Geometry-based structural form-finding to design architected cellular solids

In this paper, we introduce a geometry-based structural design method as an alternative approach for designing low-density structures applicable to material science and mechanical engineering. This method will provide control over internal force-flow, boundary condition, and applied loads. The methodology starts with an introduction to the principles of geometric equilibrium and continues by introducing multiple design techniques to generate truss cellular, polyhedron cellular, and shell cellular (or Shellular) materials by manipulating the geometry of the equilibrium of force. The research concludes by evaluating the mechanical performance of a range of cellular structures designed by this approach.