Lamé's Ellipsoid and Mohr's Circles (Part 3: Meridians)

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

For a continuous body, the stress tensor is a symmetric matrix representing the stresses at a point. The traction vector on a plane defined by its unit normal vector is the matrix product of the stress tensor with . The stress tensor has three real eigenvalues (the principal stresses, , , and ) and three associated eigenvectors (the principal directions). In the coordinate system defined by these eigenvectors, the Lamé's ellipsoid represents the locus of the traction vector heads.

[more]

This Demonstration shows ellipses, called meridians, obtained by cutting Lamé's ellipsoid by sheaves of planes through the , , and axes, with equations

,

,

.

In the first two cases, is the angle between the plane and the - plane (); in the third case is the angle between the plane and the - plane ().

The points of the meridians are endpoints of the traction vectors, whose intrinsic components (normal and tangential) are represented by green loci within the Mohr circles.

[less]

Contributed by: Luis Martín Yagüe, Agustín Lacort Echeverría, and Antonio Sánchez Parandiet (March 2011)
After work by: Eugenio Bravo Sevilla
Open content licensed under CC BY-NC-SA


Snapshots


Details



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send