Adaptive F.E. method for the shakedown and limit analysis of pressure vessels

Upper bound estimates of limit and shakedown loads for pressure vessels are calculated by using the technique described in this paper. These have been achieved by applying Koiterʹs theorem and by discretizing the shell into finite elements. The flow law associated with an hexagonal prism yield surface, relates the plastic strain increments and curvatures to plastic multipliers. A suitable matrix also relates such a plastic strain field to a displacement field through a classical relation. A novel method enforces a consistent relationship between nodal displacements and nodal plastic multipliers by minimizing the residual between the two independent descriptions of the plastic increments, measured with respect to the energy norm. The discretized problem is then reduced to a minimization problem and solved by linear programming. An a posteriori error indicator in the energy norm is derived with and adaptive mesh refinement scheme.