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

Conference paper (2019)

Authors

Y.-C. Chiang Structural Design & Mechanics - Architecture and the Built Environment
A. Borgart Structural Design & Mechanics - Architecture and the Built Environment
Q. Li Nanjing University
Research Group
Structural Design & Mechanics (Architecture and the Built Environment) (TU Delft)
Copyright: © 2019 Y.-C. Chiang, A. Borgart, Q. Li
Conceptual design Parametric design BIM Associative design Concrete viaducts Knowledge model
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Published Date

2019

Language

English

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Faculty

Architecture and the Built Environment

Department

Architectural Engineering +Technology

Research Group

Structural Design & Mechanics

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.