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.