  The dramatic effect kirigami, such as hole cutting, has on the elastic
properties of thin sheets invites a study of the mechanics of thin elastic
frames under an external load. Such frames can be thought of as modular
elements needed to build any kirigami pattern. Here we develop the technique of
elastic charges to address a variety of elastic problems involving thin sheets
with perforations, focusing on frames with sharp corners. We find that holes
generate elastic defects (partial disclinations) which act as sources of
geometric incompatibility. Numerical and analytic studies are made of three
different aspects of loaded frames - the deformed configuration itself, the
effective mechanical properties in the form of force-extension curves and the
buckling transition triggered by defects. This allows us to understand generic
kirigami mechanics in terms of a set of force-dependent elastic charges with
long-range interactions.
