Smooth finite elements

Stéphane Bordas (1) , Nguyen-Xuan Hung (2) , Nguyen-Dang Hung (3)

1 University of Glasgow
2 University of Natural Sciences - HoChiMinh City
3 LTAS - Aerospace and Mechanical Engineering Department [Liège]

present a method which we believe can serve as a mid-way solution between computationally expensive meshfree methods and mesh-distortion-sensitive finite element methods. The method is almost insensitive to mesh distortion and is naturally suited to polygonal meshes. More precisely, we show results concerning the application of strain smoothing or stabilized conforming nodal integration to the finite element method. The technique was coined the Smooth Finite Element Method by G.R. Liu et al. We show that some versions of the method completely suppress locking in incompressible elasticity and elasto-plasticity. Additionally, locking can be suppressed in the case of plate and shell formulations. More importantly perhaps, these smooth finite elements helped discover a remarkable link between displacement and equilibrium finite elements.

Mots clés: Smooth finite elements; locking; incompressibility; plates; shells; equilibrium ele- ments; displacement elements; plasticity; selective integration

Domaines: Mécanique [physics]

Stéphane Bordas, Nguyen-Xuan Hung, Nguyen-Dang Hung. Smooth finite elements. 8e Colloque national en calcul des structures, CSMA, May 2007, Giens, France. ⟨hal-01504172⟩