On direct methods for shakedown and limit analysis

Direct methods apt to evaluate the load-carrying capacity of structural systems are those analysis procedures which provide essential information without following step-by-step inelastic structural responses to an assigned loading history. Direct methods of concern herein are only those intended for limit and shakedown analysis. The recent and present research trends, and some aspects of earlier results, are concisely surveyed in order to provide a broad unifying conspectus of the field, together with an up-to-date, though incomplete, bibliography. Subsequently, some aspects of two recent developments (subjects of the writers’ current research) are briefly presented with illustrative examples: a kinematic method applied to the homogenization of periodic ductile composite materials; a shakedown theory and bounds on post-shakedown quantities in poroplasticity of fully saturated media.