Guest lectures and seminars - Page 197

This seminar will be focused on some elementary structural systems such as the cantilever beam. The cantilever is an old problem in structural mechanics already investigated by Galileo (1638) from equilibrium and strength arguments. This structural paradigm will be reconsidered here using buckling, post-buckling and inelastic theory. We will first present some fundamental buckling results for axially loaded columns. This model covers the case of a tree under its own weight or gives an answer to Babel mythology, at least from the stability theory point of view. This in-plane buckling problem in presence of distributed and concentrated axial forces has been recently exactly solved using hypergeometric functions. The post-buckling behavior associated with a nonlinear boundaryvalue problem will be also discussed using some asymptotic and numerical methods. The out-of-plane buckling problem of this cantilever beam will be further investigated. The lateral-torsiona l buckling problem of Prandtl (1899) dealing with the stability boundary of a beam loaded by its own weight and a concentrated force will be also solved. The convexity theorem of Papkovitch and Schaefer (1934) will be shown for these structural problems. The seminar will be concluded by the inelastic analysis of the beam in bending. We will show the need to develop a nonlocal plasticity law to describe the post-failure behavior of a beam in presence of softening. Wood’s paradox (1968) is overcome by using a nonlocal plasticity model. The Galileo problem is then revisited in the light of nonlocal mechanics. Applications of such theoretical studies can be found in the field of civil engineering at the macro scale (reinforced concrete design, timber beams, steel or composite beams…), but also at micro- or nano-scales including for instance nanostructures.

Challamel is Professor of Civil Engineering, University of South Brittany, Lorient, France, and Marie Curie Fellow in solid mechanics (faststoffmekanikk) at UiO (2011/2012).

Volume tracking is a popular method for the computation of two phase flow problems. In this talk we present a reformulation of volume tracking in two dimensions in terms of an explicit tracking of the interface between the two immiscible phases. This allows for a higher order accurate representation of the interface with respect to the spatial discretization while conserving the mass up to roundoff precision.

Joris Verschaeve is postdoc at the Mechanics Division, Department of Mathematics, University of Oslo.

Ocean Engineering (OE) is considered by many to be a matured field which is mainly controlled by the oil industries. However, due to the growing interdiciplinary nature of OE, it presents new exciting challenges for scientists and engineers with a solid background in topics like hydrodynamics, acoustics, physio-chemistry as well as electro-kinetics, electromagnetics and control theory. Some practical examples will be discussed.

Touvia Miloh is professor at Tel Aviv University.

An idealized mathematical model of tsunami evolution in deep sea and across the continental shelf is proposed. The initial value problem in deep sea is related to the well known Cauchy- Poisson problem, and the tsunami propagation across the continental shelf is derived using the linearized shallow water equations.

When analyzing different cases of tsunamis in deep sea it was found that tsunamis evolve into two basic wave types. One resembles a single wave and the other a wave packet. The analysis of different cases of tsunamis at the shoreline reveals that the continental shelf, due to its geometrical properties, serves as a tsunami amplifier, producing tsunami amplitudes up to 20 times larger than those at the edge of the continental shelf.

A comparison with tsunami measurements suggests that the idealized model may be used for a reliable assessment of the principle hydrodynamic properties of the tsunami, such as the tsunami amplitude and its half- period.

The new mathematical model for tsunami evolution is used to derive a synthetic tsunami database for the southern part of the Eastern Mediterranean coast. Information about coastal tsunami amplitudes, half-periods, currents, and inundation levels is presented.

Michael Stiassnie is professor at the Department of Civil and Environmental Engineering, Technion – Israel Institute of Technology.