A posteriori error estimator and adaptive procedures for computation of shakedown and limit loads on pressure vessels

Adaptive finite element procedures are presented for the computation of upper bounds estimates of limit and shakedown loads for pressure vessels. The method consists of an h-type adaptive mesh refinement strategy based upon an a-posteriori error estimator measured by the energy norm. The problem is formulated in a kinematic approach using Koiter's shakedown theorem. A constitutive model, for elastic-perfectly plastic materials, relates the plastic strains increments and curvatures to plastic multipliers through the flow law associated with a shell piecewise-linear yield surface (hexagonal prism). A consistent relationship between nodal displacements and nodal plastic multipliers is enforced by minimizing the strain residual between the total strain and the plastic strain increments, which is measured with respect to the energy norm. Discretization of the shell into finite elements allows the reduction of the problem to a minimization problem which is solved by linear programming.