Structural Surfaces

It is a common misbelief that curvature automatically lends structural capacities to any surface. While geometry and structural properties are indeed closely related, the precise interdependency escapes simple formulas; it is rather complex. This seminar provides an introduction to structural surfaces through a series of lectures, physical and computational modeling workshops, and design explorations. We generally look at geometry first, then address how different shapes generate structural action, and finally investigate applications in architecture, product design, and related fields. The basis for understanding structural surfaces is to understand surface geometry. The course begins with an introduction to shapes derived from conic sections, and covers basic issues common to typical convex and concave surfaces, including ruled and developable surfaces. Central here is the topic of curvature, as well as the related topic of geodesics and the notion of parametric representations. The discussion then moves toward more complex mathematical surfaces, with an emphasis on minimal surfaces. These shapes occur in nature, and they can be derived from physical experiments. They can also be modeled mathematically. We will employ both physical as well as computational models in the exploration of minimal surfaces. Applications for mechanically and pneumatically pre-stressed fabric structures will be discussed in some detail. Reference to other mathematical surfaces will also be made, even though their structural properties are far from clear. These shapes include complex, one-sided surfaces such as the Klein Bottle or the Mvbius Strip.Equilibrium shapes are the third and last topic of the course. The seminar will introduce students to a variety of physical and computational form-finding techniques and to the analysis of these complex shapes. Case studies will highlight the formidable construction challenges of equilibrium shapes in architectural applications, and discuss the impact of computer-aided manufacturing techniques on their making.The format of the course includes lectures and workshops, research assignments, and design exercises. Software tutorials and computer labs, as well as physical form-finding workshops, are integral parts of the course. Students will be introduced to the use of the GSD\'s digitizing equipment in the CAD/CAM lab. The qualitative understanding of structural behavior will be complemented by an introduction to common computational analysis techniques, including the use of finite-element analysis during conceptual design. A general familiarity with basic 3D modeling techniques is expected. No prior knowledge of the digital design environments employed in the course is necessary, but a readiness for immersion into unfamiliar computational environments is expected. The course introduces and employs a variety of software environments, including Maya, SolidWorks, and Cosmos Works, as well as Mathematica. Rather than attempting to completely master each environment, we will limit ourselves to very specific aspects, frequently translating data between environments in order to accomplish our goals. Course prerequisites are the GSD\'s core technology sequence including 6201 and 6202 or equivalent. The seminar can accept up to 12 students.The first class meeting is on Friday, September 24, in room 510