Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 367, Issue -, Pages -Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2020.113132
Keywords
Higher order nonlocal operators; Operator energy functional; Strong form; PDEs
Funding
- National Basic Research Program of China (973 Program) [2011CB013800]
- NSFC [51474157]
- Ministry of Science and Technology of China [SLDRCE14-B-28, SLDRCE14-B-31]
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A higher order nonlocal operator method for the solution of boundary value problems is developed. The proposed higher order nonlocal operator brings several advantages as compared to the original nonlocal operator method (Ren et al., 2020) which only ensures first-order convergence. Furthermore, it can be applied to directly and efficiently obtain all partial derivatives of higher orders simultaneously without the need of using shape functions. Only the functionals based on the nonlocal operators (termed as operator functional) are needed to obtain the final discrete system of equations, which significantly facilitates the implementation. Several numerical examples are presented to show the effectiveness and accuracy of the proposed higher order nonlocal operator method including the solution of the Poisson equation in 2-5 dimensional space, Kirchhoff and von Karman plate problems, incompressible elastic materials as well as phase field modeling of fracture. (C) 2020 Elsevier B.V. All rights reserved.
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