Implicit implementation of the nonlocal operator method: an open source code

  • In this paper, we present an open-source code for the first-order and higher-order nonlocal operator method (NOM) including a detailed description of the implementation. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combined with theIn this paper, we present an open-source code for the first-order and higher-order nonlocal operator method (NOM) including a detailed description of the implementation. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combined with the method of weighed residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. The implementation in this paper is focused on linear elastic solids for sake of conciseness through the NOM can handle more complex nonlinear problems. The NOM can be very flexible and efficient to solve partial differential equations (PDEs), it’s also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Finally, we present some classical benchmark problems including the classical cantilever beam and plate-with-a-hole problem, and we also make an extension of this method to solve complicated problems including phase-field fracture modeling and gradient elasticity material.show moreshow less

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Metadaten
Document Type:Article
Author: Yongzheng Zhang, Huilong Ren
DOI (Cite-Link):https://doi.org/10.1007/s00366-021-01537-xCite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20220216-45930Cite-Link
URL:https://link.springer.com/article/10.1007/s00366-021-01537-x
Parent Title (English):Engineering with computers
Publisher:Springer
Place of publication:London
Language:English
Date of Publication (online):2022/02/16
Date of first Publication:2022/01/08
Release Date:2022/02/16
Publishing Institution:Bauhaus-Universität Weimar
Institutes and partner institutions:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
Volume:2022
Pagenumber:35
First Page:1
Last Page:35
Tag:Dual-support; Implicit; Nonlocal operator method; Operator energy functional; Stiffness matrix; Taylor series expansion; Variational principle
GND Keyword:Strukturmechanik
Dewey Decimal Classification:500 Naturwissenschaften und Mathematik / 510 Mathematik
600 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Licence (German):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)