Numerical Limit Analysis of Pressure Pipings with Local Wall-Thinnings

摘要

Limit analysis of structures is a practically useful branch of plasticity, which can determine the load-carrying capacities of structures and provide the theoretical foundations for structural designs and integrity assessments. In this paper, a numerical procedure is developed for plastic limit analysis of 3-D elastic-perfectly plastic bodies under complex loads. The method is based on the lower-bound limit theorem and von Mises yield criterion so that the lower-bound limit analysis can be conducted by solving a nonlinear mathematical programming problem. A SQP algorithm and a dimension reduction-based technique are used to solve the discretized finite element optimization formulation. A conception of active constraint set is introduced, so that the number of constraints can be reduced greatly. The basis vectors of reduced residual stress spaces are constructed by performing an equilibrium iteration procedure of elasto-plastic finite element analysis.The numerical procedure is applied to carry out the plastic limit analysis of pressure pipings with local wall-thinnings under internal pressure, bending moment and axial force. Local wall-thinning caused by corrosion, erosion, mechanical damage or by grinding to eliminate surface cracks is a common volumetric defect on the surfaces of pipings. It may reduce the load-carrying capacities and even lead to severe failure accidents of pipings. 3-D finite element models of local wall-thinned pipings are established and used here for limit analysis. Based on a large number of calculated examples, the effects of different shapes and sizes of small area, axial, circumferential, and large area local wall-thinnings on plastic limit loads and failure modes of pressure pipings under the combined loads of internal pressure, bending moment and axial force are investigated and analyzed. The plastic limit load estimation formulae of local wall-thinned pressure pipings are derived. Some typical failure modes of local wall-thinned pipings are studied. By comparing the calculated results with the piping design criteria, an engineering safety assessment method for pressure pipings with local wall-thinnings is presented. In most cases, this assessment method needn't conduct the complicated strength calculation of piping systems by the finite element method and can be used easily and conveniently.