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The partition of unity method for the elastically supported beam. (English) Zbl 0959.74078
Summary: We use the partition of unity method to study the Timoshenko beam with elastic support. Some important features of this new method are addressed, but the main concern is to overcome locking and to resolve boundary layer. We prove that, by a proper selection of the local basis functions, the method is free of locking in the thin beam limit, and exhibits no numerical boundary layer for strong elastic support. We establish the optimal convergence rate in the energy norm, which is uniformly valid with respect to the thickness of the beam and toughness of the elastic support. Furthermore, the computed shear stress also uniformly converges with optimal rate.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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