RSDM-S: A Method for the Evaluation of the Shakedown Load of Elastoplastic Structures
To estimate the life of a structure, or a component, which are subjected to a cyclic loading history, the structural engineer must be able to provide safety margins. This is only possible by performing a shakedown analysis that belongs to the class of direct methods. Most of the existing numerical procedures addressing a shakedown analysis are based on the two theorems of plasticity and are formulated within the framework of mathematical programming. A different approach is presented herein. It is an iterative procedure and starts by converting the problem of loading margins to an equivalent loading of a prescribed time history. Inside an iteration, the recently published RSDM direct method is used, which assumes the decomposition of the residual stresses into Fourier series and evaluates its coefficients by iterations. It is proved that a descending sequence of loading factors is generated which converges, from above, to the shakedown load factor when only the constant term of the series remains. An elastic-perfectly plastic with a von Mises yield surface is currently assumed. The method may be implemented in any existing FE code and its efficiency is demonstrated by a couple of applications.
KeywordsDirect methods Shakedown analysis RSDM
- 4.Koiter W (1960) General theorems for elastic-plastic solids. In: Sneddon IN, Hill R (eds) North-Holland, AmsterdamGoogle Scholar
- 11.Maier G (1969) Shakedown theory in perfect elastoplasticity with associated and nonassociated flow-laws: a finite element, linear programming approach. Meccanica 4:1–11Google Scholar
- 13.Heitzer M, Staat M (2003) Basis reduction technique for limit and shakedown problems. In: Staat M, Heitzer M (eds) Numerical methods for limit and shakedown analysis. NIC Series, vol 15, pp 1–55Google Scholar
- 24.Gokhfeld DA, Cherniavsky OF (1980) Limit analysis of structures at thermal cycling. Sijthoff & Noordhoff, Alphen aan den RijnGoogle Scholar