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In this paper, an application of the duality principle in finite element shell analysis is presented. It is based upon Lure (Prikl. Mat. Mekh, XIV 5, 1958) and Goldenveizer's (Theory of thin shells, Pergamon Press, 1961) theory of thin shells. For the finite element analysis of thin shells, using the stress function, the problem of finding a stress fields in equilibrium and expressing their continuity across the interfaces is shown to be identical to the problem of derivation of conforming displacement fields and vice versa. It appears that one may derive from this concept of duality a new family of shell finite elements: the auto-dual shell elements. In this paper, we consider a self-dual flat element for thin shell analysis. This element is based on the already developed and implemented in LTAS department, University of Liège. It was mixed hybrid elements called ‘mixed métis’. Numerical efficiency is demonstrated by means of some examples: cylindrical shell roof simply supported by two diaphragms and submitted to its dead weight and cylinder loaded by two diametrically opposed point loads, clamped hyperbolic shell loaded by uniform normal pressure.

Application of the duality in the finite element analysis of shell: self-dual metis planar shell elements