Closed-Form Analytical Solutions for the Deflection of Elastic Beams in a Peridynamic Framework

Peridynamics is a continuum theory that operates with non-local deformation measures as well long-range internal force/moment interactions. The resulting equations are of the integral type, in contrast to classical theory, which deals differential equations. aim this paper analyze peridynamic governing for elastic beams. To end, strain energy density formulated function curvature. By applying Lagrange principle, motion derived. Examples boundary conditions, including simple support, clamped edge, roller and free presented by introducing interaction domain. Novel closed-form analytical solutions beams various clamped—simply supported, clamped–clamped, simply supported–roller-clamped, clamped–roller-clamped Furthermore, different types loadings, uniformly distributed load, concentrated force, moment, considered. results validated comparing derived against Bernoulli–Euler beam theory. A very good agreement between theories observed case small horizon sizes, shows capability proposed conditions.