Application of Limit Analysis to the Determination of Load-Carrying Capacity of Structures with Cracks

This paper introduces the plastic limit analysis to the determination of the load carrying capacity of structures with cracks. Firstly, based on the classical theorem of limit analysis, the Von Mises yielding condition and finite element method, two common mathematical programming problems for the determination of the lower and upper bounds are built and solved by an iteration scheme without search directly. Then the finite element method procedure, in which the instable state of cracks under the condition of the KC criterion is combined, for the determination of the limit load of 2D structures with crack is given. Finally, some numerical examples and valuable conclusions are presented to show the application of the procedures and the importance of plastic limit analysis in the determination of the load carrying capacity of structures with crack.