Limit state solutions, based upon linear elastic solutions with a spatially varying elastic modulus Original Research Article

The paper describes an iterative method of determining the limit state of a perfectly plastic body for the Von Mises yield condition. A sequence of incompressible linear elastic solutions are defined with a spatially varying shear modulus which provide a sequence of upper bounds to the limit load which monotonically reduce and converge to the limit state solution. For a discretized solution generated by a Rayleigh Ritz method, the sequence converges to the least upper bound associated with the class of displacement fields. An example of a finite element implementation method is given and applied to the limit state of a cracked body. A method for accelerated convergence is described for problems where the plastic region forms a small proportion of the total volume of the body.