The Limit Load Of The Cracked Structure Analysis Method

This paper makes the attempt to introduce the plastic limit analysis to the determination of the load carrying capacity of structures with defaults or/and cracks. Common formulae for the determination of the lower and upper bounds of limit load are derived, then a successive iterative algorithm, based on the optimization and finite element method, to calculate the bounds is proposed, which could be applied to general structures. Numerical solutions for some plate problems with typical cracks are presented.Firstly, based on the classical theorem of limit analysis, the von Mises yielding condition and finite element method technique, two common mathematical programs for the determination of the lower and upper bounds are built and solved by an iteration algorithm directly. In this arithmetic, the objective function is modified gradually by distinguishing the rigid zone and plastic zone before carry through more calculation, in order to obtain the optimal solution of the programs. The convergence of the algorithm is also shown in this paper. Then, the finite element method procedure of the determination of the load carrying capacity of 2D structures with defaults or/and cracks, considering the instable state of cracks, is given and is implemented by C++ language. At last, some numerical examples are presented to show the application of the procedures.