Jean-François Debongnie

Dual analysis with general boundary conditions

Abstract The dual analysis concept was introduced by Fraeijs de Veubeke [1] as a consequence of upper and lower bounds of the energy. As such bounds exist only in those cases where one type of condition is homogeneous, it is commonly admitted that a dual error measure does not exist with general boundary conditions. This paper presents a re-examination of the dual error measure by a way which avoids any use of upper and lower bounds of the energy. It is found that such an error measure holds whatever the boundary conditions be. Furthermore, it is not necessary to obtain the approximate solutions by a Rayleigh-Ritz process, so that the second analysis, which seemed necessary in the original dual analysis concept, may be replaced by any admissible approximation. This implies the possibility of a dual error measure at a simple post-processor level.

Physical interpretation and generalization of Marguerre's shallow shell theory

Abstract Marguerres shallow shell theory is interpreted by the means of the introduction of a “fictitious initial displacement”. A logical interpretation of Marguerres equilibrium equations follows directly from this point of view. The introduction of fictitious displacements is easy to generalize, and the case of quasi-conical shells is analyzed in detail.

Convergent thin-shell models using cartesian components of the displacements

Abstract Starting from the establishment of a deep-shell theory using cartesian components of the displacements, two simplifications of it are considered in the frame of moderate deflections, in view of their finite element implementation. The first one, consisting simply of the use of plane elements, is proved to converge to the deep-shell solution when the mesh is refined, and the rate of convergence is evaluated. A more refined approach is presented, which gains one order of convergence from the former one and reduces to the Marguerre shallow-shell theory when this one is applicable, a condition which is made precise in the text.

On a purely Lagrangian formulation of sloshing and fluid-induced vibrations of tanks

Abstract A general variational principle for fluid-structure interactions is obtained from a purely Lagrangian point of view, thus avoiding any difficulty at the fluid-structure interaction. This rather general variational principle is shown to degenerate, when suitable restrictions are made, in two known formulations, whose range of applicability is defined with the aid of three nondimensional numbers.