prob_08_02_01 - ⎣ ⎤ ⎥ ⎥ ⎥ ⎦:= T ε θ 0.985...

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Problem 8.2-1 Let [E'] be 3 by 3, as for a plane stress problem. Show that Eq. 8.2-10 yields [E']=[E] if the material is isotropic. Solution: For Plane Stress, Isotropic Material Em E 1 ν 2 1 ν 0 ν 1 0 0 0 1 ν 2 = Assume an arbitrary angle and ν values: θ 0.123 := ν 0.3 := T ε θ () cos θ () 2 sin θ () 2 2 cos θ ( ) sin θ () sin θ () 2 cos θ () 2 2 cos θ ( ) sin θ () cos θ ( ) sin θ () cos θ () sin θ () cos θ () 2 sin θ () 2 ()
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Unformatted text preview: ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ := T ε θ ( ) 0.985 0.015 0.244 − 0.015 0.985 0.244 0.122 0.122 − 0.97 ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ = Factoring out E 1 ν 2 − the transformation is: T ε θ ( ) T 1 ν ν 1 1 ν − 2 ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ ⋅ T ε θ ( ) ⋅ 1 0.3 0.3 1 0.35 ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ =...
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