Elasticity pp 293-317 | Cite as

# Application to Elasticity Problems

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## Abstract

From a mathematical perspective, both two-dimensional vectors and complex numbers can be characterized as ordered pairs of real numbers. It is therefore a natural step to represent the two components of a vector function
is represented by the complex function

*V*by the real and imaginary parts of a complex function. In other words,$$V \equiv iV_x + jV_y $$

(19.1)

$$V = V_x + iV_y.$$

(19.2)

In the same way, the vector operator
from equation (18.6).

$$\nabla \equiv i\frac{\partial }{{\partial x}} + j\frac{\partial }{{\partial y}} = \frac{\partial }{{\partial x}} + ii\frac{\partial }{{\partial y}} = 2\frac{\partial }{{\partial \zeta }},$$

(19.3)

## Keywords

Holomorphic Function Elasticity Problem Elliptical Hole Residue Theorem Boundary Traction
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media B.V. 2010