Numerical analysis of limit load and reference stress of defective pipelines 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 in Nuclear Electric's (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.     

Shakedown and limit analyses for 3-D structures using the linear matching method

A recently developed method for 3-D shakedown and limit analyses is evaluated in the present paper. The shakedown and limit loads of a holed plate subjected to biaxial loading are calculated by implementing the upper bound linear matching method into the commercial FE code ABAQUS. A defective pipeline under the combined action of internal pressure and axial tension is also analysed for both shakedown and limit capacities and the results compared with a standard programming method. All the numerical examples confirm the applicability of this procedure to complex 3-D structures.     

Plastic limit load of cylindrical shells with cutouts subject to pure bending moment

In this paper, the results of limit analyses of thin-walled cylindrical shells with a circular hole under the action of a pure bending moment are presented in dimensionless form for a wide range of geometric parameters. Analytical estimation of lower bound limit load is carried out using the feasible sequential quadratic programming (FSQP) technique. The finite element calculations of limit load consist of elastic–plastic and lower and upper bound predictions by elastic compensation methods. A testing device was made to perform experiments to obtain limit bending moment of cylinders with circular openings. The analytical and finite element calculations are compared with experimental results and their correlation is discussed. The finite element calculation results were found to be in good agreement with lower bound estimations by the nonlinear mathematical programming (FSQP) method and the formula proposed by Shu.     

水库调度方程组的定界迭代法

在进行水电站水库调度计算中采用逐时段递推计算时,一般求解方法是迭代算法,在生产实际中,现行迭代算法有时出现不收敛现象,通过深入分析发现,如果迭代变量的假设值小于新值,则假设值即为失代变量的下界x-,新值为其上界x^-,否则,假设值为迭代变量的上界x^-,新 值为其下界x-,迭代变量的真值必包含在上下界之间,即x^*∈（x--x^-)。随着迭代次数的增加,迭代区间将逐步减小,直至逼近真值,由此即可构造定界迭代算法,应用实例表明,提出的定界迭代算法原理简单,可保证迭代算法绝对收敛,且与迭代变量的修正方法无关。     

海上风电宽浅式筒型基础竖向极限承载力上限解

由于宽浅式筒型基础具有不同于传统筒型基础的超大直径(D≥30 m)和较浅入土深度(d≤15 m),因此其竖向承载模式和极限承载力计算方法有待研究.通过数值分析得到宽浅式筒型基础在达到竖向极限承载力时的破坏模式,引入承载力极限分析理论,构建宽浅式筒型基础竖向极限承载的地基破坏机动场;结合虚功方程采用Matlab求解宽浅式...     

薄拱坝极限承载能力研究与应用

根据塑性极限分析的静力法和机构法原理,推导了拱坝极限荷载上、下限值的线性规划数学模型,并选择两座典型薄拱坝为例,采用多拱梁塑性极限分析法计算了极限状态下的超载系数和应力状态、破坏形态,验证了薄拱坝极限承载能力及安全可靠性.     

Non-cyclic shakedown/ratcheting boundary determination – Part 1: Analytical approach

From the practical point of view, the classical elastic shakedown methods are not very useful for design, since in most components the stresses can safely exceed the elastic limit locally. This paper generalizes the static shakedown theorem (Melan’s theorem) to allow the analysis of plastic shakedown. Since the method is derived from a lower bound formulation in shakedown, it is very useful for the design purposes (safe). The ratchet boundary is analytically determined using the proposed method for several examples with uniform stress distributions. The numerical implementation of the method along with several examples is discussed in an accompanying paper.     

Limit analysis based on elastic compensation method of branch pipe tee connection under internal pressure and out-of-plane moment loading

A new method of calculating the limit load of a structure via a sequence of incompressible elastic finite element calculations with variable Young's moduli converging to the rigid perfectly plastic problem is used to study the limit load of branch pipe tee connections. Several models of branch pipe tee connection are meshed with shell elements and submitted to internal pressure with end axial load effect or out-of-plane moment. Results are compared with lower and upper bound analytical solutions and experimental results reported in the literature. Computations with 20 noded cubic elements are also proposed to validate shell studies. The J integral is also calculated by a simplified method with the limit load, using an example of a defective branch pipe tee connection.     

水平荷载下高层建筑结构数值分析模型

研究了水平荷载下高层建筑结构—桩筏基础—地基共同作用的问题,对整个结构进行了三维数值分析。把有限层法和桩基规范中的m法相结合,通过数值分析手段建立了水平荷载下高层建筑结构——桩筏基础——地基共同作用分析模型。针对一具体建筑进行了对比计算,共同作用方法与常规方法相比对上部结构的水平位移及框架柱内力的影响。通过分析对比,得出了有益的结论。本文应用Matlab编程,总体刚度矩阵一次生成,运用迭代法求解。     

Computational limit analysis of anisotropic axisymmetric shells

In this paper a numerical method is suggested for the limit analysis of axisymmetric shells using Hill's 1948 yield criterion. Since von Mises' condition is a special case of Hill's 1948 criterion, the new method can be applied to both the isotropic von Mises' material and the anisotropic Hill's material. By means of finite element techniques and the kinematic theorem for limit analysis, we introduce an efficient iteration algorithm to compute the upper bound of the collapse load. Numerical results of the limit analysis of cylindrical-conical-cylindrical combined shells subjected to internal pressure are presented by means of Hill's as well as von Mises' conditions. From the present investigation, some comments are made on the design of anisotropic pressure vessels of cylindrical-conical-cylindrical combined shells.     

基于非线性有限元法的风电叶片动态频率研究

针对风电叶片设计阶段,如何准确预估叶片工作状态下的动态频率进行研究.依据旋转部件结构频率改变的原理,采用非线性有限元数值计算方法,分别对叶片工作转速的下限及上限情况,进行结构的线性与非线性静力分析,通过对计算结果的比较,探讨了惯性载荷对叶片结构的非线性影响程度.利用静力分析的结果,开展叶片动态频率的计算与比较工作,分析...     

Temperature and entropy generation behavior in rectangular ducts with 3-D heat transfer coupling (conduction and convection)

Temperature and entropy generation fields are evaluated for 3-D heat transfer coupling (conduction and convection) using a mathematical and computational model. Results are obtained from numerical simulation and analyzed for conditions of fully developed laminar flow inside rectangular ducts. Thermal boundary conditions, at the walls cross section and axial direction, are non-uniform and not imposed. A numerical method of modified TDMA algorithm combined with an iterative solution for the system of algebraic equations obtained was developed. Equations were discretised by finite differences. Convergence is guaranteed by applying the first law of thermodynamics. Considering the thinness of the walls, conduction effectiveness is well represented as 1-D. The methodology applied considers air, water and oil as working fluids at 300 K and carbon-steel as wall material. Results for these cases are presented with the intention of finding, the best fluid heating conditions as a first approach to the design of heat exchangers systems.     

Structural integrity evaluation of X52 gas pipes subjected to external corrosion defects using the SINTAP procedure

In the present study, the SINTAP procedure has been proposed as a general structural integrity tool for semi-spherical, semi-elliptical and long blunt notch defects. The notch stress intensity factor concept and SINTAP structural integrity procedure are employed to assess gas pipelines integrity. The external longitudinal defects have been investigated via elastic–plastic finite element method results. The notch stress intensity concept is implemented into SINTAP procedure. The safety factor is calculated via SINTAP procedure levels 0B and 1B. The extracted evaluations are compared with the limit load analysis based on ASME B31G, modified ASME B31G, DNV RP-F101 and recent proposed formulation [Choi JB, Goo BK, Kim JC, Kim YJ, Kim WS. Development of limit load solutions for corroded gas pipelines. Int J Pressure Vessel Piping 2003;80(2):121–128]. The comparison among extracted safety factors exhibits that SINTAP predictions are located between lower and upper safety factor bounds. The SINTAP procedure including notch-based assessment diagram or so-called ‘NFAD’ involves wide range of defect geometries with low, moderate and high stress concentrations and relative stress gradients. Finally, some inspired and advanced viewpoints have been investigated.     

Limit loads for pipe bends under combined pressure and in-plane bending based on finite element limit analysis

Approximate plastic limit load solutions for pipe bends under combined internal pressure and bending are obtained from detailed three-dimensional (3-D) FE limit analyses based on elastic-perfectly plastic materials with the small geometry change option. The FE results show that existing limit load solutions for pipe bends are lower bounds but can be very different from the present FE results in some cases, particularly for bending. Accordingly closed-form approximations are proposed for pipe bends under combined pressure and in-plane bending based on the FE results.     

水库群系统分析的一个数学规划模型

本文为树枝状水库群的系统分析和优化运行建立了以水量守恒方程为约束条件,以发电效益为目标函数的数学规划模型;讨论了模型在水资源系统规划与电力生产系统运行中的应用;为数值解的方便,还给出了模型的等价的动态规划形式和非线性网络规划形式。     

多波长消光法粒径测量下限影响因素分析

介绍了根据Lambert-Beer定理并采用多波长消光法测量颗粒粒径分布的方法。提出了基于数值模拟和数理统计对多波长消光法粒径测量下限进行估计的方法。通过数值模拟分析讨论了入射光波长、颗粒相对折射率和透光率对粒径测量下限的影响。研究为多波长消光法粒径测量在实际应用中的可行性提供了指导。     

Minimum weight design of inhomogeneous rotating discs

There are numerous applications for gas turbine discs in the aerospace industry such as in turbojet engines. These discs normally work under high temperatures while subjected to high angular velocities. Minimizing the weight of such items in aerospace applications results in benefits such as low dead weights and lower costs. High speed of rotation causes large centrifugal forces in a disc and simultaneous application of high temperatures reduces disc material strength. Thus, the latter effects tend to increase deformations of the disc under the applied loads. In order to obtain a reliable disc analysis and arrive at the corresponding correct stress distribution, solutions should consider changes in material properties due to the temperature field throughout the disc. To achieve this goal, an inhomogeneous disc model with variable thickness is considered. Using the variable material properties method, stresses are obtained for the disc under rotation and a steady temperature field. In this paper this is done by modelling the rotating disc as a series of rings of different but constant properties. The optimum disc profile is arrived at by sequentially proportioning the thicknesses of each ring to satisfy the stress requirements. This method vis-à-vis a mathematical programming procedure for optimization shows several advantages. Firstly, it is simple iterative proportioning in each design cycle not requiring involved mathematical operations. Secondly, due to its simplicity it alleviates the necessity of certain simplifications that are common in so-called rigorous mathematical procedures. The results obtained, compared to those published in the literature show agreement and superiority. A further advantage of the proposed method is the independence of the end results from the initially assumed point in the iterative design routine, unlike most methods published so far.     

A Node-based Smoothed Point Interpolation Method (NS-PIM) for Three-dimensional Thermoelastic Problems

A node-based smoothed point interpolation method (NS-PIM) is formulated to analyze 3-D steady-state thermoelastic problems subjected to complicated thermal and mechanical loads. Gradient smoothing technique with node-based smoothing domains is utilized to modify the gradient fields and to perform the numerical integration required in the weak form formulation. Numerical results show that NS-PIM can achieve more accurate solutions even when the 4-node tetrahedral mesh is used compared to the finite-element method (FEM) using the same mesh, especially for strains and hence stresses. Most importantly, it can produce an upper bound solution of the exact solution in energy norm for both temperature and stress fields when a reasonably fine mesh is used. Together with FEM, we now for the first time have a simple means to obtain both upper and lower bounds of the exact solution to complex thermoelastic problems.     

An enthalpy method for modeling dendritic growth in a binary alloy

An enthalpy fixed grid method is developed for modeling dendritic growth in an under-cooled binary alloy. The proposed numerical method couples explicit finite difference solutions of equations expressing the conservation of enthalpy and solute to an iterative procedure that enforces node by node consistency between enthalpy, solute, liquid fraction, and interface under-cooling. Calculations made with the scheme, are consistent with previously reported work, agree well with limit analytical solutions, approach the correct steady-state tip operating conditions, show grid size independence, are relatively free of grid anisotropy, and can be obtained with a low CPU cost.     

水平轴风力机静态失速特性

采用叶片表面边界层理论分析,三维旋转流场的数值模拟以及实验风力机模型的流动测量方法对水平轴风力机的静态失速特性进行了较为系统的研究。研究表明,旋转速度使得实际三维旋转风轮翼型表面的静压分布与二维非旋转条件下翼型表面静压分布产生较大差别,这是造成静态失速的原因之一。