SHAKEDOWN ANALYSIS BY BEM

Abstract

In the ambit of the symmetric Galerkin boundary element formulation the statical shakedown load multiplier and the limit analysis are reformulated making use of macrozone modelling. The subdivision of the domain into macroelements makes it possible to deal with piecewise homogeneous materials of the body. For each macroelement a discretization of the boundary and a subdivision of the domain into portions called cells are performed in order to introduce the unknowns (i.e. traction and displacement discontinuities) on the boundary and material plastic laws appropriately interpolated. The weighed regularity imposed between adjacent macroelements produces algebraic operators which are symmetric and sign-definite, thus preserving the meaningful properties of the continuum. The load multiplier computed by this strategy is only an approximation to the actual value due to the modelling of the boundary unknown functions and to the yield conditions of the material. The plastic collapse load multiplier is dealt with as a special case of shakedown in which a proportional load is applied in the body.