1.7 Stress Tensor - MIT OpenCourseWare

- Marine Hydrodynamics, Spring 2005. Lecture 3. Marine Hydrodynamics Lecture 3. Stress Tensor Stress Tensor ij The Stress (force per unit area) at a point in a uid needs nine components to be completely speci ed, since each component of the Stress must be de ned not only by the direction in which it acts but also the orientation of the surface upon which it is acting. The rst index i speci es the direction in which the Stress component acts, and the second index j identi es the orientation of the surface upon which it is acting. Therefore, the ith component of the force acting on a surface whose outward normal points in the j th direction is ij . X2. 22. 12. 32. 21. 23. 11. 13 31. 33 X1. X3. Figure 1: Shear stresses on an in nitesimal cube whose surfaces are parallel to the coordinate system. 1. X2. 2. P n . A1. 1. A3. X1. Q. 3. R. area A0. A2. X3. Figure 2: In nitesimal body with surface PQR that is not perpendicular to any of the Cartesian axis.

X 1 X 2 X 3 31 11 21 22 12 32 13 23 33 Figure 1: Shear stresses on an infinitesimal cube whose surfaces are parallel to the coordinate system. 1 2.20 - Marine Hydrodynamics, Spring 2005 2.20. X 2 2 A 1 X 3 3 A 2 1 A 3

Tags:

  Marines, Stress, Tensor, Mit opencourseware, Opencourseware, Stress tensor

Information

Related search queries