Page 169 - Introduction to Continuum Mechanics
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154 Components of Deformation Tensors in other Coordinates
l
l
Again, the components of C can be obtained by using the equation dX = F d* and Eq.
(ix). We list here two of the six components. The other four components can be easily written
down following the patterns of these two equations.
(B) Cylindrical coordinates (r,0,z ) for the current configuration and rectangular Cartesian
coordinates (X,Y,Z) for the reference configuration.
Let
describe the motions. Then using the same procedure as described for the case where one
single cylindrical coordinate is used, it can be derived that [see Prob.3.76].
The matrix
