Consider a change of basis from a Cartesian to the rotated Cartesian frame shown in Fig. 2. By studying the figure, you should recognize that strains €rx, Eyy, Ery, after transformation into the coordinate system rotated by relative to the original coordinate system, are simply Err, E90, Ero at a point (r, 0). Use the change of basis formula for a second-order tensor to write the strain components Err, €00, Ero as a function of €xx, Ery, Exy and 0.

Elements Of Electromagnetics
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Consider a change of basis from a
Cartesian to the rotated Cartesian frame shown in Fig. 2. By studying the figure, you should
recognize that strains €xx, ¤yy, Exy, after transformation into the coordinate system rotated by
relative to the original coordinate system, are simply Err, €00, €re at a point (r, 0). Use the
change of basis formula for a second-order tensor to write the strain components Err, €00, Ero
as a function of Exx, Ery, Exy and 0.
Transcribed Image Text:Consider a change of basis from a Cartesian to the rotated Cartesian frame shown in Fig. 2. By studying the figure, you should recognize that strains €xx, ¤yy, Exy, after transformation into the coordinate system rotated by relative to the original coordinate system, are simply Err, €00, €re at a point (r, 0). Use the change of basis formula for a second-order tensor to write the strain components Err, €00, Ero as a function of Exx, Ery, Exy and 0.
L
€00 = €y'y'
y
ев
er
ед
er
Err = €x'x
\€ro = Ery
+ Х
€00 = Eyy
Ere = Exy
Err = Exx
Figure 2: A change of basis.
6
Transcribed Image Text:L €00 = €y'y' y ев er ед er Err = €x'x \€ro = Ery + Х €00 = Eyy Ere = Exy Err = Exx Figure 2: A change of basis. 6
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