Interactive Equilibrium Modelling

This paper presents a novel method for computer-aided equilibrium modelling of structures in early design stages. Based on the force density method, an iterative procedure is developed that enables the generation of spatial kinematic pin-jointed structures that are in equilibrium close to a given input geometry, while satisfying additional constraints on both geometry and forces. This method forms the core of an interactive form-finding process that consists of alternating steps of modelling and computational optimization. In each modelling step, the user is able to modify geometry, topology, external forces and constraints of the structure. In each optimization step, equilibrium is re-established while respecting the user-defined constraints. A prototype has been implemented within an existing CAD software package, and three examples illustrate the use of the presented method, ranging from a playful exploration of surprising shapes to the rationalization of structural geometry. The method allows to intuitively explore the formal freedom of spatial equilibrium shapes with mixed compression and tension forces, within hard, user-defined constraints. In conclusion, it is claimed that by providing interactive equilibrium modelling methods, the design of new, surprising spatial forms with efficient structural behaviour is facilitated.

[1]  Oliver Tessmann.  Collaborative Design Procedures for Architects and Engineers , 2008 .

[2]  H. Schek.  The force density method for form finding and computation of general networks , 1974 .

[3]  Philippe Block,et al.  THRUST NETWORK ANALYSIS : A NEW METHODOLOGY FOR THREE-DIMENSIONAL EQUILIBRIUM , 2007 .

[4]  M. Barnes,et al.  Form Finding and Analysis of Tension Structures by Dynamic Relaxation , 1999 .

[5]  Die Gleichgewichtsberechnung von Seilnetzen unter Zusatzbedingungen , 1974 .

[6]  Axel Kilian,et al.  PARTICLE-SPRING SYSTEMS FOR STRUCTURAL FORM FINDING , 2005 .

[7]  Mark Pauly,et al.  Shape‐Up: Shaping Discrete Geometry with Projections , 2012, Comput. Graph. Forum.

[8]  Roman Kemmler.  Formfindung: Die Interaktion von Kraft und Geometrie , 2012 .

[9]  Johannes Wallner,et al.  Architectural geometry , 2007, Comput. Graph..

[10]  Mohsen Mostafavi.  Structure as Space , 2006 .

[11]  Toni Kotnik,et al.  Curved Bridge Design , 2011 .

[12]  Knut Göppert,et al.  A Spoked Wheel Structure for the World’s largest Convertible Roof – The New Commerzbank Arena in Frankfurt, Germany , 2007 .

[13]  K. Linkwitz,et al.  Einige Bemerkungen zur Berechnung von vorgespannten Seilnetzkonstruktionen , 1971 .

[14]  Philippe Block,et al.  An overview and comparison of structural form finding methods for general networks , 2012 .

[15]  Philippe Block,et al.  Interactive Vault Design , 2012 .

[16]  Jorg Schlaich,et al.  Design and detailing of structural concrete using strut-and-tie models , 1991 .

[17]  Masaaki Miki,et al.  EXTENDED FORCE DENSITY METHOD FOR FORM-FINDING OF TENSION STRUCTURES , 2010 .

[18]  Jaan Kiusalaas,et al.  Numerical methods in engineering with Python , 2005 .

[19]  D. H. Young,et al.  Theory of Structures , 1965 .

[20]  Massimo Laffranchi.  Zur Konzeption gekrümmter Brücken , 1999 .

[21]  Tomohiro Tachi.  Interactive Freeform Design of Tensegrity , 2012, AAG.

[22]  Aurelio Muttoni,et al.  Design of Concrete Structures with Stress Fields , 1996 .

[23]  Lorenz Lachauer,et al.  Interactive Equilibrium Modelling. A new approach to the computer‐ aided exploration of structures in architecture , 2015 .