Christian Wielgosz

Deflections of inflatable fabric panels at high pressure

Inflatable structures made of modem textile materials with important mechanical characteristics can be inflated at high pressure (up to a several hundreds of kPa). They can be used as strong building elements thanks to their mechanical strength. The aim of the paper is to present experimental and analytical studies on the behaviour of inflated fabric panels at high pressure and submitted to bending loads. It is shown that inflatable structures cannot be viewed as ordinary plates or beams, because their deformation pattern is quite different. Experiments show that their behaviour depends on the applied load, the inflation pressure, and the constitutive law of the fabrics. Equilibrium equations are written in the deformed state to take into account the influence of geometrical stiffness and the following forces. A Timoshenkos beam theory must be used because sections of the panels do not satisfy the usual Bernoullis beam theory. A new inflatable beam theory is developed. Wrinkling loads are derived from equilibrium equations. Deflections satisfy the fact that the compliance of the inflatable panel is the sum of the beam compliance and of the yarn compliance. Comparisons between the results of our modelling and experimental results are shown and prove the accuracy of this theory on the mechanical strength of inflatable structures at high pressure.

Continuous and Finite Element Methods for the Vibrations of Inflatable Beams

Inflatable structures are under increasing development in various domains. Their study is often carried out by using 3D membrane finite elements and for static loads. There is a lack of knowledge in dynamic conditions, especially for simple and accurate solutions for inflatable beams. This paper deals with the research on the natural frequencies of inflatable Timoshenko beams by an exact method: The continuous element method (CEM), and by the classical finite element method (FEM). The dynamic stiffness matrix D(ω) is here established for an inflatable beam; it depends on the natural frequency and also on the inflation pressure. The stiffness and mass matrixes used in the FEM are deduced from D(ω). Natural frequencies and natural modes of a simply supported beam are computed, and the accuracy of the CEM is checked by comparisons with the finite element method and also with experimental results.

Strength of inflatable fabric beams at high pressure

Inflatable structures made of modern textile materials can be inflated at high pressure in order to be used as strong building elements. The aim of the paper is to present results from research on the mechanics of highly inflated structures. Experimental, analytical and numerical studies on the behavior of inflatable fabric beams are displayed. We will first describe experimental studies on two kinds of inflatable prototypes: flat panels and tubes. Experiments show that their behavior is a linear combination of yarns and beams shapes. The usual theory of collapse analysis is then applied to the computation of wrinkling loads of these fabric beams. The second section of the paper is devoted to build a new inflatable beam theory and to show that the compliance of the inflatable beams is the sum of the beam compliance and of the yarn compliance. A new inflatable beam finite element is developed in the third section and used to compute deflections of hyperstatic beams. Our first results on the buckling of inflatable panels are displayed in the last section. Comparisons between experimental and analytical results are shown and show that this new theory on the mechanical strength of inflatable structures at high pressure is satisfactory.

Modélisation du plissage dans les structures membranaires

Dans cet article on traite de l’apparition des plis dans les membranes. La mise en oeuvre numérique est basée sur la formulation lagrangienne totale et les éléments finis utilisés sont des quadrilatères à 8 noeuds ou des triangles à 6 noeuds, sans rigidité à la flexion. Le matériau constitutif est modélisé par une loi hyperélastique compressible. Le plissage est simulé à l’aide des techniques de calcul de bifurcation pure, sans recours aux imperfections. La méthode classique de longueur d’arc quadratique est modifiée au moyen d’un procédé spécifique pour faire face aux racines complexes qui apparaissent dans l’équation du second degré de longueur d’arc. L’application de la formulation proposée à un ensemble d’exemples numériques typiques montre sa capacité à modéliser correctement les plis dans les membranes.

Complete analytic elastic study of a 90° branch connection of a cylinder on a sphere subjected to a bending load

Abstract This paper proposes a complete analytic formulation for the elastic mechanical calculation of a 90° branch connection of a cylinder on a sphere under a bending load. It is validated and simplified by comparison with shell-type finite element calculations in Fourier mode using the CEAs Castem 2000 code. The general calculations of the cylinder were obtained by minimisation of the deformation energy. The sphere study was conducted without particular consideration to Donnell-Vlasovs shallow shell theory. The mathematical analysis is based on the classical system which couples the radial displacement and a stress function. Solutions are provided in complex Legendre functions. An algorithm is presented to facilitate their calculation. Lastly, well chosen continuity conditions on the cylinder and the sphere provide an easily solvable system.