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IASS 2016 Tokyo Symposium: Spatial Structures in the 21st Century


IASS Symposium 2016

SESSION: Form Finding & Optimization

Gradient-based optimization of closest-fit funicular structures

< Table of Contents for Form Finding & Optimization
  • Proceedings Name: IASS 2016 Tokyo Symposium: Spatial Structures in the 21st Century
  • ISSN: (Electronic Version) 2518-6582
  • Session: Form Finding & Optimization
  • Pages: 10
  • Title: Gradient-based optimization of closest-fit funicular structures
  • Author(s): Pierre Cuvilliers, Renaud Danhaive, Caitlin Mueller
  • Keywords: form finding, funicular structures, optimization, closest fit, force density method
Abstract
The aim of this research is to solve an inverse form-finding problem: construct funicular, axial-only structures as close as possible to a target surface defined by the designer. The scope is limited to grid-like, node-and-branch only networks, which can be solved efficiently using the force density method (FDM). This problem is formulated as a least-squares nonlinear optimization problem, and is solved using the constrained nonlinear solvers implemented in MATLAB. Two nonlinear constrained solving methods, interior-point and trust-reflective region, are found to be the fastest with a large convergence domain. The first and second-order derivatives of the objective function are found analytically. Lastly, the problem is shown to have several degeneracies; one in particular cannot be removed with physical arguments and leads to new insights in the numerical form finding of funicular surfaces.

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