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Bubble-enhanced smoothed finite element formulation: a variational multi-scale approach for volume-constrained problems in two-dimensional linear elasticity. (English) Zbl 1352.74451
Summary: This paper presents a bubble-enhanced smoothed finite element formulation for the analysis of volume-constrained problems in two-dimensional linear elasticity. The new formulation is derived based on the variational multi-scale approach in which unequal order displacement-pressure pairs are used for the mixed finite element approximation and hierarchical bubble function is selected for the fine-scale displacement approximation. An area-weighted averaging scheme is employed for the two-scale smoothed strain calculation under the framework of edge-based smoothed FEM. The smoothed fine-scale solution is shown to naturally contain the stress field jump of the smoothed coarse-scale solution across the boundary of edge-based smoothing domain and thus provides the possibility to stabilize the global solution for volume-constrained problems. A global monolithic solution strategy is employed, and the fine-scale solution is solved without the consideration of approximating the strong form of the fine-scale equation. Several numerical examples are analyzed to demonstrate the accuracy of the present formulation.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 74B05 Classical linear elasticity
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