The concepts of limit load and reference stress have been widely used in structural engineering design and component integrity assessment, especially considering multi-loading systems. The limit analysis of structures and the reference stress method (RSM) have been proven to be successful in problems pertaining to two-criteria failure assessment, creep growth, rupture damage, and more recently, elastic-plastic fracture toughness. However, the determination of limitload and reference stress of 3-D structures under multi-loading systems is not a simple task. In the present paper, a solution method for radial loading is presented, the mathematical programming formulation is derived for the upper bound limit analysis of 3-D structures under multi-loading systems, and moreover, a direct iterative algorithm used to determine the reference stress is proposed which depends on the evaluation of limitload. The penalty function method is used to deal with the plastic incompressibility condition. All the numerical examples show that the proposed radial loading path scheme is reasonable and effective. The mathematical programming method without search used here can overcome the difficulties caused by the nonlinearity and nonsmoothness of the objective function and avoid the complicated computations of incremental elastic-plastic analysis.
- limit analysis
- reference stress
- mathematical programming
- loading path
Chen, H., Liu, Y. H., Cen, Z. Z., & Xu, B. Y. (1999). On the solution of limit load and reference stress of 3-D structures under multi-loading systems. Engineering Structures, 21(6), 530-537. https://doi.org/10.1016/S0141-0296(98)00001-7