  An infinite class of nonuniform antiplane shear fields is considered for a
linear elastic isotropic space and (non-intersecting) isotoxal star-shaped
polygonal voids and rigid inclusions perturbing these fields are solved.
Through the use of the complex potential technique together with the
generalized binomial and the multinomial theorems, full-field closed-form
solutions are obtained in the conformal plane. The particular (and important)
cases of star-shaped cracks and rigid-line inclusions (stiffeners) are also
derived. Except for special cases (addressed in Part II), the obtained
solutions show singularities at the inclusion corners and at the crack and
stiffener ends, where the stress blows-up to infinity, and is therefore
detrimental to strength. It is for this reason that the closed-form
determination of the stress field near a sharp inclusion or void is crucial for
the design of ultra-resistant composites.
