Collapse load computation of defective pipelines under multi-loading system

Based on the kinematic theorem of limit analysis, a finite element mathematical programming formulation of 3-D rigid-perfectly plastic bodies is presented. The penalty function method is used to deal with the plastic incompressibility. A direct iterative algorithm is employed in solving the above formulation. The numerical procedure has been applied to carry out the limit analysis of pipelines with or without defects on the outside surface under multi-loading system. The effects of ellipsoidal and rectangular part-through slots on the collapse loads of pipelines under multi-loading system are investigated in detail. All the numerical examples are given to illustrate its application