Deployable structures typically consist of rigid elements connected via rotational joints which have compact rest states and deploy into 3D target surfaces. Such structures are widely used in industrial and consumer products, medical devices, aerospace applications, and civil installations.

The authors propose a new deployable material system, called umbrella mesh, that combines rigid linkage mechanisms and elastic beams to enable a wide variety of shapes. Umbrella meshes are composed of regular arrangements of parameterized cells. All cells cover the same area footprint, but the differing cell heights cause this area to expand by different amounts during deployment and result in a curved shape.

The authors provide a model to simulate the deployment of such structures and present an algorithm to optimize the free design parameters to best approximate a given target shape. These results are validated with physical prototypes and show that umbrella meshes allow to obtain surface geometries that are not possible with other existing methods.

The authors rely on Artelys Knitro to determine the optimal shape parameters for approximating a given target surface. The optimization problem is nonlinear, and the Artelys Knitro interior-point Conjugate gradient algorithm is exploited to rapidly converge to an optimal design.