Page 187 - Introduction to Continuum Mechanics
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172 Problems
3.71. Given
u
where (r, 6, z) is cylindrical coordinates for the current configuration and (X, Y, Z) are
rectangular Cartesian coordinates for the reference configuration.
(a) Calculate the change of volume.
(b) Obtain the components of the left Cauchy-Green tensor B with respect to the basis at the
current configuration.
3.72. Given
where (r, B ,z) and (X,Y,Z) are cylindrical coordinates and rectangular Cartesian coor-
dinates for the current and reference configuration, respectively. Obtain the components of
the right Cauchy-Green tensor C with respect to the basis at the reference configuration
3.73. From Eqs.(3.30.4a), obtain Eqs.(3.30.5).
3.74. Verify Eq.(3.30.8b) and (3.30.8d).
3.75. Verify Eq.( 3.30.9b) and (3.30.9d).
3.76. Derive Eqs.(3.30.10).
3.77. Using Eqs.(3.30.10) derive Eqs.(3.30.12a) and (3.30.12d).
3.78. Verify Eqs. (3.30.13 a) and (3.30.13d).
