A challenging task in nonlocal continuum mechanics consists in formulating constitutive relations leading to well-posed structural problems. Several strategies have been adopted to overcome issues inherent applicability of Eringen’s pure nonlocal theory to nanostructures, such as local/nonlocal mixtures of elasticity and integral models involving modified averaging kernels. These strategies can be applied to the ill-posed problem of flexure of a beam on Wieghardt nonlocal foundation without considering any fictitious boundary forces of constitutive type. A consistent formulation of nonlocal elastic foundation underlying a Bernoulli–Euler beam is thus conceived in the present paper by requiring that transverse displacements are convex combination of reaction-driven local and nonlocal phases governed by Winkler and Wieghardt laws, respectively. The proposed integral mixture is proven to be equivalent to a more convenient differential problem, equipped with nonlocal boundary conditions, which can be effectively exploited to solve nonlocal problems of beams resting on mixture reaction-driven continuous foundation. Effectiveness of the developed nonlocal approach is illustrated by analytically solving simple elasto-static problems of structural mechanics.

Elasticity problems of beams on reaction-driven nonlocal foundation / Pinnola, F. P.; Vaccaro, M. S.; Barretta, R.; Marotti de Sciarra, F.; Ruta, G.. - In: ARCHIVE OF APPLIED MECHANICS. - ISSN 0939-1533. - 93:1(2023), pp. 41-71. [10.1007/s00419-022-02161-x]

Elasticity problems of beams on reaction-driven nonlocal foundation

Pinnola F. P.;Vaccaro M. S.;Barretta R.;Marotti de Sciarra F.;
2023

Abstract

A challenging task in nonlocal continuum mechanics consists in formulating constitutive relations leading to well-posed structural problems. Several strategies have been adopted to overcome issues inherent applicability of Eringen’s pure nonlocal theory to nanostructures, such as local/nonlocal mixtures of elasticity and integral models involving modified averaging kernels. These strategies can be applied to the ill-posed problem of flexure of a beam on Wieghardt nonlocal foundation without considering any fictitious boundary forces of constitutive type. A consistent formulation of nonlocal elastic foundation underlying a Bernoulli–Euler beam is thus conceived in the present paper by requiring that transverse displacements are convex combination of reaction-driven local and nonlocal phases governed by Winkler and Wieghardt laws, respectively. The proposed integral mixture is proven to be equivalent to a more convenient differential problem, equipped with nonlocal boundary conditions, which can be effectively exploited to solve nonlocal problems of beams resting on mixture reaction-driven continuous foundation. Effectiveness of the developed nonlocal approach is illustrated by analytically solving simple elasto-static problems of structural mechanics.
2023
Elasticity problems of beams on reaction-driven nonlocal foundation / Pinnola, F. P.; Vaccaro, M. S.; Barretta, R.; Marotti de Sciarra, F.; Ruta, G.. - In: ARCHIVE OF APPLIED MECHANICS. - ISSN 0939-1533. - 93:1(2023), pp. 41-71. [10.1007/s00419-022-02161-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/907021
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