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

摘要

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.