Calculating Stress Tensor for MEMS Project

[leofur]

Hi all,
I'm doing a MEMS project, I have a cantilever beam with a mass at its end, I need to calculate the stress tensor at the beam contact point, there is a piezoelectric matirial there, and I want to calculate the voltage it generates. somebody can please help me and explain how to calculate the stress tensor there, I don't know solid state physics that good, and the last 2 days I was searching the web for this, but couldn't find anything.

 

[FredGarvin]

If you want to get into the theory, you'll need a book like Timoshenko's that goes into elasticity. The tensor is simply made up of all of the stresses at that location. There are 9 components in the tensor but only 6 are independent.

http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/stress.cfm

 

[fisico30]

Hello, I am wondering about the actual usefulness of the stress tensor.
I know it fully defines the state of stress at a point inside a material which is under the action of external forces.
But if the stress tensor has components and eigenvalues that change from point to point, how can it be practically useful? Also, we cannot really measure it directly, right?
The inertia tensor, for instance, is a global property of the body (it only depends on the choice of the rotation axes).
I "guess" the answer to my question is maybe related to the Mohrs circle? (which I do not know what it really is)...
thanks

 

[FredGarvin]

Even though the stress tensor is applicable at a point, unlike the inertia tensor, it is still very applicable. This requires some engineering judgement of where to evaluate the stresses in a body. Granted, numerical methods now make this easier to know where to really look. The tensor is measurable by strai gauges. There are assumptions made with them because strain gauges are actually an average over a finite area in stead of at a point. However, for the engineering purpose, they are quite good.