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Elasticity problems of beams on reaction-driven nonlocal foundation.
- Source :
- Archive of Applied Mechanics; Jan2023, Vol. 93 Issue 1, p41-71, 31p
- Publication Year :
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09391533
- Volume :
- 93
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Archive of Applied Mechanics
- Publication Type :
- Academic Journal
- Accession number :
- 161191408
- Full Text :
- https://doi.org/10.1007/s00419-022-02161-x