Publication de 6 numéros par an
ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352
Indexed in
STOCHASTIC ANALYSIS OF ONE-DIMENSIONAL HETEROGENEOUS SOLIDS WITH LONG-RANGE INTERACTIONS
RÉSUMÉ
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.
-
Aifantis, E. C. and Frantziskonis, G., On the stochastic interpretation of gradient-dependent constitutive equations. DOI: 10.1016/S0997-7538(01)01201-3
-
Aifantis, E. C., Gradient effects at macro micro and nanoscales.
-
Altan, B. S. and Aifantis, E. C., On some aspects in the special theory of gradient elasticity.
-
Bažant, Z. P. and Belytschko, T. B., Continuum theory for strain-softening.
-
Bažant, Z. P. and Jirásek, M., Nonlocal integral formulations of plasticity and damage: survey of progress. DOI: 10.1061/(ASCE)0733-9399(2002)128:11(1119)
-
Cottone, G., Di Paola, M., and Zingales, M., Elastic waves propagation in 1D fractional non-local continuum. DOI: 10.1016/j.physe.2009.09.006
-
Di Paola, M. and Zingales, M., Long-range cohesive interactions of non-local continuum faced by fractional calculus. DOI: 10.1016/j.ijsolstr.2008.06.004
-
Di Paola, M., Failla, G., and Zingales, M., Physically-based approach to the mechanics of strong non-local linear elasticity theory. DOI: 10.1007/s10659-009-9211-7
-
Di Paola, M., Marino, F., and Zingales, M., A generalized model of elastic foundation based on long-range interactions: Integral and fractional model. DOI: 10.1016/j.ijsolstr.2009.03.024
-
Di Paola, M., Pirrotta, A., and Zingales, M., Mechanically based approach to non-local elasticity: Variational principles. DOI: 10.1016/j.ijsolstr.2009.09.029
-
Di Paola, M., Failla, G., and Zingales, M., The mechanically based approach to 3D non-local linear elasticity theory: Long-range central interactions. DOI: 10.1016/j.ijsolstr.2010.02.022
-
Di Paola, M., Pirrotta, A., and Zingales, M., Stochastic dynamics of linear elastic trusses in presence of structural uncertainties (virtual distortion approach). DOI: 10.1016/j.probengmech.2003.11.001
-
Di Paola, M., Probabilistic analysis of truss structures with uncertain parameters (virtual distortion method approach). DOI: 10.1016/j.probengmech.2003.10.001
-
Elishakoff, I., Ren, Y. J., and Shinozuka, M., Improved finite element method for stochastic problems. DOI: 10.1016/0960-0779(94)00157-L
-
Eringen, A. C. and Kim, B. S., Stress concentration at the tip of a crack. DOI: 10.1016/0093-6413(74)90070-6
-
Eringen, A. C., Nonlocal polar elastic continua. DOI: 10.1016/0020-7225(72)90070-5
-
Falsone, G. and Ferro, G., A dynamical stochastic finite element method based on the moment equation approach for the analysis of linear and nonlinear uncertain structures.
-
Falsone, G. and Impollonia, N., A new approach for the stochastic analysis of finite element modelled structures with uncertain parameters. DOI: 10.1016/S0045-7825(02)00437-1
-
Frantziskonis, G., Stochastic approaches for damage evolution in standard and non-standard continua.
-
Gutkin, M. Yu., Nanoscopics of dislocations and disclinations in gradient elasticity.
-
Impollonia, N. and Sofi, A., A response surface approach for the static analysis of stochastic structures with geometrical nonlinearities. DOI: 10.1016/S0045-7825(03)00379-7
-
Kröner, E., Elasticity theory of materials with long range cohesive forces. DOI: 10.1016/0020-7683(67)90049-2
-
Mindlin, R. D. and Eshel, N. N., On first strain-gradient theories in linear elasticity. DOI: 10.1016/0020-7683(68)90036-X
-
Mindlin, R. D., Micro-structure in linear elasticity. DOI: 10.1007/BF00248490
-
Muscolino, G., Ricciardi, G., and Impollonia, N., Improved dynamic analysis of structures with mechanical uncertainties under deterministic input. DOI: 10.1016/S0266-8920(99)00021-1
-
Pisano, A. A., Sofi, A., and Fuschi, P., Finite element solutions for nonhomogeneous nonlocal elastic problems. DOI: 10.1016/j.mechrescom.2009.06.003
-
Polizzotto, C., Gradient elasticity and non standard boundary conditions. DOI: 10.1016/j.ijsolstr.2003.06.001
-
Polizzotto, C., Nonlocal elasticity and related variational principles. DOI: 10.1016/S0020-7683(01)00039-7
-
Rogula, D., Introduction to nonlocal theory of material media.
-
Shinozuka, M. and Deodatis, G., Response variability of stochastic finite element systems. DOI: 10.1061/(ASCE)0733-9399(1988)114:3(499)
-
Shinozuka, M., Simulation of multivariate and multidimensional random processes. DOI: 10.1121/1.1912338
-
Silling, S. A., Reformulation of elasticity theory for discontinuities and long-range forces. DOI: 10.1016/S0022-5096(99)00029-0
-
Silling, S. A.,Weckner, O., Askari, E., and Bobaru, F., Crack nucleation in a peridynamic solid. DOI: 10.1007/s10704-010-9447-z
-
Silling, S. A., Zimmermann, M., and Abeyaratne, R., Deformation of a peridynamic bar. DOI: 10.1023/B:ELAS.0000029931.03844.4f
-
Sobczyk, K. and Kirkner, D. J., Stochastic Modeling of Microstructures.
-
Sobczyk, K. and Trebicki, J., Fatigue crack growth in random residual stresses. DOI: 10.1016/j.ijfatigue.2004.03.012
-
Zingales, M., Di Paola, M., and Inzerillo, G., The finite element method for the mechanically based model of non-local continuum. DOI: 10.1002/nme.3118
-
Zingales, M., Wave propagation in 1D elastic solids in presence of long-range central interactions. DOI: 10.1016/j.jsv.2010.10.027
-
Muscolino Giuseppe, Sofi Alba, Zingales Massimiliano, One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis, Computers & Structures, 122, 2013. Crossref
-
Di Paola Mario, Failla Giuseppe, Pirrotta Antonina, Sofi Alba, Zingales Massimiliano, The mechanically based non-local elasticity: an overview of main results and future challenges, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371, 1993, 2013. Crossref
-
Di Paola Mario, Failla Giuseppe, Zingales Massimiliano, Non-local stiffness and damping models for shear-deformable beams, European Journal of Mechanics - A/Solids, 40, 2013. Crossref
-
Dal Corso Francesco, Deseri Luca, Residual stresses in random elastic composites: nonlocal micromechanics-based models and first estimates of the representative volume element size, Meccanica, 48, 8, 2013. Crossref
-
Alotta Gioacchino, Failla Giuseppe, Zingales Massimiliano, Finite element method for a nonlocal Timoshenko beam model, Finite Elements in Analysis and Design, 89, 2014. Crossref
-
Failla Giuseppe, Sofi Alba, Zingales Massimiliano, A new displacement-based framework for non-local Timoshenko beams, Meccanica, 50, 8, 2015. Crossref
-
Muscolino G., Sofi A., Zingales M., Long-Range Interactions in 1D Heterogeneous Solids with Uncertainty, Procedia IUTAM, 6, 2013. Crossref
-
Paola Mario Di, Failla Giuseppe, Zingales Massimiliano, Mechanically Based Nonlocal Euler-Bernoulli Beam Model, Journal of Nanomechanics and Micromechanics, 4, 1, 2014. Crossref