Mechanics and Modeling of Geometric Nonlinearities: A Tutorial by Dr. Paolo Tiso, June 2023

Mechanics and Modeling of Geometric Nonlinearities: A Tutorial

Dr. Paolo Tiso

ETH Zurich

June, 2023

Abstract:

Geometric nonlinearities arise when the deflections of a structure cause a non-negligible redirection of internal forces. This can be due to large rigid rotations, large elastic deformations, or both. Unlike linear systems, for which the deformations are proportional to the applied load, geometrically nonlinearities generate a wide range of peculiar phenomena. In some cases, geometric nonlinearities significantly affect the load-carrying capacity and the fatigue life of a given structure and should therefore properly assessed in the design phase. In other cases, the exploitation of the nonlinearities allows to achieve new functionalities.

This tutorial discusses the main sources of geometric nonlinearities and the qualitative features of the structural responses one may encounter, namely hardening, softening, mixed load-displacement relations, buckling, snap-through, snap-back, etc. The popular approximate kinematical model of von-Karman is discussed, and its limitations illustrated.

Next, the main response features the dynamic responses of geometrically nonlinear systems are overviewed. We discuss the existence and stability of multiple solutions, the dependence on initial conditions, modal interaction, and internal resonance.

The tutorial proceeds by illustrating the main numerical solution tools for geometrically nonlinear systems both in frequency and time domain, namely harmonic balance, shooting, and numerical time integration.

Lastly, we will briefly illustrate some clever applications of geometric nonlinearities in micro electro-mechanical systems.

Biography:

Paolo Tiso is a Senior Scientist at ETH Zürich since 2015, and he is affiliated to the Chair in Nonlinear Dynamics. Before joining ETH, he was a tenured Assistant Professor at the Delft University of Technology, Faculty of Mechanical, Material, and Maritime Engineering. He holds a PHD degree in Aerospace Engineering, obtained in 2006, from the same university. He received his engineering education at Politecnico di Milano (Italy) and Worcester Polytechnic Institute (Worcester, MA).

Paolo Tiso is a member of the editorial board of Journal of Sound and Vibration and Scientific Reports of Nature – _Mechanical Engineering. His current research interests are focused on model order reduction for nonlinear structural mechanics and coupled problems, with special emphasis on light-weight structures, thermo-elastic, thermo-aero-elastic systems and systems featuring contact and friction.