The components of the displacement vector (u) at a point (X, X2, X3), with respect to...

 

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The components of the displacement vector (u) at a point (X₁, X2, X3), with respect to (x₁, x2, x3) coordinate system, are given as: = = a^(X²X² + X²X₂) + aX²X²X² U₂ = ba² (X2X3) + aX³X3 1 U3 = = ax₁x²x³ Find: a. The components of the displacement gradient tensor (Vu). b. The components of the linear strain tensor (E) at the point (P): (3,3,1) and (b = 12) c. The value of (a) if a unit elongation at (P) with respect to the direction n=- [101] 1 √2 is given as (Enn = 1.5 x 10-8) d. The shear strain at (P) with respect to the directions 1 √3 k = m = [1 1 1], =110 The components of the displacement vector (u) at a point (X₁, X2, X3), with respect to (x₁, x2, x3) coordinate system, are given as: = = a^(X²X² + X²X₂) + aX²X²X² U₂ = ba² (X2X3) + aX³X3 1 U3 = = ax₁x²x³ Find: a. The components of the displacement gradient tensor (Vu). b. The components of the linear strain tensor (E) at the point (P): (3,3,1) and (b = 12) c. The value of (a) if a unit elongation at (P) with respect to the direction n=- [101] 1 √2 is given as (Enn = 1.5 x 10-8) d. The shear strain at (P) with respect to the directions 1 √3 k = m = [1 1 1], =110