DYNAMIC SHAKEDOWN ANALYSIS AND BOUNDS FOR ELASTOPLASTIC STRUCTURES WITH NONASSOCIATIVE, INTERNAL VARIABLE CONSTITUTIVE LAWS

摘要

Reference is made to discrete (finite element) structural models formulated in terms of generalized variables. The constitutive laws adopted are elastic-plastic, nonlinear-hardening with internal variables and generally nonassociative. The notion of reduced domain is employed as a generalization of a similar concept introduced in earlier developments of shakedown theory. On this basis, a unified theory is presented, which encompasses: necessary and, separately, sufficient conditions for shakedown by a static approach as a further generalization of classical Melan's theorem; bounds on various post-shakedown quantities; sufficient and necessary shakedown criteria by a kinematic approach as a further extension of Neal-Symonds-Koiter theorem. By suitable specializations and relaxations of the achievable results, the criteria and bounding inequalities established here are formulated as mathematical programming problems in view of numerical applications. [References: 77]