This research addresses the limitations of optimization algorithms in producing reasonable strut-and-tie configurations. For example, in the case of topology optimization, translation of the material distribution layout to a workable truss geometry is not trivial and may require iterations. On the other hand, the method of graphic statics proved to be helpful in the generation of in-equilibrium truss patterns including a visual representation of force magnitudes or constant stresses in truss elements. This study will also highlight the potentials of using the algebraic formulation of graphic statics to create a range of appropriate truss models and examines the reciprocal characteristics of the form and force diagrams for the visualization of their corresponding stress fields. This research has established computational procedures to utilize algebraic graphic statics and layout optimization methods independently or cooperatively to create suitable truss models and stress fields for two-dimensional cases. The computational routines for three-dimensional problems are the work in progress and the challenges of the effort will be addressed.

The multi-material 3D printed truss was created by Teng Teng and Yefan Zhi in 2023.