含局部减薄弯头塑性极限载荷的数值分析

局部减薄是一种压力管道表面常见的体积型缺陷，它不仅会降低管道的承载能力，而且还可能引起管道破坏，导致严重的事故．采用数值分析方法，对内压和面内弯矩作用下含局部减薄弯头的极限载荷进行了研究，分析了载荷组合、缺陷形状、位置、尺寸对弯头极限承载能力的影响，讨论了导致弯头破坏的典型失效模式．提出了含局部减薄缺陷弯头的塑性极限载荷工程估算式．计算结果为含缺陷弯头的安全评定提供了理论依据．     

Limit and shakedown analysis of pressurized pipelines containing defects

In this paper, the integrity assessment of pressurized pipelines containing defects is performed by direct simplified methods of limit and shakedown analysis. The defects considered are part-through slots of various geometrical configurations. The engineering situation considered here has practical importance in the pressure vessel and pipe industry. The results are compared with those obtained by a step-by-step procedure using the professional code ABAQUS and where possible, with those provided by semi-empirical formulae used in engineering. The simplified methods are found more economical and more reliable than marching solutions achieved by step-by-step evolutive elastic-plastic analysis. The effects of various part-through slots on the load-carrying capacities of pipelines are investigated. The project was supported by the National Science and Technology Commission of China and by the Department of Structural Engineering, Technical University of Milan, Italy     

NUMERICAL INVESTIGATION OF THE LIMIT LOADS FOR PRESSURE VESSELS WITH PART-THROUGH SLOTS

A numerical investigation of the limit loads is carried out for pressurevessels with part-through slots using a general computational method for the limitanalysis of 3-D structures.The limit pressures are given for a comprehensive range ofgeometric parameters.Some of the calculated results are compared with the results of3-D elastic-plastic finite element analysis and existing numerical solutions.The effectsof various shapes and sizes of part-through slots on the load carrying capacity ofcylindrical shells are investigated and evaluated.Two kinds of typical failure modescorresponding to different dimensions of slots are studied.Based on the numericalresults,a geometric parameter G which combines the slot dimensions and the cylindergeometry is presented.It reasonably reflects the overall effect of slots on the limit loadsof cylinders.An empirical formula for estimating the limit pressures of cylindricalshells with part-through slots is obtained.     

在冲击载荷作用下弹塑性圆板的反直观动力行为数值分析

对周边简支理想弹塑性圆板受脉冲载荷作用时的动力行为进行了数值计算与分析,揭示了板类结构反直观动力行为的客观存在性．通过分析发现,随着脉冲强度的增加,存在几个窄的载荷区域,板的响应是反直观的,而且在此附近,结构参数、载荷等因素的微小改变将导致响应模式的很大差异,表明反直观行为对这些参数的极其敏感性．进一步计算表明,这一特殊的动力行为主要与板内力间的相互耦合作用密切相关,同时,卸载后的结构反弹到另一侧时发生较大的反向塑性变形,导致能量的进一步耗散,使板呈现反常的动力响应．这一现象是几何与材料两种非线性相互作用的结果。     

Experimental and numerical investigations into collapse behaviour of thin spherical shells under drop hammer impact

A study of the collapse behaviour of hemi spherical and shallow spherical shells and their modes of deformation under impact loading are presented in this paper. Aluminium spherical shells of various radii and thicknesses were made by spinning. These were subjected to impact loading under a drop hammer and the load histories were obtained in all the cases. Three-dimensional numerical simulations were carried out for all the tested specimen geometries using LS-DYNA^®. Material, geometric and contact nonlinearities were incorporated in the analysis. The uni-axial stress–strain curve for the material was obtained experimentally and was assumed to be piecewise linear in the plastic region. The results from impact experiments are used for the validation of the numerical simulations. Three distinct modes of deformation, namely local flattening, inward dimpling and formation of multiple numbers of lobes were analysed and influence of various parameters on these modes is discussed.     

Shakedown and Inadaptation Mechanisms of Bellows Subject to Constant Pressure and Cyclic Axial Force

Abstract

In the design of pipelines, a thermal expansion of the pipes is usually compensated for by a thin-walled, flexible shell of revolution, called a bellows. The process of cyclic loading of the structure may result in the formation of a sequence of plastic strain fields in the shell, which often leads to the collapse of the structure. Therefore, the question of whether the structure shakes down or collapses under the combined, cyclic loading is of particular importance to engineers

The Reissner-type equations for the perfectly elastoplastic model of the shell are formulated on the basis of the geometrically nonlinear third-order theory. Various mechanisms of plastic collapse (e.g., maximal load or formation of plastic hinge) are discussed for the quasistatically loaded S-type bellows, as well as for the bellows subjected to cyclic, complex loadings. The analogy between these cases, as far as the failure modes are concerned, is explained. The adaptation (shakedown) and inadaptation (nonsymmetric alternating plasticity, incremental collapse) domains for the particular case of the S-type bellows (C-type geometry) acted upon by internal pressure and variable repeated axial force are presented.     

Non-shakedown collapse of a doubly-reinforced rectangular plate under cyclic loads

A typical doubly-reinforced concrete rectangular plate is subjected to quasi-static (and more general quasiperiodic dynamic) transverse loads. The amount of reinforcements can be different in the upper and lower layers, in the central and rear parts of the plate, and in different directions, as usually designed in practice. An upper bound kinematic approach, which involves construction of potential collapse kinematic fields with plastic hinge lines, is developed to evaluate the non-shakedown loads corresponding to the respective collapse modes. The relations between the non-shakedown load parameters (frequency, amplitude limits) and the reinforcement parameters are derived for practical use. The kinematic assumptions with plastic hinge lines reduce the set of admissible kinematic fields for our upper bound approach, however the procedure appears relatively simple, visual, and can be developed to investigate the behaviour of other plates in various loading and reinforcement schemes, like the respective approach of plastic limit analysis, which was restricted to static loading.     

含凹坑缺陷石油管件塑性极限的分析

在役石油管件安全可靠运行是目前世界各国油气储运业界普遍关注和迫切需要解决的重大课题,而在役石油管件塑性极限强度评价则是为保障在役石油管件安全可靠运行的基础工作。本文对含有椭球形凹坑缺陷石油管件分别在轴向拉力、内压力和轴向拉力与内压力联合作用下的塑性极限强度问题,基于Von.Mises准则和平衡应力场原理,建立管件塑性极限强度理论分析模型,并就具体算例,利用三维弹塑性有限元法,对该模型进行分析比较。结果表明:当凹坑缺陷相对尺寸较小时,此模型可以有效预测含有缺陷管件的塑性极限强度,是一种简便、有效的工程评定方法。     

Stability and extremum principles for post yield analysis of finite plasticity

The post yield behavior of rigid-perfectly plastic solids at the collapse load is studied based on the finite deformation theory. By using the general duality theory developed by Gao-Strang (1989), a global stability criteria is proposed and a pair of dual extremum principles, expressed in terms of displacements, displacement rates and the Kirchhoff stresses are established for plastic collapse analysis. It is proved that under large deformations, the existence of the plastic limit state at the collapse load depends on the directional derivative of a so-called complementary gap function. The application to the nonlinear plastic collapse theory yields a pair of dual bounding theorems for limit loading factor associated with any transient displacement of the deformed body when the global extremum criteria are satisfied. Dedicated to Professor Y.K. Cheung on the occasion of his 60th birthday     

含凹坑缺陷圆柱壳的数值极限分析

使用文［１］提出的三维结构塑性极限分析的一般计算方法，我们对含凹坑缺陷的圆柱壳进行了数值极限分析．对凹坑和筒体各种组合的几何参数，本文给出了筒壳极限压力的上限．计算结果与现有的理论、实验和数值解进行了比较．本文调查和评估了各种形状和尺寸的凹坑对筒壳极限承载能力的影响规律，研究了对应于不同凹坑尺寸的筒壳两种典型的破坏模式．根据以上数值结果，本文采用几何参数Ｇ来反映凹坑各参数对筒壳极限压力的综合影响，并给出了估计带凹坑筒体极限压力的拟合公式．本文结果对含凹坑缺陷压力容器的安全评估具有重要参考价值     

Shakedown reduced kinematic formulation,separated collapse modes,and numerical implementation

Our shakedown reduced kinematic formulation is developed to solve some typical plane stress problems, using finite element method. Whenever the comparisons are available, our results agree with the available ones in the literature. The advantage of our approach is its simplicity, computational effectiveness, and the separation of collapse modes for possible different treatments. Second-order cone programming developed for kinematic plastic limit analysis is effectively implemented to study the incremental plasticity collapse mode. The approach is ready to be used to solve general shakedown problems, including those for elastic–plastic kinematic hardening materials and under dynamic loading.     

Plastic collapse of a circular plate under cyclic loads

The shakedown kinematic approach is used to analyze the collapse modes for a circular plate subjected to cyclic loads distributed axisymmetrically. Depending upon the loading scheme and parameters, the plate may fail by instantaneous, incremental, or alternating plasticity collapse. For quasistatic processes the nonshakedown load may be smaller than the instantaneous plastic limit load. In the case of periodic dynamic loading, which lies outside the framework of plastic limit analysis, the frequency parameter, besides the load amplitudes, can significantly influence the nonshakedown behavior of the plate.     

On the effect of corrosion defects on the collapse pressure of pipelines

The loss of metal in a pipeline due to corrosion usually results in localized pits with various depths and irregular shapes on its external and internal surfaces. The effect of corrosion defects on the collapse pressure of offshore pipelines was studied through the combination of small-scale experiments with nonlinear numerical analyses based on the finite element method. After calibrated based on the experimental results, the model was used to determine the collapse pressure as a function of material and geometric parameters of different pipes and defects. An extensive parametric study using 2-D and 3-D numerical models was carried out encompassing different defect geometries and their interaction with pipe ovalization.     

海底管道的弹塑性稳定性和屈曲传播

本文根据我国南海海底输油气铺管的要求系统分析了海底管道在弯曲与外水压力共同作用下的弹塑性稳定性和屈曲传播.研究了管道的极值型屈曲和分枝型屈曲.在考虑管道的初始非圆度和材料的物理非线性的情况下提出了临界屈曲载荷的计算方法.综述和评论了屈曲传播现象的本质和各种计算方法.介绍了我们所进行的全尺寸管道实验.在分析理论结果时与现行的有关设计规程进行了比较和评论.     

A bipotential approach for plastic limit loads of strip footings with non-associated materials

This paper is concerned with a bipotential approach for estimating the plastic collapse loads of a half-space made with a non-associated Mohr–Coulomb material and indented by a rigid punch. In geotechnics, this problem is called the bearing capacity of shallow strip footing for which the analytical solution is derived by Prandtl (1920) [46] and Hill (1950) [35] in the context of associated plasticity. However, when the plastic model is not associated, no analytical methods have yet been developed. Here we explore this issue in a rigorous mathematical framework coupling the bipotential concept and limit analysis. First, the method proposed makes use of the method of characteristics to build a statically and plastically admissible stress field that enables a lower estimate of the plastic limit loads. Next, the extended kinematic theorem of limit analysis to non-standard plasticity is applied to derive an upper quasi-bound of the collapse loads. For this aim, the internal rate of plastic dissipation is obtained thanks to the bipotential functional depending on both a trial stress field and a Prandtl-like collapse mechanism. The analytic estimates are compared to the formulae and numerical results provided in literature.     

Elasto-plastic vibrational analysis of tapered bars under uniform axial loading considering shear deformation and rotary inertia

The analysis of structures in the plastic regime is important in order to develop an adequate and competitive design in engineering. This paper presents a study of the small-amplitude free vibration of tapered bars under pre-stress in the post-elastic regime due to a uniform axial loading. The plastic behavior is taken into account using an energy approach. The method does not require an iterative procedure, unlike conventional methods used in plasticity. The Timoshenko beam theory and the dynamic version of the principle of virtual work are used to derive the eigenvalue problem. The solution is carried out using beam finite elements. The results are validated using 3D finite element software and results from the open literature. A variety of numerical results are given in order to analyze the influence of plastic behavior for various bar geometries and material parameters. The combined effect of the stiffening due to the axial loading and the plastic softening may produce an increase or decrease of the natural frequencies as the tensile load increases. The plastic softening effect is seen to be pronounced for short bars and for high taper ratios. In addition, axial normal modes are more affected than bending modes.     

弯管结构塑性极限分析的数值方法及应用

从塑性极限分析数值计算的角度,分析了多组载荷联合作用下弯管结构的塑性极限承载能力。为了克服塑性极限上限分析中目标函数非线性非光滑所导致的数值困难,提出了一种弯管结构塑性极限上限分析的无搜索优化迭代算法;采用一种改进的弯管单元并利用加载路径的径向射求解方案处理多组载荷系统。通过对典型弯管结构进行塑性极限分析得出了一些有价值的结论。     

Limit analysis of space grids

The paper presents generalized, unique solutions for the limit design of pin-connected, double-layer space grids of regular construction, simply-supported along the sides of a rectangle and carrying a uniform concentration of normal nodal loading applied to the upper layer of the structure. The principal assumption upon which the foregoing results are obtained is that member forces increase monotonically with the applied loads, therefore insuring against the inducement of higher than ultimate loads in the compressive elements at anytime prior to structure failure. The virtual work method of the plastic analysis has been employed in conjunction with the techniques of the finite difference calculus to study the various collapse modes of the system. The work is concluded with an illustrative example to demonstrate the simplicity of the proposed solutions.     

THREE DIMENSIONAL DYNAMIC ELASTICPLASTIC ANALYSIS OF THE INTERACTION OF A SET OF PERCUSSION BITS WITH ROCK MASSES

A three dimensional dynamic elastic-plastic finite element analysis of the interaction ofpercussion bits with rock roasses is presented.The dynamic contact problem was investigated with thenumerical method developed for high velocity impact calculations.The numerical analysis was carried out for three simultaneously loaded percussion bits arrangedon a straight line on the rock surface,the loading time was kept constant throughout this work.Thenumerical calculation for various strengths of the dynamic load on the percussion bits shows that a crit-ical minimum dynamic load exists for the generation of plastic deformations in the rock.For this criti-cal value of the load the maximum normal stress of the longitudinal wave in the percussion bit exceedsthe yield stress of the rock mass.