Exploring form and force through topology and stiffness: Tools for early sketching processes in architectural education

Paper i proceeding, 2026

The principle “Form follows function”, famously articulated by architect Louis Sullivan, posits that a structure’s form should emerge naturally from the flow of forces imposed by loads and environmental constraints, rather than conforming to a preconceived aesthetic shape. From a structural mechanics perspective, this concept can be reframed as “Force follows stiffness”, which encompasses all the factors that create structural stiffness, from a sound topology to the various variables of stiffness: geometry, material properties, boundary conditions, and the dependence on mechanical phenomena such as tension, compression, bending, and prestressing. Effective structural design rests on three interrelated fundamentals: the hierarchy of external loads, the topology of structural elements, and the stiffness of statically indeterminate systems. These principles have guided the development of computational tools for architectural education, realized through collaborative research between Chalmers University of Technology and Lund University. The theoretical underpinning of these tools draws directly on the concept of stress trajectories, initially introduced by J. C. Maxwell and elaborated by Karl Coleman. Stress trajectories show the natural pathways through which internal forces propagate within a structure, offering a visual and analytical framework for understanding load transfer. This concept is operationalized in the computer tool ForcePAD, allowing users to sketch lines and surfaces, where shading intensity encodes stiffness. With real-time feedback, force flow and deformation are illustrated, thereby translating classical structural theory into an interactive design medium. While ForcePad paints a continuum of stiffness, the pointSkech and ObjectiveFrame tools do the opposite. By sketching a topology of discrete points, the user is allowed to manipulate and investigate how topology and stiffness affect force distribution. The article discusses the pedagogical concepts behind the computer programs and demonstrates their use as primary tools for teaching structural design within the Chalmers architecture program. All three tools are freely available for educational purposes.