Lecture

Kirchhoff Rods: Kinematics and Twisted Solutions

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In course

ME-411: Mechanics of slender structures

Analysis of the mechanical response and deformation of slender structural elements. ...

Description

This lecture delves into the kinematics of 3D structures based on the Kirchhoff equation, exploring twisted solutions and recent developments in rod mechanics, including the mechanics of knots. The presentation covers the framework of the Kirchhoff equation, differential geometry of curves, and the relationship between moment and strain. It also discusses force and moment balances, the use of the Kirchhoff equation, and the derivation of equations for the Darboux vector. The lecture concludes with examples of kinematics, twisted solutions, and the implications of elasticity and geometry in rod mechanics.

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Instructor

Pedro Miguel Nunes Pereira de Almeida Reis

Pedro M. Reis is a Professor of Mechanical Engineering at the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland, where he is the Director of the Institute of Mechanical Engineering. Prof. Reis received a B.Sc. in Physics from the University of Manchester, UK (1999), a Certificate of Advanced Studies in Mathematics (Part III Maths) from St. John’s College and DAMTP, University of Cambridge (2000), and a Ph.D. in physics from the University of Manchester (2004). He was a postdoc at the City College of New York (2004-2005) and at the CNRS/ESPCI in Paris (2005-2007). He joined MIT in 2007 as an Instructor in Applied Mathematics. In 2010 he moved to MIT’s School of Engineering, with dual appointments in Mechanical Engineering and Civil & Environmental Engineering, first as the Esther and Harold E. Edgerton Assistant Professor and, since the summer of 2014 as Gilbert W. Winslow Associate Professor. In October 2013, the Popular Science magazine named Prof. Reis to its 2013 “Brilliant 10” list of young stars in Science and Technology. He has received the 2014 CAREER Award (NSF), the 2016 Thomas J.R. Hughes Young Investigator Award (Applied Mechanics Division of the ASME), the 2016 GSOFT Early Career Award for Soft Matter Research (APS), he is a Fellow of the APS, and he is the 2021 President of the Society of Engineering Science (SES).

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