Z.Z. Cen

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.

On the solution of limit load and reference stress of 3-D structures under multi-loading systems

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 limit load 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 limit load. 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.

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.

A simulation of fatigue crack propagation in a welded T-joint using 3D boundary element method

A general procedure to investigate the fatigue propagation process of a 3D surface crack based on multi-region Boundary Element Method is detailed in this paper. The mesh can be automatically regenerated as the crack propagates. A new formula for estimating the effective stress intensity factor is used to calculate the crack extension. The maximum principal stress criterion is then employed to predict the crack growth direction. Comparison between numerical and experimental results of a welded T-joint shows that the proposed procedure is reliable.

A numerical method for reference stress in the evaluation of structure integrity

The important concepts of reference stress has been widely used in structural component integrity assessments, both below and within the creep range of temperatures, mainly in Nuclear Electrics (fomerly CEGB) R5 an R6 procedures. The reference-stress method (RSM) has been proven to be successful in problems pertaining to creep growth, rupture damage, creep buckling, and, more recently, elastic-plastic fracture toughness. However, determination of the reference stress is not always a simple task. In the present paper, some existing methods for reference stress in evaluation of structure integrity are investigated in detail. In accordance with the relationship between the reference stress and limit load under certain applied loads or moments, a direct iterative algorithm used to determine the reference stress is proposed which depends on the solution of limit load. The penalty-function method is used to deal with the plastic-incompressibility condition. The numerical difficulties caused by the nonlinearity and nonsmoothness of the goal function are overcome. Numerical examples are given to demonstrate the applicability of the procedure.

Numerical analysis of dynamic behavior of stream turbine blade group

This paper considers the stream turbine blade group as a rotationally periodic structure and the complex constraint method has been induced. The effect of the centrifugal force to dynamic vibration frequency has been considered by introducing a nonlinear large deformation equation. A method has been given to introduce the special constraint between the fin heaves of every blade during dynamic analysis.

Plastic analysis by quasi-high order Galerkin BEM

Abstract A two-stage interpolation method called the quasi-high order element method is proposed for solving elastoplastic problems. In the initial stage, it uses high-order elements to interpolate the coordinates and the field variables. For the numerical integration involved, it further uses interpolation to decompose the high-order elements into low-order elements so that the existing analytical integration formulas can be applied. By doing this, the proposed method yields good adaptability and reduces the computational cost. Numerical examples are given to demonstrate the efficiency of the method.

Collapse load computation of defective pipelines under multi-loading system

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China Based on the kinematic theorem of limit analysis, a finite element mathematical programming formulation of 3-D rigid-perfectly plastic bodies is presented. The penalty function method is used to deal with the plastic incompressibility. A direct iterative algorithm is employed in solving the above formulation. The numerical procedure has been applied to carry out the limit analysis of pipelines with or without defects on the outside surface under multi-loading system. The effects of ellipsoidal and rectangular part-through slots on the collapse loads of pipelines under multi-loading system are investigated in detail. All the numerical ex-amples are given to illustrate its application.