Elasticity pp 293-317

# Application to Elasticity Problems

• J. R. Barber
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 172)

## 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 V by the real and imaginary parts of a complex function. In other words,
$$V \equiv iV_x + jV_y$$
(19.1)
is represented by the complex function
$$V = V_x + iV_y.$$
(19.2)
In the same way, the vector operator
$$\nabla \equiv i\frac{\partial }{{\partial x}} + j\frac{\partial }{{\partial y}} = \frac{\partial }{{\partial x}} + ii\frac{\partial }{{\partial y}} = 2\frac{\partial }{{\partial \zeta }},$$
(19.3)
from equation (18.6).

## 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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