ICCM Conferences, The 8th International Conference on Computational Methods (ICCM2017)

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A weakened weak (W2) form and a G space
Ming Li

Last modified: 2017-06-30


This paper represents some basic mathematic theories for Gs spaces of functions that can be used for weakened weak (W2) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solving mechanics problems. We first introduce and prove properties of Gs spaces, such as the upper boundedness and convergence of the norms, which are in contrast with H1 spaces. We then prove the equivalence of the Gsnorms and its corresponding semi-norms. These mathematic theories are important and essential for the establishment oftheoretical frame and the development of relevant numerical approaches. Finally, we apply S-FEM modelsto solve some practical problems with large deformations.

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