Direct and dual theorems of Castigliano and Clapeyron for generalized elastic models

The structural problem is cast within the framework of the structural models with convex constraints. Resorting to the convex optimization theory, the generalized form of the two theorems of Castigliano-Cotterill is recovered and unified in a unique theorem. Conjugate relations between convex and saddle funtionals provide the tools to derive the dual form of the theorem. Afterwards, two generalized clapeyron's theorems and their dual forms are shown. These theorems are thus specialized to some common non-linear structural models.