Thrust Network Analysis: Exploring Three-dimensional Equilibrium

Block P.
Department of Architecture, Massachusetts Institute of Technology
Cambridge, MA, USA

This dissertation presents Thrust Network Analysis, a new methodology for generating compression-only vaulted surfaces and networks. The method finds possible funicular solutions under gravitational loading within a de fined envelope. Using projective geometry, duality theory and linear optimization, it provides a graphical and intuitive method, adopting the same advantages of techniques such as graphic statics, but o ffering a viable extension to fully three-dimensional problems. The proposed method is applicable for the analysis of vaulted historical structures, speci cally in unreinforced masonry, as well as the design of new vaulted structures. This dissertation introduces the method and shows examples of applications in both fields.


    author      = "Block, P.",
    title       = "Thrust Network Analysis: Exploring Three-dimensional Equilibrium",
    institution = "Massachusetts Institute of Technology",
    year        = "2009",
    address     = "Cambridge, MA, USA",
    month       = "May",
    doi         = "",
    note        = "PhD dissertation",

Related publications

Block P. and Ochsendorf J.Thrust Network Analysis: A new methodology for three-dimensional equilibrium,Journal of the International Association for Shell and Spatial Structures,48(3): 167-173,2007 (December).
Block P., Lachauer L. and Rippmann M.Thrust Network Analysis - Design of a cut-stone masonry vault,Shell Structures for Architecture: Form Finding and Optimization,Adriaenssens, S., Block, P., Veenendaal, D. and Williams, C. (editors),Routledge,London,2014.
Rippmann M., Lachauer L. and Block P.RhinoVAULT - Interactive Vault Design,International Journal of Space Structures,27(4): 219-230,2012 (December).
Rippmann M.Funicular Shell Design: Geometric Approaches to Form Finding and Fabrication of Discrete Funicular Structures,ETH Zurich, Department of ArchitectureZurich,2016 (February).
Block P. and Lachauer L.Three-dimensional Funicular Analysis of Masonry Vaults,Mechanics Research Communications,56: 53-60,2014.
Block P. and Lachauer L.Three-dimensional Equilibrium Analysis of Gothic Masonry Vaults,International Journal of Architectural Heritage,8(3): 312--335,2014.
Van Mele T., Panozzo D., Sorkine-Hornung O. and Block P.Best-fit Thrust Network Analysis - Rationalization of freeform meshes,Shell Structures for Architecture: Form Finding and Optimization,Adriaenssens, S., Block, P., Veenendaal, D. and Williams, C. (editors),Routledge,London,2014.
Panozzo D., Block P. and Sorkine-Hornung O.Designing Unreinforced Masonry Models,ACM Transactions on Graphics - SIGGRAPH 2013,32(4): 91:1-91:12,2013 (July).
Bhooshan V., Reeves D., Bhooshan S. and Block P.MayaVault - A Mesh Modelling Environment For Discrete Funicular Structures,Nexus Network Journal,20(3): 567–582,2018 (December).
Van Mele T. and Block P.A Novel Form Finding Method for Fabric Formwork for Concrete Shells,Proceedings of the International Association for Shell and Spatial Structures Symposium 2010,Shanghai, China,2010 (November).
Van Mele T. and Block P.Algebraic Graph Statics,Computer-Aided Design,53: 104-116,2014.
Liew A., Pagonakis D., Van Mele T. and Block P.Load-path optimisation of funicular networks,Meccanica,53(1): 279-294,2018.
Liew A., Maia Avelino R., Moosavi V., Van Mele T. and Block P.Optimising the load path of compression-only thrust networks through independent sets,Structural and Multidisciplinary Optimization,60: 231-244,2019.
Miki M., Igarashi T. and Block P.Parametric self-supporting surfaces via direct computation of airy stress functions,ACM Transactions on Graphics - SIGGRAPH 2015,34(4): 89:1-11,2015.


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