ISSN 打印: 1543-1649
ISSN 在线: 1940-4352

# 国际多尺度计算工程期刊

DOI: 10.1615/IntJMultCompEng.v9.i4.30
pages 379-394

## STOCHASTIC ANALYSIS OF ONE-DIMENSIONAL HETEROGENEOUS SOLIDS WITH LONG-RANGE INTERACTIONS

Mario Di Paola
Dipartimento di Ingegneria Strutturale, Aerospaziale e Geotecnica, Università degli Studi di Palermo, Viale delle Scienze, I-90128, Palermo, Italy
Alba Sofi
Dipartimento Patrimonio Architettonico ed Urbanistico, University Mediterranea di Reggio Calabria, Italy
Massimiliano Zingales
Dipartimento di Ingegneria Strutturale, Aerospaziale e Geotecnica, Università degli Studi di Palermo, Italy

### ABSTRACT

Random mass distribution in one-dimensional (1D) elastic solids in the presence of long-range interactions is studied in this paper. Besides the local Cauchy contact forces among adjacent elements, long-range forces depending on the product of interacting masses, as well as on their relative displacements, are considered. In this context, the random fluctuations of the mass distribution involve a stochastic model of the nonlocal interactions, and the random displacement field of the body is provided as the solution of a stochastic integro-differential equation. The presence of the random field of mass distribution is reflected in the random kernel of the solving integro-differential equation with deterministic static and kinematic boundary conditions, since the long-range interactions have no effects at the borders. Numerical applications are reported to highlight the effects of fluctuations of the mass field along the body on the long-range forces and the mechanical response of the 1D elastic body considered.

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