A numerical method to optimize the design of a space inflatable membrane reflector

International audienceA numerical method is proposed to optimize the design of a space inflatable membrane reflector. The initial geometry is expressed by polynomial series weighted by a set of shape parameters. The problem is formulated as a minimization of a cost function representing the difference between the effective shape of the reflector and a perfect parabolic surface. The minimization is performed using the Nelder-Mead method or downhill simplex method. The cost function is computed at each vertex of a simplex defined in the space of optimization parameters by solving direct problem thanks to a finite element method. The finite element model handles geometrical non-linearities and takes into account phenomena like membrane wrinkling and torus buckling which may affect the reflector shape when inflated

A numerical method to optimize the design of a space inflatable membrane reflector

International audienceA numerical method is proposed to optimize the design of a space inflatable membrane reflector. The initial geometry is expressed by polynomial series weighted by a set of shape parameters. The problem is formulated as a minimization of a cost function representing the difference between the effective shape of the reflector and a perfect parabolic surface. The minimization is performed using the Nelder-Mead method or downhill simplex method. The cost function is computed at each vertex of a simplex defined in the space of optimization parameters by solving direct problem thanks to a finite element method. The finite element model handles geometrical non-linearities and takes into account phenomena like membrane wrinkling and torus buckling which may affect the reflector shape when inflated

Membrane form finding by means of functional minimization

This study deals with the methods of architectural design of structures made of textile membranes. We consider the problem of form finding of membranes strained by rigid skeletons and cables installed along the free edges of the membrane. First, we recall the methods used to solve the simple problem of finding form in the case of constant surface tension. Then we propose a method based on the minimization of the total potential energy. The problem is discretized using membrane triangular finite elements. The potential considered is an energy density per unit area of uniform and constant surface tension. The minimization of this potential leads to the minimal surface solution. However the problem is singular with respect to the in-plane displacement. To handle this problem, the potential is enhanced by an elastic energy in order to regularize the numerical scheme and prevent the mesh degeneration. It is also enhanced by the elastic energy due to the cable tensions. The solution is obtained by minimizing the potential energy using the conjugate gradient method

Behavior of unbound granular materials - Part I: isotropic case

International audienceThe paper discusses the modeling of the behavior of unbound granular materials. A representative approach that highlights some salient features of the behavior is proposed. This approach is essentially based on experimental results and the study is extended to the construction of the elastic potential from test results. to complete the analysis, two no-linear elastic models involving 3 parameters are proposed. In the construction of these models, two important aspects-the accuracy and the numerical stability-are analyzed

Behavior of unbound granular materials - Part I: isotropic case

International audienceThe paper discusses the modeling of the behavior of unbound granular materials. A representative approach that highlights some salient features of the behavior is proposed. This approach is essentially based on experimental results and the study is extended to the construction of the elastic potential from test results. to complete the analysis, two no-linear elastic models involving 3 parameters are proposed. In the construction of these models, two important aspects-the accuracy and the numerical stability-are analyzed

Membrane form finding by means of functional minimization

This study deals with the methods of architectural design of structures made of textile membranes. We consider the problem of form finding of membranes strained by rigid skeletons and cables installed along the free edges of the membrane. First, we recall the methods used to solve the simple problem of finding form in the case of constant surface tension. Then we propose a method based on the minimization of the total potential energy. The problem is discretized using membrane triangular finite elements. The potential considered is an energy density per unit area of uniform and constant surface tension. The minimization of this potential leads to the minimal surface solution. However the problem is singular with respect to the in-plane displacement. To handle this problem, the potential is enhanced by an elastic energy in order to regularize the numerical scheme and prevent the mesh degeneration. It is also enhanced by the elastic energy due to the cable tensions. The solution is obtained by minimizing the potential energy using the conjugate gradient method

Dimensionnement optimal des structures membranaires préssurisées - Application à une antenne gonflable parabolique.

National audienceSee http://hal.archives-ouvertes.fr/docs/00/59/27/86/ANNEX/r_3K3833XY.pd

Solution semi-analytique de la déformée d'une structure membranaire de forme cylindrique circulaire sous pression externe en grandes transformations

International audienceCe travail s'intéresse à la détermination de la déformée, en hypothèses de grandes transformations, d'une structure membranaire de forme cylindrique circulaire sous pression externe et sous tension à ses extrémités. Sous ces sollicitations mécaniques, l'état d'équilibre stable de la structure membranaire présente des plis consécutifs à des flambements locaux. La recherche de l'état d'équilibre statique par des méthodes numériques classiques converge lentement voire peut ne pas converger vers la solution (méthodes de type longueur d'arc, Riks, relaxation dynamique...). Des méthodes s'appuyant sur le principe du minimum de l'énergie potentielle totale permettent alors d'obtenir efficacement une solution à moindre coût. Une solution semi-analytique de l'état d'équilibre est obtenue en utilisant le principe du minimum de l'énergie potentielle totale. Les expressions analytiques de l'énergie potentielle totale, du gradient de l'énergie et du jacobien sont dans un premier temps établies. La recherche de la solution au problème mécanique est ensuite effectuée numériquement au moyen d'un algorithme de Newton dont les opérateurs sont mis à jour à l'aide des expressions analytiques. Les résultats obtenus par cette approche originale sont finalement comparés à ceux obtenus avec le code de calcul éléments finis ABAQUS pour différentes valeurs de chargements mécaniques (tension, pression)