Structural Optimization Using Catenary and Other Natural Shapes

Authors: Mitchell Gohnert

Abstract:

This paper reviews some fundamental concepts of structural optimization, which is focused on the shape of the structure. Bending stresses produce high peak stresses at each face of the member, and therefore, substantially more material is required to resist bending. The shape of the structure has a profound effect on stress levels. Stress may be reduced dramatically by simply changing the shape to accommodate natural stress flow. The main objective of structural optimization is to direct the thrust line along the axis of the member. Optimal shapes include the catenary arch or dome, triangular shapes, and columns. If the natural flow of stress matches the shape of the structures, the most optimal shape is determined. Structures, however, must resist multiple load patterns. An optimal shape is still possible by ensuring that the thrust lines fall within the middle third of the member.

Keywords: optimization, natural structures, shells, catenary, domes, arches