Nonlocal operator method with numerical integration for gradient solid

摘要

The nonlocal operator method (NOM) is initially proposed as a particle-based method, which has difficulties in imposing accurately the boundary conditions of various orders. In this paper, we converted the particle-based NOM into a scheme with approximation property. The new scheme describes partial derivatives of various orders at a point by the nodes in the support and takes advantage of the background mesh for numerical integration. The boundary conditions are enforced via the modified variational principle. The particle-based NOM can be viewed as a special case of NOM with approximation property when nodal integration is used. The scheme based on numerical integration greatly improves the stability of the method. As a consequence, the requirement of the operator energy functional in particle-based NOM is avoided. We demonstrate the capabilities of the proposed method by solving gradient elasticity problems and comparing the numerical results with exact solutions. (C) 2020 Elsevier Ltd. All rights reserved.