One-dimensional nonlocal and gradient elasticity: Assessment of high order approximation schemes

We investigate the application and performance of high-order approximation techniques to one-dimensional nonlocal elastic rods. Governing equations and corresponding discrete forms are derived for the integro-differential formulation proposed by Eringen and the laplacian-based strain gradient formulation developed by Aifantis and coworkers. Accuracy and convergence rate of the numerical solutions obtained with Lagrange, Hermite, B-spline finite elements and C∞ generalized finite elements are assessed against the corresponding analytical solutions.