Discretised Airy stress functions and body forces

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This paper extends polyhedral Airy stress functions to incorporate body forces. Stresses of an equilibrium state of a 2D structure can be represented by the sec- ond derivatives of a smooth Airy stress function and the integrals of body forces. In the absence of body forces, a smooth Airy stress function can be discretised into a polyhedron as the corresponding structure is discretised into a truss. The differ- ence in slope across a creases represents the axial force on the bar, while the zero curvatures of the planar faces represent zero stresses voids of the structure. When body forces are present, the zero-stress condition requires the discretised Airy stress function to curve with the integrals of these body forces. Meanwhile, the isotropic angles on the creases still indicate concentrated axial forces. This paper discretises the integrals of body forces into step-wise functions, and discretises the Airy stress function into quadric faces connected by curved creases. The proposed method could provide structural designers (e.g. architects, structural engineers) with a more intuitive way to perceive stress fields.
Original languageEnglish
Title of host publicationAdvances in Architectural Geometry 2020
EditorsOliveir Baverel, Cyril Douthe, Romain Mesnil, Caitlin Mueller, Helmut Pottmann, Tomohiro Tachi
PublisherPresses des Ponts
Number of pages22
ISBN (Print)987-2-85978-540-6
Publication statusPublished - 2021
EventAdvances in Architectural Geometry 2020: 7th AAG Conference (Virtual) -
Duration: 28 Apr 202129 Apr 2021


ConferenceAdvances in Architectural Geometry 2020


  • Architectural geometry
  • Reciprocal force polygons
  • Isotropic geometry
  • Static equilibrium


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