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Shakedown and collapse of elastic-plastic structures under variable and cyclic loads

The paper presents an introduction to the results obtained mainly by the author in shakedown analysis of elastic plastic structures, with the shakedown theorems for elastic plastic kinematic hardening materials playing the central role. Some illustrative examples of application are given. | Vietnam Journal of Mechanics, VAST, Vol. 30, No. 4 (2008), pp. 233 – 240 Special Issue of the 30th Anniversary SHAKEDOWN AND COLLAPSE OF ELASTIC-PLASTIC STRUCTURES UNDER VARIABLE AND CYCLIC LOADS Pham Duc Chinh Institute of Mechanics, 264 Doi Can, Hanoi Abstract. The paper presents an introduction to the results obtained mainly by the author in shakedown analysis of elastic plastic structures, with the shakedown theorems for elastic plastic kinematic hardening materials playing the central role. Some illustrative examples of application are given. 1. INTRODUCTION Plastic collapse, along with Euler elastic instability of geometrically-thin structural members and Griffiths critical crack fracture of brittle-like solids, are among the outstanding phenomena limiting the load-bearing capacity of structures. Attainment of the ultimate yield state at a point within a structure does not imply plastic collapse but that at entire sections to make the structure a mechanism, which could not sustain the larger loads, does. Plastic instantaneous collapse of structures is determined by the static and kinematic theorems of plastic limit analysis. A structure subjected to loads varying arbitrarily within certain limits may fails even at lower load limits than those set by the instantaneous collapse criterion because the plastic deformations would accumulate unrestrictively or be bounded but vary cyclically and unceasingly. Otherwise, the total plastic dissipation in the structure would be bounded, hence its overall response to the external agencies should shake down to some purely elastic state due to a finite residual stress field developed inside the structure. Classical shakedown theory for elastic-perfectly plastic bodies has been well established in the literature. As for the plastic limit theory, the essential contents of the classical shakedown theory are its dual static and kinematic theorems, which are path-independent (loading-history-independent): both theorems .