Title: Explicit implementation of the non-local operator method: a non-local dynamic formulation for elasticity solid
Authors: Yongzheng Zhang
Addresses: Institute of Structural Mechanics, Bauhaus-University Weimar, 99423 Weimar, Germany
Abstract: This paper presents an explicit non-local operator method (NOM) for the dynamic analysis of elasticity solid problems. The NOM is based on so-called dual-supports, non-local operators and an operate energy functional ensuring stability. The non-local operators are the generalisation of the conventional differential operators. Combined with the variational principle, the non-local governing equations and non-local operator energy functional for linear elasticity solid are derived. The non-local governing equations and non-local operator energy functional are expressed as the integral forms of support and dual-support. The explicit NOM avoids the calculation of the tangent stiffness matrix as in the implicit NOM model. The NOM does not necessitate the use of any shape functions which may be complicated to construct and drastically facilitate the implementation. Several numerical examples are provided to highlight the method's capabilities.
Keywords: non-local operator method; dual-support; variational principle; operator energy functional; Verlet-velocity algorithm.
International Journal of Hydromechatronics, 2022 Vol.5 No.1, pp.3 - 21
Received: 14 Oct 2021
Accepted: 04 Nov 2021
Published online: 25 Apr 2022 *