A deformation is given by the following equation (1): x 1 = X 1 c o s ? ? X 2 s

ID: 1853260 • Letter: A

Question

A deformation is given by the following equation (1):

x1=X1cos??X2sin?

x2=X1sin?+X2cos?

x3=(1+??)X3

where k, lamda are constants such that k lamda is greater than or equal to O and the coordinate systems Xk, xi coincide so that im=deltamkIk

1. Determine xi, k , Ckm and show that the determinate of xi, k is greater than O.

2. Give an interpretation of each element of Ckm

3. Show that ANY line element originally parallel to the I1-I2 plane remains parallel to the plane and suffers no change in length

4. Show that any line element originally in the I3 direction remains in that direction. Compute its deformed length.

5. IS the deformation given by equation (1) homogeneous?

m=?m?I?

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