engleski

On the numerical behavior of the MLPG mixed approach in structural analysis

Although the mixed Meshless Local Petrov-Galerkin (MLPG) methods do not have to satisfy Ladyzhenskaja-Babuška-Brezzi (LBB) conditions to achieve stability, spurious oscillations in displacement and strain fields have sometimes been observed. In order to reveal the causes of such behavior, mixed formulations for 2-D linear elasticity will be considered in this contribution, whereby special attention will be dedicated to the stability and accuracy of solution. Various approximations techniques for the strains will be proposed, which could serve as a remedy for the alleviation of the above mentioned problems. These include using different sets of field nodes for the approximation of strains and displacements, and the imposition of compatibility conditions between the approximated strains and displacements at the strain field nodes via a collocation method. Alternatively, a strain smoothing technique will be proposed. The local weak form (LWF) of 2-D equilibrium equations will be derived over rectangular local sub-domains surrounding the nodes used for the approximation of displacements. The interpolating Moving Least Squares (MLS) technique will be applied, which allows a simple imposition of essential BCs, like in FEM. The performance of the presented algorithms will be demonstrated by numerical examples.

mixed MLPG method; structural analysis; accuracy; stability; locking

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