Strain from rosettes using tensors?

[randomtaskk]

Hi,

As part of my recent employment graduate training I'm required to do some material testing etc.

As part of this I'm required to find strains along various axes from a 0/60/120 degree strain rosette readout.

The problem is I have to do this via a tensor based approach, which I can't seem to find exmaples of in any of the books lying around the office or that I otherwise have access too.

I remember from Uni that we always used equations to do it, and never covered a tensor based approach. Does anyone know where I might be able to find an example, or could otherwise advise on the tensor based method?

I'm familiar with combining three states of stress on varying axes using directional cosines etc. to determine principal stresses in a section, and I presume the method follows something fairly similar, but I just can't work out how to go about it.

Any help appreciated, thanks.

 

[hdp]

The tensor method is mostly a matrix method that uses principles that you already know (from what you have written). A tensor of order 0 is a scalar. A tensor of order 1 is a vector. The state of mechanical stress in a solid is a tensor of order 2 (9 elements, principal and shear stresses). Check wikipedia, they have a decent page on "stress".

 

[EdR]

This is just a standard stress/strain rotation problem....Use the standard rotation equations you know and just arrange them in matrix form if someone wants them in that form......

Ed.R.

 

[druminman]

"Experimental Stress Analysis" by Daily is an excellent source for stress analysis methods. I'm pretty sure it can still be had new, but an older edition would suffice (the analysis hasn't changed since the days of Euler) and cost significantly less.