One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis

• One-dimensional non-local elastic solids with uncertain Young’s modulus.
• Non-local effects result in long-range forces between non-adjacent volume elements.
• A novel interval field concept able to account for spatial dependency is proposed.
• The upper and lower bound of the displacement field are determined in closed-form.
• The interval response region is compared to the probabilistic confidence interval.

The analysis of one-dimensional non-local elastic solids with uncertain Young’s modulus is addressed. Non-local effects are represented as long-range central body forces between non-adjacent volume elements. For comparison purpose, the fluctuating elastic modulus of the material is modeled following both a probabilistic and a non-probabilistic approach. To this aim, a novel definition of the interval field concept, able to limit the overestimation affecting ordinary interval analysis, is introduced. Approximate closed-form expressions are derived for the bounds of the interval displacement field as well as for the mean-value and variance of the stochastic response.