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

Di Paola, M., Sofi, A., Zingales, M. (2011). STOCHASTIC ANALYSIS OF ONE-DIMENSIONAL HETEROGENEOUS SOLIDS WITH LONG-RANGE INTERACTIONS. INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, 9(4), 379-394 [10.1615/IntJMultCompEng.v9.i4.30].

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

DI PAOLA, Mario;ZINGALES, Massimiliano
2011-01-01

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
Settore ICAR/08 - Scienza Delle Costruzioni
Di Paola, M., Sofi, A., Zingales, M. (2011). STOCHASTIC ANALYSIS OF ONE-DIMENSIONAL HETEROGENEOUS SOLIDS WITH LONG-RANGE INTERACTIONS. INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, 9(4), 379-394 [10.1615/IntJMultCompEng.v9.i4.30].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/63775
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