Dr. Josef Kiendl - Isogeometric Methods in Structural Analysis

Department of Marine Technology, Norwegian University of Science and Technology, Norway

Abstract

Isogeometric analysis is a novel method of computational analysis where functions used to describe geometries in Computer Aided Design (CAD) are adopted as basis for analysis. Due to this unified geometric representation, the model transfer from design to analysis, called mesh generation, is omitted providing a better integration of design and analysis. NURBS are the most widespread technology in today’s CAD modeling tools and therefore are adopted as basis functions for analysis. Apart from the geometrical advantages, NURBS-based isogeometric analysis has proven superior approximation properties compared to standard finite element analysis for many different applications. Furthermore, the high continuity between elements also allows the discretization of higher order PDEs, which is especially useful in structural mechanics, where the classical plate and shell theories, based on Kirchhoff’s kinematic assumption, can be implemented in a straightforward way.

We show an isogeometric shell analysis framework with formulations ranging from linear, geometrically nonlinear, and fully nonlinear shell models. All formulations are based on the Kirchhoff-Love shell theory and are rotation-free, i.e., using only displacement degrees of freedom. These formulations are then employed for the simulation of various problems of structural mechanics, including large deformations, buckling, elastoplasticity, and brittle fracture as well as for fluid-structure-interaction problems including high-fidelity FSI simulations of offshore wind turbine blades and bioprosthetic heart valves.

A further development of IGA are isogeometric collocation methods (IGA-C), where the partial differential equations are solved in the strong form. This avoids the need of computing integrals by numerical quadrature and, thus, reduces the computational costs by several orders. We show isogeometric collocation formulations for different problems in structural mechanics, like spatial beams, plates, and shells.

Prof. Dr. Luca Dedé - Isogeometric Analysis of High Order, Surface, and Geometric Partial Differential Equations with Applications

Department of Mathematics, Politecnico di Melano, Italy

Abstract

In this talk, we consider the spatial approximation of high order, surface, and geometric Partial Differential Equations (PDEs) by means of Isogeometric Analysis (IGA). Specifically, we discretize the PDEs by means of NURBS-based IGA in the framework of the Galerkin method and we show that IGA is particularly suitable for approximating these classes of PDEs. Indeed, NURBS-basis IGA straightforwardly encapsulates the exact representation of the computational domain (the geometry) in the numerical approximation of the PDE, thus significantly enhancing the accuracy of the solution of surface and geometric PDEs. Moreover, we consider trial spaces of NURBS basis functions with high degree of continuity in the computational domain, a feature that is particularly efficient for approximating high order PDEs. We show the efficiency and accuracy of the method by solving high order PDEs on both open and closed surfaces and phase field problems driven by the Cahn-Hilliard and crystal growth equations. Moreover, we approximate by means of NURBS-based IGA some benchmark geometric PDEs, specifically the mean curvature and Willmore flow problems and the Canham-Helfrich curvature model. The latter is indeed suited to model the shape of biomembranes and vescicles as red blood cells. Finally, we present and discuss a dynamical model for the simulation of the interaction of the biomembranes with the fluid.

Prof. Dr. Daniel Cremers - Novel Algorithms for 3D Computer Vision

Department of Computer Science, Technical University of Munich

Abstract

Prof. Dr. Shakti Gupta - Carbon nanostructures: Molecular Simulations, Continuum Models and Some Related Issues

Department of Mechanical Engineering, Indian Institute of Technology, India

Abstract

Continuum hypothesis based properties, for example, elastic modulli or
thermal conductivity of a material at small lengths scale can be derived
efficiently using molecular mechanics or dynamics. While doing so one
makes a few key assumptions and develops what are called as equivalent
continuum structures (ECSs). Accuracy of the derived quantity for a given
structure thus depends strongly on its ECS. In this talk we will first
present development of ECSs for single-walled carbon nanotubes (SWCNTs)
and graphene based on the theory of linear vibrations and show instances
when these ECSs may fail or behave counterintuitively. Subsequently,
results from two methods leading to conflicting values of critical
buckling strain in SWCNTs under compression will be presented. Lastly, we
will present some very recent results on instabilities in carbon nanocone
stacks motivating to development of continuum models.

Prof. Dr. Matthieu Verstraete - Ab Initio Phonon Limited Transport

QMAT CESAM Research Unit, Department of Physics, Université de Liege, Belgium

Abstract

We revisit the thermoelectric (TE) transport properties of two champion materials, PbTe and SnSe, using fully first principles methods. In both cases the performance of the material is due to subtle combinations of structural effects, scattering, and phase space reduction. In PbTe anharmonic effects are completely opposite to the predicted quasiharmonic evolution of phonon frequencies and to frequently (and incorrectly) cited extrapolations of experiments. This stabilizes the material at high T, but also tends to enhance its thermal conductivity, in a non linear manner, above 600 Kelvin. This explains why PbTe is in practice limited to room temperature applications. SnSe has recently been shown to be the most efficient TE material in bulk form. This is mainly due to a strongly enhanced carrier concentration and electrical conductivity, after going through a phase transition from 600 to 800 K. We calculate the transport coefficients as well as the defect concentrations ab initio, showing excellent agreement with experiment, and elucidating the origin of the double phase transition as well as the new charge carriers. If I have time I will show you something weird about transition metal dichalcogenides.

References 

• [1] Hellman, IA Abrikosov, and SI Simak, PRB 84 180301 (2011)
• [2] AH Romero, EKU Gross, MJ Verstraete, and O Hellman PRB 91, 214310 (2015)
• [3] A Dewandre, S Bhattacharya, O Hellman, AH Romero, GKH Madsen, MJ Verstraete PRL 117 276601 (2016)