval Std. 1788 does not prescribe functionality for simulating multiplication/division of generalized (Kaucher) intervals.

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

    Evgenija D. Popova

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  1. Evgenija D. Popova
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Popova, E.D. Improved solution to the generalized Galilei’s problem with interval loads. Arch Appl Mech 87, 115–127 (2017). https://doi.org/10.1007/s00419-016-1180-2

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