Proving Theory: Transforming Step 1 to Step 2

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The discussion focuses on the mathematical transformation of shear strain theory, specifically proving the equation τxy = (E/1-v^2) [((1-v)/2) (ωxy)], where ωxy = 1/G (τxy). Participants clarify the steps needed to derive this equation, emphasizing the importance of manipulating matrices and understanding the inverse of matrix operations. The term E/1-v^2 is central to the proof, and the discussion highlights the necessity of defining all terms and operators involved in the mathematical proof.

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  • Understanding of shear strain theory
  • Familiarity with matrix operations and inverses
  • Knowledge of Young's modulus (E) and Poisson's ratio (v)
  • Basic principles of mechanics of materials
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mink_man
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How does the first step transform into the second step. I have no idea :(

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Consider:

If A = B*C

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

But B-1B = I

so that C = B-1A
 
I still don't understand where the E/1-v^2 comes from.
 
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? :(
 
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.
 
mink_man said:
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.
 

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