B.Y. Xu

A numerical method for plastic limit analysis of 3-D structures

Abstract Based on the upper bound theorem of plasticity, the 3-D limit analysis of rigid-perfectly plastic structures is formulated as a discrete nonlinear mathematical programming problem with only equality constraints by means of the finite element technique. The penalty function method is used to deal with the plastic incompressibility condition. A direct iterative algorithm is employed in solving this formulation. At each step of the iteration, the rigid and plastic zones are continually distinguished, the respective constraint conditions are imposed on them, and the goal function is modified appropriately. The numerical difficulties caused by the nonlinearity and nonsmoothness of the goal function and the incompressibility of plastic deformation are overcome. The limit load multiplier and the associated velocity field computed by the iteration procedure converge monotonically to the upper bounds of real solutions. The numerical procedure has been used to carry out the limit analysis for cylindrical shells with part-through slot-type defects under internal pressure. Numerical examples are given to demonstrate the applicability of the procedure.

Numerical analysis of limit load and reference stress of defective pipelines under multi-loading systems

Abstract The concepts of limit load and reference stress have been widely used in structural engineering design and component integrity assessment, especially in Nuclear Electrics (formerly CEGB) R5 and R6 procedures. The reference stress method has been proven to be successful in problems pertaining to creep growth, rupture damage, creep buckling, and more recently, elastic–plastic fracture toughness. An approximate method of reference stress determination relies on prior knowledge of limit loads for various configurations and loadings. However, determination of the limit loads for the problems with complicated geometric forms and loading conditions is not a simple task. In the present paper, a numerical solution method for radial loading is presented, the mathematical programming formulation is derived for the kinematic limit analysis of 3D 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 limit load. The numerical procedure is applied to determine the limit load and reference stress of defective pipelines under multi-loading systems. The effects of four kinds of typical part-through slots on the collapse loads of pipelines are investigated and evaluated in detail. Some typical failure modes corresponding to different configurations of slots and loading forms are studied.

Numerical limit analysis of cylindrical shells with part-through slots

Abstract A numerical limit analysis is performed for cylindrical shells with part-through slots using a general computational method for limit analysis of 3-D structures. The upper bounds for the limit pressures are given for a comprehensive range of geometric parameters. Some of the calculated results are compared with the results of detailed 3-D elastoplastic finite element analysis and where possible, with existing theoretical, experimental or numerical solutions. The effect of various shapes and sizes of part-through slots on the load-carrying capacity of cylindrical shells is investigated and evaluated. Two kinds of typical failure modes corresponding to different dimensions of slots are studied. Based on the numerical results, a geometric parameter G which combines the slot dimensions and the cylinder geometry is presented. It reflect reasonably the overall effect of slot on the limit load of a cylinder. An empirical formula for estimating the limit pressure of a cylindrical shell with part-through slot is obtained.

Plastic collapse analysis of defective pipelines under multi-loading systems

Abstract In this paper, a finite element mathematical programming formulation is presented for the kinematic limit analysis of 3-D rigid–perfectly plastic bodies. A numerical path scheme for radial loading is adopted to deal with complex multi-loading systems. A direct iterative algorithm is employed in solving the above optimization formulation. The numerical procedure has been applied to carry out the plastic collapse analysis of defective pipelines under multi-loading systems. The engineering situation considered has a practical importance in the pipeline industry. The effects of four kinds of typical part-through slots on the collapse loads of pipelines are investigated and evaluated. Some typical failure modes corresponding to different configurations of slots and loading forms are studied.

Lower-bound shakedown analysis of axisymmetric structures subjected to variable mechanical and thermal loads

This paper is concerned with axisymmetric structures subjected to various combinations of steady and (irregularly) pulsating mechanical and thermal loads. The numerical method is based on the static shakedown theorem, which deals with elastic-perfectly-plastic bodies. Linear temperature dependence of the yield condition in a 4D stress space is considered. The pseudo-residual stress field is simulated by the Temperature Parameter Method and the yield surface is linearized, so that the shakedown analysis is transformed into a linear programming problem and hence the computational difficulties otherwise encountered are overcome. The shakedown analysis of cylinders and spherical shells with and without defects is presented in this paper. Results presented show that the method is beneficial for the shakedown analysis of complicated structures subjected to various combinations of loads.

Finite element analysis for buckling of pressure vessels with ellipsoidal head

In this paper, a finite element analysis is performed for buckling of the pressure vessels with ellipsoidal head subjected to uniform pressure. According to the characteristic of deformation of the pressure vessel, it is divided into some identical substructures. The degrees of freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain distributions of the whole structure are obtained by solving the static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method has been used to get the buckling load and mode for the whole structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. Some numerical examples have been given to illustrate the high efficiency and validity of this method.

The Parameter Identification of Thermal Visco‐plastic Model Considering Dynamic Recrystallization

A study on parameter identification of thermal visco‐plastic model considering dynamic recrystallization is presented in this paper. A hybrid global optimization method is constructed and applied in the parameter identification. The hybrid global optimization method is a combination of the Real‐coded genetic algorithm (RGA) and some classical local search methods (such as Levenberg‐Marquardt method, augmented Gauss‐Newton algorithm and the flexible tolerance method) in order to accommodate the characters of the objective function used for parameter identification of the thermal visco‐plastic model considering dynamic recrystallization. A special numerical procedure of the parameter identification is also made through cooperation of the hybrid global optimization and a thermal rigid‐plastic FEM for simulation of hot forging process. Finally, as numerical example, a set of satisfactory material parameters for 26Cr2Ni4MoV steel is presented by the numerical procedure.