Zurich Colloquium in Applied and Computational Mathematics

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Speaker

Title

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26 February 2025
16:30-17:30

Prof. Dr. Philippe Ciarlet
Institut für Mathematik, Universität Zürich

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Speaker invited by

Prof. Dr. Stefan Sauter

Abstract

As is well-known, Koiter's model is often used in numerical simulations, because it is a two-dimensional model that captures well the "membrane-dominated" and "flexural-dominated" effects that arise in a nonlinearly elastic shell subjected to applied forces and specific boundary conditions. Finding a satisfactory existence theory for this nonlinear shell model has stood as an open problem for a very long time. The present work, which is a joint work with Cristinel Mardare, provides a two-dimensional model that preserves all the virtues of Koiter's model, while being in addition amenable to a satisfactory existence theory. More precisely, our new two-dimensional mathematical model for a nonlinearly elastic shell takes the form of a minimization problem with a stored energy function that is polyconvex and orientation-preserving, and more generally satisfies all the other assumptions of John Ball's existence theorem. In addition, the most noteworthy feature of this model is that it is "of Koiter's type", in the sense that for a specific class of deformations that are "to within the first order" identical to those introduced by W.T. Koiter for defining his model, the "lowest order part" of its stored energy function coincides with the stored energy function of Koiter's model.

A two-dimensional nonlinear shell model of Koiter's type

HG G 19.2

12 March 2025
16:30-17:30

Dr. Enrico Zampa
University of Vienna

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