ABSTRACT
A new approach to the computation of the limit load of plane stress solids is assessed in this chapter. Under limit state conditions, the deformation of solids tends to concentrate on thin failure bands known as slip lines. This makes the finite element analysis a challenging task as a mesh needs to be adapted to capture these bands accurately. Thus an adaptive technique is required to measure the error generated over each finite element. In measuring the error, both an upper and lower bound of the exact solution need to be evaluated. A lower bound is found from a state of stresses abiding boundary conditions. The proposed technique obtains a state of stresses from an upper bound analysis, performed by means of a Lagrangian optimization technique, providing an element piece-wise contribution to the upper bound. These stresses, although not strictly in equilibrium, can be balanced using procedures available in the literature. A lower bound is thus computed by equilibrating inter-element surface fluxes and kinematically solving a series of local problems, using balanced fluxes to set a local loading state in order to quantify the element-wise contribution to the lower bound. An adaptive mesh refinement technique based on the piece-wise contribution to the bracketing error, known as the bound gap, is implemented, providing an adaptive indicator for the refinement process. An evaluation of these techniques for the analysis of plane stress solids and structures is presented.
