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A5_Strain_Tensor

A5_Strain_Tensor - ASSIGNMENT 5 EATS 2470 EATS 2470...

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ASSIGNMENT 5 EATS 2470 Page 1 of 2 EATS 2470 INTRODUCTION TO CONTINUUM MECHANICS ASSIGNMENT 5 1. Prove that: j r i r i j j i ij a u a u a u a u L 2 1 and j r i r i j j i ij y u y u y u y u E 2 1 are: (a) second order tensors (Hint: Verify that they satisfy tensor transformation law) (b) symmetrical tensors 2. For the flow t a t a a y 3 4 2 1 1 2 1 2 2 t a a y t a a y 2 3 3 determine the: (a) Lagrangian non-linear strain tensor at 2 t (b) Eulerian non-linear strain tensor at 2 t 3. For the displacements (assuming small displacement gradients) T i y y y y y y y y y a u 2 2 1 3 2 3 1 2 2 3 2 1 ) ( , ) ( , ) ( 4 find the: (a) linear strain tensor (b) linear rotation tensor 4. Prove that ij l jk l ki l is invariant, where ij l is the Lagrangian linear strain tensor.

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