Continuum Mechnices Flashcards
What does a stress tensor σxy mean?
It tells us its a shear stress acting on the x plane and it acting in the positive y direction.
Why is it assumed that the stress distribution is uniform?
- Small quantities of higher order are ignored as they are negligible
- If it is assumed that mean stresses are acting at the centre of the element then the resulant forces will be the same. therefore you can assume uniform stress and moment distribution.
Why are only 6 of the 9 stress components in a 3D element?
Only 6 are independent as the shear stress acting opposite to each other are equal to each other.
How do you construct kinematic relations for a deformed body?
The mathematical description of how two points within the body move relative to each other is determined using u,v and w.
For example a point (x,y,z) will be displaced to (x+u, y+v, z+w)
Define normal strain.
In terms of u define εxx.
The normal strain in a given direction is defined as the unit change in length of a line which was originally orientated in the given direction.
εxx = ((du/dx)*dx)/dx = du/dx
Why do engineers make 2D approximations?
It can lead to a much reduced computational cost in terms of storage, run time and pre and post-processing.
What makes a problem plane strain and describe what this means in terms of calculations?
Plane strain is generaly emplyoed when one dimension of the structure is very much larger than the other two dimensions. The external forces are applied perpendicular to the longest dimension and the displacements parallel to the longest length are assumed to be 0.
Therefore strains in the z direction (longest dimension) are equal to 0.
εzz = γzx = γyz = σyz = σzx = 0
What makes a problem plane stress and describe what this means in terms of calculations?
Plane stress is generally employed when one of the dimensions is so small in comparison to the other two and the is no load applied along the smallest dimension (z-direction).
σzz = σyz = σzx = 0
How can a 3D problem be solved as an axisymmetric problem?
If there is rotatioanlly symmetric geomrety and loading and the boundary conditions are also axisymmetric
