Page 45 - Introduction to Continuum Mechanics

30 Tensors

Fig. 2B.5

2B13 Transformation Law for Cartesian Components of a Tensor
Consider any tensor T, then the components of T with respect to the basis {e,- }are:

T = c -Te
e ie
L
i] » ;
Its components with respect to {e/ }are:
: ;
T.'. = e -Te v
e
1
ij
i * j
:
With e, = Q mie m,
e
' ij ~ Qtnfim' *vj/i/ /i ~ \2m&£nj\*m' * ®n)
i.e.,
In matrix notation, Eq. (2B13.1a) reads
- )
Tn T'n T^\ \Q n Q 2l 0 31 1 |"r n T n T 13\ \Q n Q n Qi3\ < 2B13 lb
T T T T T T
2l 22 23 ~ Ql2 Qn 032 21 22 23 Qzi Ql2 Q23
TII T^ 2 7*33 ^13 023 033 T 31 T 32 T 33 031 032 033

or