Flow-Informed Design of Topologies

Demi Fang
MIT/PhD 2023
1 TopEval can be applied to truss design (top) or floor system design (bottom).

One strategy for efficient structural design is to place material where it is most needed. Often, this structural demand can be visualized using a vector field across a continuum domain. For example, in the case of a beam under vertical point loads, the vector field of principal stress lines may inform a truss design across the same continuum domain (Allen and Zalewski 2010). Alternatively, in the case of a floor system under uniformly distributed load, the vector field of principal bending moment may inform a topology of floor ribs (Gatti Wool Factory, 1953, by Pier Luigi Nervi).

Both instances demonstrate the value of a metric that summarizes a topology’s conformity with a given stress field in early-stage structural design. While structural topologies might conventionally be evaluated using structural analysis, this approach is a geometric one. TopEval is a Grasshopper component that calculates a topology’s conformity to a vector field, enabling live feedback during design. With TopEval and an effective visualization workflow, designers can both compare and improve structural topologies during early-stage design without the need for iterative structural analysis.

Project video
2 These visualizations color-code the underlying vector field with each point’s respective conformity value.
3 Given a topology and vector field, TopEval outputs conformity values as a list. Visualization is up to the designer.