Proving Theory: Transforming Step 1 to Step 2

[mink_man]

How does the first step transform into the second step. I have no idea :(

 

[gneill]

Consider:

If A = B*C

then B^-1A = B^-1B*C

But B^-1B = I

so that C = B^-1A

 

[mink_man]

I still don't understand where the E/1-v^2 comes from.

 

[mink_man]

also its asked to prove shear strain, ill use this symbol for it. ω

it asks to prove τxy (tau xy) = (E/1-v^2) [((1-v)/2) (ωxy)]

given ωxy = 1/G (τxy)

Any help? :(

 

[gneill]

I still don't understand where the E/1-v^2 comes from.

Starting with the first equation, first multiply the 1/E into the 2x2 matrix. Then find the inverse of that matrix, then factor out the constant term.

 

[gneill]

also its asked to prove shear strain, ill use this symbol for it. ω

it asks to prove τxy (tau xy) = (E/1-v^2) [((1-v)/2) (ωxy)]

given ωxy = 1/G (τxy)

Any help? :(

Sorry, I'm not familiar with the mechanics of shear strain theory. However, if it's just a mathematical proof that's required and all the terms and operators are completely defined, then I'm sure that someone here can help you with the mathematics.