Bi-directional algebraic graphic statics. (December 2017)

• Record Type: Journal Article
• Authors: Alic, Vedad; Åkesson, Daniel
• Is Part Of: Computer aided design. Volume 93(2017)
• Page Start: 26
• Page End: 37
• Publication Date: 2017-12
• Subjects: Interactive graphic statics -- Matrix analysis of structures -- Graph theory -- Reciprocal figures -- Force diagram manipulations -- Conceptual design; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2017.08.003
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: A pre-existing algebraic graphic statics method is extended to allow for interactive manipulations of the force diagram, from which an updated form diagram is determined. Newton's method is used to solve a set of non-linear equations, and the required Jacobian matrix is derived. Additional geometric constraints on the form diagram are introduced, and methods for improving the robustness of the method are presented. We discuss the implementation of the method as a back-end to an interactive application, and demonstrate the usability of the method in several examples where the qualities of directly manipulating the force diagram are emphasized. Highlights: General non-procedural approach to graphical analysis of two-dimensional structures. Enables interactive manipulations of the force diagram. Presents derivation of the required Jacobian matrix. Shows that the null space of the Jacobian matrix contains alternative solutions. Presents how to use as a back-end for interactive graphic statics applications.