Page 229 - Intro to Tensor Calculus

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Figure 2.3-12. Displacement of element ABCD to A B C D 0
0
0
0
Expanding u and v in (2.3.32) in Taylor series about the point (x, y) we find
∂u
x = x +∆x + u + ∆x + h.o.t.
∂x (2.3.33)
∂v
y = y + v + ∆x + h.o.t.,
∂x
where h.o.t. denotes higher order terms which have been neglected. The equations (2.3.33) require that the
coefficients b ij satisfy the matrix equation
∂u
x + u +∆x + ∆x b 11 b 12 x +∆x
∂x = . (2.3.34)
y + v + ∂v ∆x b 21 b 22 y
∂x