RBF-based meshless modeling of strain localization and fracture

Le, Phong (2010) RBF-based meshless modeling of strain localization and fracture. [Thesis (PhD/Research)]

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This work attempts to contribute further knowledge and understanding in the discipline of computational science in general and numerical modeling of discontinuity
problems in particular. Of particular interest is numerical simulation of dynamic strain localization and fracture problems. The distinguishing feature in this study is the employment of neural-networks-(RBF)-based meshfree
methods, which differentiates the present approach from many other computational approaches for numerical simulation of strain localization and fracture mechanics.

As a result, new meshfree methods based on RBF networks, namely moving RBF-based meshless methods, have been devised and developed for solving PDEs. Unlike the conventional RBF methods, the present moving RBF is locally supported and yields sparse, banded resultant matrices, and better condition numbers. The shape functions of the new method satisfy the Kroneckerdelta property, which facilitates the imposition of the essential boundary conditions.
In addition, the method is applicable to arbitrary domain and scattered nodes. To capture the characteristics of discontinuous problems, the method is further improved by special techniques including coordinate mapping and
local partition of unity enrichment. Results of simulation of strain localization and fracture, presented in the latter chapters of the thesis, indicate that the proposed meshless methods have been successfully applied to model such problems.

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Item Type: Thesis (PhD/Research)
Item Status: Live Archive
Additional Information: Doctor of Philosophy (PhD) thesis.
Faculty/School / Institute/Centre: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Faculty/School / Institute/Centre: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Supervisors: Tran-Cong, Thanh
Date Deposited: 25 Aug 2011 02:02
Last Modified: 13 Jul 2016 01:31
Uncontrolled Keywords: RBF, meshless, meshfree, strain localization, fracture
Fields of Research (2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490303 Numerical solution of differential and integral equations
40 ENGINEERING > 4017 Mechanical engineering > 401706 Numerical modelling and mechanical characterisation
URI: http://eprints.usq.edu.au/id/eprint/19539

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