Elasticity problems of beams on reaction-driven nonlocal foundation

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