# Exercises in continuum mechanics

1. Sep 12, 2015

### geotechnique

Hello
Please forgive me if i am not posting in the correct forum. Also you may find my English a bit rusty since i am basically French

Ok so i wanna solve some exercises in continuum mechanics . The first exercise states :
we have a stress tensor in a Cartesian coordinate system with the point O ; origin of the system , such as :

calculate σx so that one face of the stress vector is nil at point 0 ( i know it sounds odd)
Then , calculate the components of the vector n on this face .

Another exercise states : the function of a stress for a plain stress condition is given by :

Where a and b are constants and the volume forces are ignored .
Determine the expressions of σx and σy if for the point M(1,1) the shear stress is equal to 1/2.

For the last exercise , what i have done is calculate the derivative of Φ with respect to x and did that again for y , then calculate the the two derivative functions for the point M so it gave me :
σ1 =a+3b
σ2=4a+2b
after that i applied the know functions to calculate σx and σy for a plain stress problem
it gave me these results :
σx =a+3b
σy= 4a+2b which equal exactly my first results ( not sure if this is correct tho )
Thanks

Last edited: Sep 12, 2015
2. Sep 17, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Sep 18, 2015

### geotechnique

yea well i found out the responses to the question . for the first one , you just need to resolve the serie of nul equations ( the stress tensor multiplied by the n vecteur equal 0)
for the last problem , that function is called the Airy function .