A Hybrid Photoelastic Stress Analysis Around Holes in Tensile-Loaded P

The presented technique employs general expressions for the stress functions with traction-free
conditions which are satisfied at the geometric discontinuity using conformal mapping and analytical
continuation. In the absence of body forces and rigid body motion, the stresses under plane and
rectilinear orthotropy can be found in the references [1, 2]. For homogeneous and isotropic material,
the two complex stress functions, 0(^,) and ^ ( f , ) can be related to each other by the conformal
mapping and analytic continuation. These functions within sub-region Q. as shown in Figure 1, for a
traction-free physical boundary T , can be written as Laurent expansions

where

• B and C are complex quantities depending on material properties [1].
• c;. = a. + ib. , where a. and b. are real numbers.