Generalized-strain mesh-free method (GSMF) for two-dimensional elasticity problems
Wilber Vélez1; Tiago da Silva Oliveira1; Elvis Pereira de Santana1; Artur Portela1
1 University of Brasília
doi:10.20906/CPS/CILAMCE2017-0930
Resumo
Recently the meshless methods are becoming more used due to their accuracy and performance in numerical analysis. Some of them are derived from a weak - form formulation on global domain and others from local sub - domains. The weighted - residual method is the basis for the meshless formulation. The Generalized - Strain Mesh - free (GSMF) local method, it is derived through a weighted-residual formulation that leads to the work theorem of structures theory. In a local region, the work theorem establishes an energy relationship between a statically - admissible stress field and an independent kinematically - admissible strain field. In the GSMF formulation, the local form of work theorem is simply an integration - free formula. The Moving Least Squares (MLS) approximation of the elastic field is used to construct the trial function in this local meshless formulation. GSMF has a highly computational efficiency leading to accurate numerical results in two-dimensional elasticity problems. This paper is concerned with the numerical comparison of the energy and displacement error for different regular nodal distribution, for the Timoshenko cantilever beam and the infinite plate with circular hole. The results are compared with the exact solution and optimal parameters have been determined.
Palavras-chave: Generalized-Strain Mesh-free (GSMF); Elasticity problems; Moving Least Squares (MLS) ; Work theorem; Energy error