RT Journal Article ID 143ce5132e29c67f A1 Sofi, Alba A1 Di Paola, Mario A1 Zingales, Massimiliano T1 STOCHASTIC ANALYSIS OF ONE-DIMENSIONAL HETEROGENEOUS SOLIDS WITH LONG-RANGE INTERACTIONS JF International Journal for Multiscale Computational Engineering JO JMC YR 2011 FD 2011-06-30 VO 9 IS 4 SP 379 OP 394 K1 nonlocal elasticity K1 long-range interactions K1 random mass density field K1 response statistics AB 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. PB Begell House LK https://www.dl.begellhouse.com/journals/61fd1b191cf7e96f,2c2262e958d8b1f7,143ce5132e29c67f.html