Patterns of Optimal Structural Layouts

Abstract

Flexural systems are ubiquitous in structural design and constitute a significant portion of the structural material in many infrastructural constructions. The study of optimization of flexural systems is of great interest to structural designers and architects seeking to reduce embodied carbon. A significant reduction of material of a given flexural system may be achieved by optimal layout of flexural elements in a twodimensional space. Analytical solutions for optimal structural layouts of plates and beam systems comprised of one-dimensional elements were derived by Rozvany et al. in the 1970s. This thesis explores optimal structural layouts in the context of conventional and other nonconventional beam layouts (e.g. derived from principal stresses) and proposes interpretations of patterns. A variety of beam layouts for a variety of boundary and support conditions are compared for optimality, including square domains with both clamped and simple corner supports, and other regular polygonal domains (triangular, hexagonal) with clamped point supports. A method for constructing optimal beam layouts for regular polygonal column grids using transformations of the Delaunay mesh and Voronoi diagram is presented, and certain Euclidean tilings are presented as optimal beam layouts.