Unification of Eringen’s nonlocal parameter through an optimization-based approach

An evolutionary optimization approach is presented to provide unified material properties through focusing on sample problems of one-dimensional (1D) atomic chains and armchair SWCNTs. Optimum values are calculated by matching the buckling loads and natural frequencies obtained from the atomistic simulations and Eringen’s nonlocal theory based finite element models for bars and beams. Sufficiently accurate results regardless of dimensions, mechanical problems, and boundary conditions of aforementioned types of structures are provided, and the feasibility of the integral form of nonlocal theory along with the inadequate character of local theory in the existence of long range interactions are clearly presented.