Numerical Methods For Limit Analysis And Reference Stress Determination Of Structures Under Multi-Loading Systems And Their Engineering Applications

In the present paper, the numerical theories and computational methods for limit analysis and reference stress determination of structures under multi-loading systems are systematically studied and applied to the safety assessment of engineering structures such as pipelines with volume defects. This research project is supported by China National Commission of Science and Technology .A numerical method is developed for the determination of limit load and reference stress of the axisymmetric structures under multi-loading systems. Introducing the concept of reference stress to limit analysis, this paper proposes a direct iterative algorithm without search used to determine the reference stress which depends on the evaluation of limit load. Numerical results show that the proposed method can overcome the difficulties caused by the nonlinearity and nonsmoothness of the objective function and avoid the complicated computations of incremental elastic-plastic analysis. Furthermore, The numerical procedure is applied to determine the limit load and reference stress of axisymmetric pipelines with defects on the outside and inside surfaces under the combined action of internal pressure and axial tension. Some typical failure modes corresponding to different configurations of defects and loading forms are studied in detail.A solution method for radial loading is presented, the mathematical programming formulation is derived for the kinematic limit analysis and reference stress determination of 3-D structures under multi-loading systems, and the corresponding finite element program is made. The penalty-function method is used to deal with the plastic incompressibility condition successfully. By distinguishing the rigid from the plastic zones, and modifying the objective function and the constraint conditions accordingly at each iteration, the numerical difficulties caused by the nonlinearity and nonsmoothness of the objective function are overcome. All the numerical examples show that the proposed radial loading path scheme is reasonable and effective, and the proposed method possesses high efficiency, little computation and good numerical stability for the complicated structures under multi-loading.For the safety assessment of structures under the combined action of initial constant loadings and variable loadings, a numerical method for limit analysis of 3-D structures considering initial constant loadings and proportional loadings is developed. Using the Mises yield condition and the finite element technique, this paper presents an efficient algorithm based on the mathematical programming formulation of the classical kinematic theorem of plasticity theory. The penalty function'method is used to deal with the plastic incompressibility condition. Every step of the iteration is equivalent to solving a relevant elastic problem.A numerical method for the lower bound limit analysis of 3-D structures under multi-loading systems is presented. Based on the static limit theorem of plasticity, a finite element mathematical programming formulation is established by adopting the stress solutions of kinematic limit analysis to construct the equilibrated stress fields. The difficulties caused by the nonlinear yield conditions of static limit analysis are overcome. The dimension obstacle of large scale nolinear programming is avoided by decreasing the numbers of freedom and variable. Some numerical examples are given to demonstrate the applicability of the procedure.The proposed numerical procedures for 3-D structures are applied to determine the limit load and reference stress of defective pipelines under multi-loading systems. The effects of various shapes and sizes of typical part-through slots on the limit load and reference stress of pipelines are investigated and evaluated comprehensively and systematically. Some typical failure modes corresponding to different configurations of slots and loading forms are studied. Numerical results can provide theoretical foundations for the safety assessment of the pressure pipings with slots under multi-loading systems.