The partition of unity method for the elastically supported beam

The partition of unity method (PUM) is used to solve 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 at the thin beam limit and exhibits no numerical boundary layer for strong elastic support. Optimal convergent rate is established in the energy norm, and it is uniformly valid with respect to the thickness of the beam and toughness of the elastic support. Furthermore, the computed shear stress is also convergent uniformly with optimal rate.