Stationary and extremum variational formulations for the elastostatics of cable networks (Q1072747)

The static analysis of elastic cable networks submitted to generic, conservative loads and prescribed dislocations is considered in this paper. The cables are assumed as stress-unilateral (only tensile stresses are admitted), and represented according to a Lagrangian standpoint, under the customary large displacements hypothesis. A variational formulation of the problem is given, as the stationary of a saddle functional with respect to displacements and (sign-constrained) tractions. Uniqueness properties for the solution are derived from this statement, together with two complementary (constrained) minimum formulations, which correspond to the well-known extremum principles of the total potential energy and the complementary energy. The case of a network loaded only at the nodes is exposed as a specialization.