Hybrid‐stress models for elastic–plastic analysis by the initial‐stress approach

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Abstract
Two alternative numerical methods are presented, based on the assumed‐stress hybrid finite element model and the initial‐stress approach, for the elastic–plastic small‐deflection analysis of structures under static loading. The use of the initial‐stress approach results in a set of simultaneous linear algebraic incremental equations to be solved at each loading step, with the elastic stiffness matrix remaining unchanged throughout the loading process and the effects of plasticity included as equivalent element loads. The derivation of these alternative methods differs in the assigning of the incremental stress which satisfies equilibrium; in one case it is the actual stress increment while in the other it is a fictitious stress increment. An equilibrium imbalance correction is included in each of these methods to prevent drifting of the solution during the incremental process. Example solutions are presented which demonstrate the accuracy of the two methods and permit comparisons of the relative efficiencies of the two methods.