Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Plates III: Mechanics of Slender Structure

In course

ME-411: Mechanics of slender structures

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

Description

This lecture covers the Föppl-von Kármán equations written with respect to resultant membrane stresses and bending moments, the Airy potential (or Stress Function), and simplifications of Föppl-von Kármán plate theory including Linear Theory and Membrane Theory. It also discusses buckling of plates, including buckling equations derived from perturbation of Föppl-von Kármán theory, with an example of uniaxial compression of a rectangular plate.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

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).

Official source

Ontological neighbourhood

Mathematics

Geometry: Differential geometry

Related concepts (32)

Cell membrane

The cell membrane (also known as the plasma membrane or cytoplasmic membrane, and historically referred to as the plasmalemma) is a biological membrane that separates and protects the interior of a cell from the outside environment (the extracellular space). The cell membrane consists of a lipid bilayer, made up of two layers of phospholipids with cholesterols (a lipid component) interspersed between them, maintaining appropriate membrane fluidity at various temperatures.

Semipermeable membrane

Semipermeable membrane is a type of biological or synthetic, polymeric membrane that will allow certain molecules or ions to pass through it by osmosis. The rate of passage depends on the pressure, concentration, and temperature of the molecules or solutes on either side, as well as the permeability of the membrane to each solute. Depending on the membrane and the solute, permeability may depend on solute size, solubility, properties, or chemistry. How the membrane is constructed to be selective in its permeability will determine the rate and the permeability.

Bending

In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two. When the length is considerably longer than the width and the thickness, the element is called a beam.

Buckling

In structural engineering, buckling is the sudden change in shape (deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have buckled. Euler's critical load and Johnson's parabolic formula are used to determine the buckling stress of a column.

Membrane technology

Membrane technology encompasses the scientific processes used in the construction and application of membranes. Membranes are used to facilitate the transport or rejection of substances between mediums, and the mechanical separation of gas and liquid streams. In the simplest case, filtration is achieved when the pores of the membrane are smaller than the diameter of the undesired substance, such as a harmful microorganism.

Related lectures (35)

General Covariance in Gravity

Explores general covariance in gravity, covering equations, curvature tensor, and static gravity field.

Beams under Flexure

Discusses stresses in beams under flexure, including shear forces and bending moments.

Riemann Tensor and Ricci Scalar

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Gaussian Curvature in Plates Log in to Mediaspace to watch this video

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.

Plates III: Buckling Theory and Applications Log in to Mediaspace to watch this video