A finite element analysis for the Signorini problem in plane elastostatics
Two problems are considered describing dynamic processes for a class of rate-type elastic-viscoplastic materials with or without internal state variable. The existence and uniqueness of the solution is proved using classical results of linear elasticity theory together with a fixed point method.
In this paper the contact problem for a cylindrical shell and a stiff punch is studied. The existence and uniqueness of a solution is verified. The finite element method is discussed.
The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain. Fot both types a priori error estimates in -norm and in -norm are established, provided the solution is smooth enough. These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too.
We prove -regularity for the stresses in the Prandtl-Reuss-law. The proof runs via uniform estimates for the Norton-Hoff-approximation.