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Form finding in elastic gridshells.

Changyeob Baek1, Andrew O Sageman-Furnas2, Mohammad K Jawed1

  • 1Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139.

Proceedings of the National Academy of Sciences of the United States of America
|December 20, 2017
PubMed
Summary
This summary is machine-generated.

Elastic gridshells form complex shapes through rod buckling. Their geometry, dictated by inextensibility, aligns with Chebyshev nets, aiding in rational design and understanding complex deformations.

Keywords:
Chebyshev netsbucklingelastic structuresgridshellsmechanical instabilities

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Area of Science:

  • Mechanics of Materials
  • Computational Geometry
  • Structural Engineering

Background:

  • Elastic gridshells are initially planar networks of elastic rods actuated into shell structures via end loading.
  • The final form is determined by elastic buckling under inextensibility constraints, leading to complex, non-intuitive geometries.
  • Understanding and designing these shapes is crucial for novel architectural and engineering applications.

Purpose of the Study:

  • To investigate the rational design of shapes formed by elastic gridshells.
  • To explore the relationship between initial configurations, actuation, and resulting complex geometries.
  • To utilize the theory of smooth Chebyshev nets for inverse design and understanding gridshell behavior.

Main Methods:

  • Precision desktop experiments to observe gridshell formation and geometry.
  • Numerical simulations to capture non-intuitive behavior and explore parameter space for multistable states.
  • Application of smooth Chebyshev net theory for inverse design of hemispherical gridshells.

Main Results:

  • Experiments and simulations revealed complex geometries from simple setups, with simulations showing excellent quantitative agreement.
  • Multistable states were identified through parameter space exploration.
  • Rod inextensibility, rather than elastic response, was found to dictate the fundamental shape, resembling a household strainer.
  • A method to quantify enclosed regions was developed to rationalize nonlocal deformation and form-finding challenges.

Conclusions:

  • The geometry of Chebyshev nets provides a theoretical framework for understanding elastic gridshells.
  • Inextensibility is the primary driver of the zeroth-order shape, simplifying design considerations.
  • The developed methods aid in rationalizing complex deformations and the challenges in form finding.
  • Concatenating gridshell units offers potential for creating larger, more complex structures.