TY  - JOUR
A1  - Ren, Huilong
A1  - Zhuang, Xiaoying
A1  - Oterkus, Erkan
A1  - Zhu, Hehua
A1  - Rabczuk, Timon
T1  - Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method
JF  - Engineering with Computers
N2  - The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of nonlocal forms for elasticity, thin plate, gradient elasticity, electro-magneto-elasticity and phase-field fracture method. The nonlocal governing equations are expressed as an integral form on support and dual-support. The first example shows that the nonlocal elasticity has the same form as dual-horizon non-ordinary state-based peridynamics. The derivation is simple and general and it can convert efficiently many local physical models into their corresponding nonlocal forms. In addition, a criterion based on the instability of the nonlocal gradient is proposed for the fracture modelling in linear elasticity. Several numerical examples are presented to validate nonlocal elasticity and the nonlocal thin plate.
KW  - Bruchmechanik
KW  - Elastizität
KW  - Peridynamik
KW  - energy form
KW  - weak form
KW  - peridynamics
KW  - variational principle
KW  - explicit time integration
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20211207-45388
UR  - https://link.springer.com/article/10.1007/s00366-021-01502-8
VL  - 2021
SP  - 1
EP  - 22
ER  - 
TY  - JOUR
A1  - Zhang, Yongzheng
T1  - Nonlocal dynamic Kirchhoff plate formulation based on nonlocal operator method
JF  - Engineering with Computers
N2  - In this study, we propose a nonlocal operator method (NOM) for the dynamic analysis of (thin) Kirchhoff plates. The nonlocal Hessian operator is derived based on a second-order Taylor series expansion. The NOM does not require any shape functions and associated derivatives as ’classical’ approaches such as FEM, drastically facilitating the implementation. Furthermore, NOM is higher order continuous, which is exploited for thin plate analysis that requires C1 continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for the time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.
KW  - Angewandte Mathematik
KW  - nonlocal operator method
KW  - nonlocal Hessian operator
KW  - operator energy functional
KW  - dual-support
KW  - variational principle
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220209-45849
UR  - https://link.springer.com/article/10.1007/s00366-021-01587-1
VL  - 2022
SP  - 1
EP  - 35
PB  - Springer
CY  - London
ER  -