## Slab analogy in theory and practice of conforming equilibrium stress models for finite element analysis of plane elastostatics.(English)Zbl 0577.73067

In the first section of this paper the author recalls some classical functional analysis results and the notion of ”slab analogy”. In the second section the author recalls the definitions of three classical $$C^ 1$$-finite elements. Then he describes the stress equilibrium finite element derived from each of these $$C^ 1$$-finite elements by using the slab analogy. This technique is not a novel one. The original contribution of the author is the choice of the degrees of freedom which have an evident physical meaning since they are directly connected to the normal trace of the stress tensor.
The following sections are devoted to the variational formulation of the stress problem by means of the complementary energy functional, the proof of an existence result for this problem, the proof of the convergence of the approximation of the continuous problem by means of a finite element method based on the equilibrium finite elements described above. For that purpose the author adopted some classical techniques to the problem studied here.
This paper is a good synthesis of known results but contains also some original contributions.