Journal of Elasticity

, Volume 134, Issue 2, pp 193–217

# Intrinsic Formulation and Lagrange Duality for Elastic Cable Networks with Geometrical Nonlinearity

• Yoshihiro Kanno
Article

## Abstract

The intrinsic approach to elasticity is a variational problem that characterizes the static equilibrium state and is formulated only in terms of the unknown strain tensor field. This paper establishes an intrinsic approach to elastic cable networks undergoing large deformations. In this formulation, the potential energy function attains a global minimum at strains in any equilibrium state. It is clearly explained that both the classical displacement formulation and the intrinsic strain formulation can be derived as the Lagrange dual problems of the stress formulation, and that the difference between these two formulations stems from the variety of perturbation functions used to derive the Lagrangian in the Lagrange duality theory.

## Keywords

Duality Lagrangian Legendre–Fenchel transform Second-order cone programming Elasticity Cable network

## Mathematics Subject Classification

90C25 90C46 49N15

## Notes

### Acknowledgement

This work is partially supported by JSPS KAKENHI 17K06633.

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