Analytical simulation of nonlinear elastic–plastic average stress–average strain relationships for un-corroded/both-sides randomly corroded steel plates under uniaxial compression

• Derivation of a simplified analytical method for generating the average stress–average strain curves for the plates.
• Taking into consideration of weld-induced initial deflections.
• Applicability to both un-corroded and both-sides corroded plates.

In this paper, an analytical simplified method for derivation of the average stress–average strain relationship of imperfect steel plates taking into account of both geometric and material nonlinearities is presented. The method utilizes the theory of elastic large deflection analysis of plates in the elastic region, and also the theory of rigid-perfectly plastic mechanism analysis of plates in the plastic region. The ultimate strength of the plate is predicted using an empirical formulation. The steel plates may be entirely un-corroded or both-sides randomly corroded. The algorithm can be easily implemented in methods for evaluation of ship hull girder ultimate strength as well as in the estimation of the ultimate capacity of offshore structures.