Finding Membrane Shells Subjected to Horizontal Body Forces with Radial Basis Functions

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Abstract

Membrane shells, which have minimized bending moments under certain load conditions, are regarded as ideal structural forms in terms of material efficiency. Most of the existing numerical form-finding methods are based on discretizing membranes into finite panels or funicular networks and focusing on gravitational loading only. In order to obtain smooth shells and to consider horizontal loads, this paper presents a method to find the equilibrium forms of the membrane shells by solving Pucher’s equation. Radial base functions (RBFs) is utilized to represent stresses and shapes of the membranes, and a least square method is applied to find the controlling coefficients which allow the functions to fit the boundary conditions (e.g. zero stresses at the free edges) and the governing equation. When all the parameters are carefully chosen, the stress and shape functions can achieve sufficient accuracy. The presented method has been preliminarily implemented to find shells on a triangle ground plan incorporating horizontal loads. The form-found geometries are then analyzed by finite element models. The result confirms that the form-found shells have the stress distributions similar to the prescribed stresses.
Original languageEnglish
Title of host publicationProceedings of the IASS Annual Symposium 2019 – Structural Membranes 2019
Subtitle of host publicationForm and Force
EditorsCarlos Lázaro, Kai-Uwe Bletzinger, Eugenio Oñate
PublisherCIMNE
Pages1556-1563
Number of pages8
ISBN (Print)978-84-121101-0-4
Publication statusPublished - 2019
EventFORM and FORCE 2019: 60th Anniversary Symposium of the International Association for Shell and Spatial Structures (IASS SYMPOSIUM 2019) and 9th International Conference on Textile Composites and Inflatable Structures (Structural Membranes 2019) - Barcelona, Spain
Duration: 7 Oct 201910 Oct 2019
http://congress.cimne.com/formandforce2019/frontal/default.asp

Conference

ConferenceFORM and FORCE 2019: 60th Anniversary Symposium of the International Association for Shell and Spatial Structures (IASS SYMPOSIUM 2019) and 9th International Conference on Textile Composites and Inflatable Structures (Structural Membranes 2019)
CountrySpain
CityBarcelona
Period7/10/1910/10/19
Internet address

Keywords

  • concrete viaducts
  • conceptual design
  • parametric design
  • associative design
  • knowledge model
  • BIM

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