- #1

Cyrus

- 3,150

- 16

Please help me out here as I self study fluid mechanics. I ran into what they are calling a second order tensor quantity, which seems to be fancy words for a 3x3 matrix of sigmas and rhos, for shear and normal stress. They have a picture of a cube, with all the positive stresses indicated on it. Now they have a convention like sigma_xx or sigma_xy. I get that. I don't get the picture of the cube, though. Is it merely an illustration? See they start with the premise that you are looking locally at point C in space. And you make a plane of area deltaA, perpendicular to the x axis, then you find the shear and normal stress to the unit normal. Then they repeat for the other two orthogonal planes. Thats fine. Then the say there are an infinite number of planes that can pass through point C and have different shear values, FINE! Then they say that any stress can be found for any plane provided that you now know these three mutually perpendicular stress planes...ok i kinda see what they mean, but I am not tooo sure...I could use some explaining on that point. Also, this damn box!? Is point C somewhere inside this box of dimensions dx,dy,dz?? Why is this thing now a box, I thought we just cared about flat planar areas that passed through point c? Is point C now surrounded by this box? Or is the box there just to explain to my stupid self the purpose of the x,y subsripts, becuase I have a feeling its going to be used as a local control surface for some reason.

Thanks for your help,

(This stuffs still great fun so far! I am just annoyed at the unclarity)