Structural optimization using graphic statics

This paper presents a method for structural optimization of discrete trusses using Graphic Statics. As opposed to traditional structural optimization techniques, which are typically conducted by manipulating the geometry of the structure (the form diagram), the approach presented in this paper establishes a Graphic Statics solution to the problem, where structural optimization is conducted using design variables in the force domain (force diagram). The proposed approach presents several attractive features compared to traditional approaches. Since it is based on reciprocal graphical relationships between form geometry and forces, member stiffnesses need not be calculated. Additionally, by working on the force diagram, equilibrium of the solution is guaranteed, and no additional methods are required to enforce this condition; for example, there is no need to triangulate the structure or to add small area members. Furthermore, because only solutions that are in equilibrium are permitted, the number of design variables can be reduced. Also, subject to certain relationships, the location of the loads (or reactions) do not need to be set a priori. Through examples, it is shown that the proposed methodology can readily accommodate different tensile and compressive stresses for volume optimization problems and that, through the use of Graphic Statics, other restrictions or constraints on the member forces can easily be incorporated. J. Carrion · A. Beghini · A. Mazurek · W. F. Baker ( ) Skidmore, Owings & Merrill, LLP, 224 S. Michigan Avenue, Chicago, IL 60604, USA e-mail: [email protected] L. L. Beghini Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 N. Matthews Ave., Urbana, IL 61801, USA