  Shape-morphing structures, which are able to change their shapes from one
state to another, are important in a wide range of engineering applications. A
popular scenario is morphing from an initial two-dimensional (2D) shape that is
flat to a three-dimensional (3D) target shape. One of the exciting
manufacturing paradigms is transforming flat 2D sheets with prescribed cuts
(i.e. kirigami) into 3D structures. By employing the formalism of the 'tapered
elastica' equation, we develop an inverse design framework to predict the shape
of the 2D cut pattern that would generate a desired axisymmetric 3D shape. Our
previous work has shown that tessellated 3D structures can be achieved by
designing both the width and thickness of the cut 2D sheet to have particular
tapered designs. However, the fabrication of a sample with variable thickness
is quite challenging. Here we propose a new strategy -- perforating the cut
sheet with tapered width but uniform thickness to introduce a distribution of
porosity. We refer to this strategy as perforated kirigami and show how the
porosity function can be calculated from our theoretical model. The porosity
distribution can easily be realized by laser cutting and modifies the bending
stiffness of the sheet to yield a desired elastic deformation upon buckling. To
verify our theoretical approach, we conduct finite element simulations and
physical experiments. We also examine the loading-bearing capacity of morphed
structures via indentation tests in both FEM simulations and experiments. As an
example, the relationship between the measured geometric rigidity of morphed
half-ellipsoids and their aspect ratio is investigated in details.
