Determination of ultimate load and possible failure path for solid

In this study, an effective and practical, h-version, enrichment mesh generation, and finite element adaptive procedure for the non-linear solution of problems in continuous media is presented. Moreover, based on the gradient recovery rule, a general recovery technique is developed to measure error and refine mesh in general finite element solutions. The recovery technique is simple and cost effective to implement. The technique has been formulated for two dimensional problems by employing triangular elements. The formulation is consistent with non-linear formulations which iteratively equilibrate the continuous media problems. In the present study, in addition to correlating various norms (such as energy norm, L2 norm for stress and L2 norm for strain), a new norm, namely, deviating stresses norm (called J norm in this study), is also correlated by the authors to estimate the error rate in the finite element method. Based on the results of this study, the J norm can be used as a tool to estimate the error rate in the finite element method, and to determine the ultimate load and the possible failure path in continuous domains. For several numerical examples, the developed algorithms are demonstrated and the resulting meshes are presented