Guest lectures and seminars - Page 189
Lateral-torsional buckling of elastic structures under combined loading will be considered in this seminar. This problem has been first reported in the habilitation thesis of Prandtl dated 1899. Closed-form solutions based on Bessel's functions are available for some specific types of loading. However, numerical methods such as the Finite Element Methods (FEM) or other approximate methods are needed in the general case. More generally, approximation of the buckling curve (limit of the stable domain in the loading parameters space) is investigated from the stationary property of the Rayleigh’s quotient. The approximation is then compared to a numerical approach, namely the iterative method of Vianello and Stodola. Closed-form solutions give upper bounds with relative error less than 0.2%. It is shown that the stable domain of the loading parameter space is convex. The Papkovitch–Schaefer theorem proven in 1934 is extended for this specific problem, despite the nonlinear dependence of the equilibrium equations on the loading parameters for the one-dimensional system. The boundary of the stable domain is clearly nonlinear, but this nonlinearity is weak. It is shown that Dunkerley’s lower bound is relevant for the two structural cases considered, and the maximum relative error induced by such a lower bound is lower than 2%. Prandtl's linear approximation is then validated approximately one century later the pioneer works of Prandtl devoted to elastic instability.
Noël Challamel is Professor at the Department of Civil Engineering (LIMATB), University of South-Brittany, Lorient, France, and Marie Curie fellow at the Department of Mathematics, University of Oslo, Oslo, Norway.
Matthijs Pronk, TU Delft (NL), holder et seminar med tittelen: Malliavin calculus in UMD Banach spaces
The fundamental mechanisms of plasticity in inorganic glasses are distinctly different from those in crystalline metals. Whereas dislocations and their mobility require plasticity in metals, mechanisms responsible for permanent deformation in glasses are to be looked at the atomistic scale. The lecture will deal with this and will involve topics such as for instance constitutive material laws, plasticity theory, dislocation theory, computational mechanics, multiscale analysis, finite element methods, crack modelling, etc.
Vincent Keryvin is professor at Department of Materials Engineering (LIMATB), University of South-Brittany, Lorient, France.
Simen Rustad (UiO) will give a talk with title "Construction of Bost-Connes type systems for function fields".
Abstract: I will try to indicate how Benoit Jacob's construction of a Bost-Connes type system for function fields fits into a more general framework.
Bora Yalkinoglu will give a talk entitled: Introduction to p-adic Bost-Connes systems.
Abstract: In this talk we want to give a gentle introduction into the recently emerging theory of p-adic Bost-Connes systems. In the first part of the talk, after reviewing the necessary background from p-adic analysis and number theory, we will explain recent work of Connes and Consani on certain p-adic representations of the classical BC-system. In the second part of the talk we will discuss recent work on generalizations of the work of Connes and Consani and, further, point out several open problems for further research.