On Work-Hardening Adaptation of Discrete Structures Subjected to Dynamic Forces in the Presence of Second-Order Geometric Effects*

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Abstract
The present paper deals with work-hardening adaptation of discrete rigid-plastic structures subjected to loadings which vary within a given domain according to an unknown history, with inertia forces, viscous forces, and second-order geometric effects also being included. Considering structural elements characterized by a piecewise linear yield surface, a piecewise linear work-hardening law, and a linear strain-rate sensitivity law, we give an adaptation criterion of “statical” type as well as a method of providing a priori bounds to deformation parameters such as displacement, plastic strain, and plastic strain intensity. These bounds can be rendered most stringent by solving a minimization problem of mathematical programming on an equivalent boundary value problem of finite plasticity. A simple application concludes the paper.