International audienceThis paper deals with the numerical computation of buckles and wrinkles appearing in membrane structures by means of the total Lagrangian formulation, using genuine membrane finite elements (with zero bending stiffness) and a prestressed hyperelastic constitutive law. The bifurcation analysis is carried out without assuming any imperfections in the structure. The standard arclength method is modified by means of a specific solution procedure to cope with the occurrence of complex roots when solving the quadratic constraint equation. Applying the proposed formulation to a set of typical numerical examples shows its ability to correctly predict the wrinkling and buckling behaviour in membrane structures
International audienceThe problem of the wrinkling of the membranes is addressed in this paper within the total Lagrangian formulation. The material obeys a compressible hyperelastic constitutive equation and the resulting finite elements are either 8-node quadrilateral or 6- node triangular membrane elements without flexural stiffness. The appearance of wrinkles in the membrane structures is dealt with using the bifurcation analysis without any imperfections. The standard spherical arclength method is modified by means of a specific solution procedure to cope with the occurrence of complex roots when solving the quadratic constraint equation. Applying the proposed formulation to a set of typical numerical examples shows its ability to correctly predict the wrinkling behaviour in membranes structures.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
This paper describes the stress and fatigue analysis of the feed water nozzles of the replacement steam generators of the Doel 2 NPP in Belgium. In the framework of the steam generators replacement, thermal stratification transients were considered in the stress and fatigue analyses of the feed water system components such as the feed water lines, their reactor building penetrations and the steam generator feed water nozzles. To do so, long term external wall temperature measurement have been performed on one feed water line of Doel 2 between the steam generator replacement in 2004 and December 2007. From those measurements a number of typical stratification phenomena were identified. For each phenomenon, a design stratification transient and its number of occurrences were derived from the measurements. A fatigue analysis and primary+secondary stress intensity analysis of the feed water nozzles of the Doel 2 NPP was performed taking into account the presence of the design thermal stratification transients in the feed water lines and feed water nozzles. The fatigue analysis was performed according to the rules of the ASME Boiler & Pressure Vessel Code, Section III, Division 1 – Subsection NB-3200 using the in-house developed computer code THERMAXS that is capable of dealing with measured stratification transients. For the analysis, one may finally conclude that the fatigue, P+Q stress intensity range and thermal ratcheting criteria are respected throughout the 40 years of plant life.
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