Limit analysis of cracked structures by mathematical programming and finite element technique

Limit analysis of cracked structures using mathematical programming and finite element method is presented. This direct algorithm is based on a proposition of the modified Markov variational principle. The obtained upper bound formula is applicable with any kinematic admissible finite elements. The regularization of plastic dissipation function is performed to overcome the indetermination of the objective gradient in the rigid region and to realize a smooth transition of the objective function between the plastified and non-plastified regions. In order to simulate the singularity of crack-tip strain field for an ideal plastic model, the separate-point degenerated finite elements are used around the crack tips. This improves the precision of limit solutions. Numerical results of plane and axisymmetric cracked structures are extensively compared with analytic ones. The application of limit analysis in fracture mechanics is illustrated by an example.