This portfolio item documents computational structural design methods for computing gridshells and trusses in equilibrium for creative architectural design applications.

This first project investigates computational form-finding methods for grid shell structures. It develops two standalone applications. One explores the Force Density Method (FDM) with a regular grid structure, the second, Dynamic Form-Finding (DFM) with Particle-Spring Systems. Both applications provide a custom interactive user-interface for designers. The applications are written in Java using the Processing API for graphics, geometry and GUI.

The FDM method is a non-dynamic method of computing pre-stressed structures in equilibrium. The GUI of this application, however, provides instant real-time feedback as the user adjusts the load vector(s). Conversely, the second application on the DFM method is a dynamic method of computing structures in equilibrium.

The second project investigates a computational geometric method for generating optimal Mitchell trusses. It uses the Processing API for graphics, geometry, and GUI. The implementation builds on a geometric solution for computing optimal trusses in their basic symmetric form. Specifically, the forces are at two fixed points along the same vertical line and a point load in between the supports at a fixed distance.

The application provides a parametric framework for generating a design space of Mitchell trusses. According to the parameters, a designer can calculate 21 trusses in total. The parameters are: h, the distance between the supports, L the distance between the supports and the load at the tip of the structure, and n the number of linear members.

The following publication describes the FDM method I use here. My implementation solves solves a grid made with 36 nodes, 25 faces, and from its Euler characteristic, 60 edges.

K. Linkwitz. (2014). “Force Density Method: Design of a Timber shell.” Ch.6 in S. Adriaenssens, P. Block, D. Veenendaal, & C. Williams. Shell Structures for Architecture: Form Finding and Optimization.

For a description of how changes in network topology lead to diverse designs for shell structures, see A. Killian. (2014). “Steering of Form.” Ibid.

The following paper describes the underlying geometric process for computing optimal Mitchell trusses.

A. Mazurek, W.F. Baker, C. Tort. (2011). “Geometrical aspects of optimum truss like structures.” Structural and Multidisciplinary Optimization 43.

I developed these applications in Spring 2015 during the first offering of 4.s48 Computational Structural Design and Optimization. The class is taught by Prof. Caitlin Mueller at the MIT Department of Architecture.

For implementation details, please read the PDF writeup for the form-finding gridshells available on the Github repository of this project and for the optimal Mitchell trusses in this Github repository .