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

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 ele- ments. 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.