Project Description

Convex solids of specific shape can be arranged in a planar tiling such that they cannot be extracted or pushed into a void underneath the tiling. Note that no adhesives or fasteners of any kind are used. Examples include anti-prisms and all Platonic polyhedra. Prior published work has shown such systems to possess interesting mechanical behavior and multifunctional properties, and realizations exist in architectural floor and wall coverings, and in mechanical engineering systems for thermal control or battery systems packaging. To-date, a planar tiling must be enclosed in a frame so as to block lateral motion of tiles.
We propose research into nonplanar tiling, such as cylinders and hemispheres. The core question is how to assign the role of the enclosing frame of a planar tiling to the geometric shape. For example, in a cylindrical tiling part of a frame is obviated by the closed rings. Only a top and bottom lid should be necessary. Similarly, hemispheric tiling should topologically require no frame, just a foundation.
By executing this research we aim to create new multifunctional structural and material systems.

Start Date

Spring 2019

Postdoc Qualifications

The successful candidate will have expertise in geometric modeling and computations, ideally in computer-aided design (CAD) and finite element analysis. S/he will be fluent in algorithm design and analysis, to the extent of devising superior computational strategies and understanding and defending the choices. Mathematical maturity is expected.  

Co-advisors

Thomas Siegmund, siegmund@purdue.edu, School of Mechanical Engineering, www.engineering.purdue.edu/MYMECH

Christoph Hoffmann, cmh@purdue.edu, Computer Science 

References