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Lecture# Plates III: Mechanics of Slender Structure

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.

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In course

ME-411: Mechanics of slender structures

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

Instructor

Related concepts (265)

Bending moment

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam. The diagram shows a beam which is simply supported (free to rotate and therefore lacking bending moments) at both ends; the ends can only react to the shear loads. Other beams can have both ends fixed (known as encastre beam); therefore each end support has both bending moments and shear reaction loads.

Map

A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes. Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although most commonly used to depict geography, maps may represent any space, real or fictional, without regard to context or scale, such as in brain mapping, DNA mapping, or computer network topology mapping.

Tensor

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product.

Outer membrane vesicles

Outer membrane vesicles (OMVs) are vesicles released from the outer membranes of Gram-negative bacteria. While Gram-positive bacteria release vesicles as well those vesicles fall under the broader category of bacterial membrane vesicles (MVs). OMVs were the first MVs to be discovered, and are distinguished from outer inner membrane vesicles (OIMVS), which are gram-negitive baterial vesicles containing portions of both the outer and inner bacterial membrane.

World map

A world map is a map of most or all of the surface of Earth. World maps, because of their scale, must deal with the problem of projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensional surface of the earth. While this is true of any map, these distortions reach extremes in a world map. Many techniques have been developed to present world maps that address diverse technical and aesthetic goals. Charting a world map requires global knowledge of the earth, its oceans, and its continents.

Related lectures (420)

Plates III: Buckling Theory and Applications

Explores Föppl-von Kármán plate theory, including buckling equations and an example of plate compression.

Plates: Föppl-von Kármán EquationsME-411: Mechanics of slender structures

Covers the Föppl-von Kármán equations, Airy potential, plate theory simplifications, and plate buckling.

Gaussian Curvature in PlatesME-411: Mechanics of slender structures

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

Linear Shell Theory: Equilibrium and Energy

Covers the expression of the Kirchhoff-Saint Venant energy in a covariant setting and explores equilibrium equations for spherical shells and linear shell theory.

Föppl-von Kármán Equations: Plates IIIME-411: Mechanics of slender structures

Covers the Föppl-von Kármán equations, Airy potential, plate theory simplifications, and plate buckling.