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Title: Development of Strong Form Methods with Applications in Computational Mechanics
Keywords: Meshfree, Strong form, Gradient smoothing, Stability, Adaptive analysis, Solid mechanics
Issue Date: 1-Jul-2008
Citation: ZHANG JIAN (2008-07-01). Development of Strong Form Methods with Applications in Computational Mechanics. ScholarBank@NUS Repository.
Abstract: This thesis focuses on the development and application of strong form methods for computational mechanics. Firstly,a novel radial point interpolation based finite difference method (RFDM) is developed to achieve both the adaptivity to irregular domain and the stability in the solution that is often encountered in the collocation methods. Results show that the RFDM has a very good performance for the analysis of solid mechanics problems. The second part is to develop and apply a gradient smoothing method (GSM), in which the gradient smoothing operation is adopted to develop the first- and second-order derivatives for a node of interest by calculating weights for a set of surrounding field nodes. The theoretical aspects of GSM are exploited in detail, and very favorable schemes are proposed. Then, the GSM is further developed and systematically applied to static, adaptive and dynamic analyses of solids and structures. The accuracy, efficiency and stability of the present GSM are well demonstrated through intensive numerical investigations.
Appears in Collections:Ph.D Theses (Open)

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