Coupling three-dimensional peridynamics and high-order one-dimensional finite elements based on local elasticity for the linear static analysis of solid beams and thin-walled reinforced structures

Peridynamics is a nonlocal theory which has been successfully applied to solid mechanics and crack propagation problems over the last decade. This methodology, however, may lead to large computational calculations which can soon become intractable for many problems of practical interest. In this context, a technique to couple—in a global/local sense–three-dimensional peridynamics with one-dimensional high-order finite elements based on classical elasticity is proposed. The refined finite elements employed in this work are based on the well-established Carrera Unified Formulation, which the previous literature has demonstrated to provide structural formulations with unprecedented accuracy and optimized computational efficiency. The coupling is realized by using Lagrange multipliers that guarantee versatility and physical consistency as shown by the numerical results, including the linear static analyses of solid and thin-walled beams as well as of a reinforced panel of aeronautic interest.