Open Access

ARTICLE

A High-Fidelity Cable-Analogy Continuum Triangular Element for the Large Strain, Large Deformation, Analysis of Membrane Structures

P.D.Gosling^1,2, L. Zhang²

1 Author for correspondence
2 Newcastle University, School of Civil Engineering & Geosciences. Drummond Building, Newcastle-upon-Tyne, NE1 7RU, UK

Computer Modeling in Engineering & Sciences 2011, 71(3), 203-252. https://doi.org/10.3970/cmes.2011.071.203

Abstract

The analysis of a continuum membrane by means of a discrete network of cables or bars is an efficient and readily tractable approach to the solution of a complex mechanics problem. However, is so doing, compromises are made in the quality of the approximation of the strain field. It is shown in this paper that the original form of the cable-analogy continuum triangle formulation is degraded by an inherent assumption of small strains in the underlying equations, in which the term ßmall" is shown to be "negligibly small". A revised version of this formulation is proposed in which a modification to the basic formulation may be made to reduce the error. However, this approach is shown to have convergence challenges, but provides a "patch" to "fix" existing codes presently used in fabric architecture engineering practice. Based on Green's strain, a new three node triangular element is presented in this paper and provides a rigorous solution to the problem of assumed small strains. The formulation has been developed within the cable-analogy framework, and makes use of the dynamic relaxation solver. It is shown to be accurate, efficient, and capable of dealing with issues such as wrinkling.

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Keywords

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