Westergaard Method for a Crack Under Concentrated Forces

Abstract

Consider a crack of length 2a in an infinite plate subjected to the concentrated forces P at a distance y₀ from the crack (Figure 1). Verify that the Westergaard function is

$$ {z_1} = \frac{p}{\pi }\left[ {1 - \frac{{{y_0}}}{{2(1 - v)}}\frac{\partial }{{\partial {y_0}}}} \right]f(z,{y_0},a) $$

((1))

where

$$ f(z,{y_0},a) = {\frac{{({a^2} + y_0^2)}}{{{z^2} + y_0^2}}^{1/2}}\frac{z}{{{{({z^2} - {a^2})}^{1/2}}}} $$

((2))

.