This paper presents revised and extended version of theory proposed in the late 1970-ties by A. ˇCyras and his co-workers. This theory, based upon the notion of duality in mathematical programming, allows us to generate variational principles and to investigate existence and uniqueness of solutions for the broad class of problems of elasticity and plasticity. The paper covers analysis of solids made of linear elastic, elastic-strain hardening, elastic-perfectly plastic and rigid-perfectly plastic material. The novelty with respect to ˇCyras’s theory lies in taking into account loads dispersed over the volume and displacements enforced on the part of surface. A new interpretation of optimum load for a rigid-perfectly plastic body is also given.
The second part of the paper presents ﬁnite-dimensional models of linear elastic, elastic-strain hardening, elastic-perfectly plastic and rigid-perfectly plastic structures. These models can be seen as a result of discretisation procedure applied to the models of solids derived in the Part I. The implications of sub-dividing degrees of freedom into those with prescribed external forces and those with given displacements are discussed. It is pointed out that the dual energy principles given in this part of the paper can serve as a direct basis for numerical computations.