A new formulation for a three-dimensional thread is presented in this paper, which can be used for equilibrium and vibration analyses of a fabric web or a cable network system under arbitrary large deformation. This formulation is in a very compact form, compared with the existing formulations, but it accounts for the extensibility of the thread, geometry nonlinearity, tension variation along the thread, and other nonlinear effects due to the large deformation of the thread. A major contribution of the current paper is the development of incremental forms of the equilibrium and vibration equations, which can be used for obtaining numerical solutions using, for example, a finite element method, without further simplifications. The incremental form equations have been solved with several numerical examples that demonstrate the effectiveness of the new formulation developed.

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