Extremum theorems for large displacement analysis of discrete elastoplastic structures with piecewise linear yield surfaces

Discrete or discretized structures are considered in the range of large displacements. Elastic plastic behavior is assumed, under the hypothesis that both yield functions and hardening rules are piecewise linear. The structural response to a single finite loading step is assumed to involve regularly progressive yielding (no local unloading). An extremum property of this structural response is established, by recognizing that the relations governing the configuration change coincide with the Kuhn-Tucker conditions of a particular nonlinear constrained optimization problem, subject to sign constraints alone. This extremum property can be regarded as an extension of the theorem of minimum potential energy. Other properties, even if computationally less attractive, broaden the theory developed, so that some results previously obtained are derived as special cases.