Plastic collapse analysis of defective pipelines under multi-loading systems

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.     

Collapse simulation of tubular structures using a finite element limit analysis approach and shell elements

This paper describes the collapse simulation of thin-walled tubular structures using a finite element limit analysis approach and degenerated four-node shell elements. The simulation traces the path of sequential deformation of the structure modelled by considering the strain-hardening effect, which is important for the analysis of collapse behaviour and energy absorption efficiency. The collapse analysis of some square tubes was used to verify the simulation method proposed. Numerical results are compared with experimental observations for sequential collapse loads and deformation modes, showing fairly good coincidence. The collapse analysis of an S-rail was then carried out for sequential collapse loads as well as deformation modes and its results are compared with elasto-plastic analysis results obtained from the explicit dynamic code PAM-CRASH. The energy absorption capacity was studied for a variety of rectangular cross-section aspect ratios. The results show that the energy absorption capacity increases as the height-to-width aspect ratio becomes larger. Results also demonstrate that the finite element limit analysis can predict the plastic collapse load and collapse mode of thin-walled structures efficiently and systematically. The present algorithm with a simple formulation has the advantage of stable convergence, computational efficiency and easy access to strain-hardening materials compared to the incremental rigid–plastic finite element analysis.     

Analysis of collapse in flattening a micro-grooved heat pipe by lateral compression

The collapse of thin-walled micro-grooved heat pipes is a common phenomenon in the tube flattening process, which seriously influences the heat transfer performance and appearance of heat pipe. At present, there is no other better method to solve this problem. A new method by heating the heat pipe is proposed to eliminate the collapse during the flattening process. The effectiveness of the proposed method is investigated through a theoretical model, a finite element(FE) analysis, and experimental method. Firstly, A theoretical model based on a deformation model of six plastic hinges and the Antoine equation of the working fluid is established to analyze the collapse of thin walls at different temperatures. Then, the FE simulation and experiments of flattening process at different temperatures are carried out and compared with theoretical model. Finally, the FE model is followed to study the loads of the plates at different temperatures and heights of flattened heat pipes. The results of the theoretical model conform to those of the FE simulation and experiments in the flattened zone. The collapse occurs at room temperature. As the temperature increases, the collapse decreases and finally disappears at approximately 130 ℃ for various heights of flattened heat pipes. The loads of the moving plate increase as the temperature increases. Thus, the reasonable temperature for eliminating the collapse and reducing the load is approximately 130 ℃. The advantage of the proposed method is that the collapse is reduced or eliminated by means of the thermal deformation characteristic of heat pipe itself instead of by external support. As a result, the heat transfer efficiency of heat pipe is raised.     

Plastic collapse analysis of thin-walled pipes based on unified yield criterion

Based on a unified yield criterion (UYC), the plastic collapse analysis of thin-walled pipes is conducted in the framework of finite strain. A unified analytical solution for the burst pressure of end-capped defect-free pipes is derived, which is fit for various kinds of non-SD (strength differential) materials. A series of solutions can be deduced from this unified solution, and those solutions of burst pressure on the basis of Tresca, von Mises, ASSY, and TS criteria are special cases of it. By comparing with existing test result, it is found that the present unified solution is very convenient and effective for the prediction of burst pressure.     

基于ANSYS的腐蚀压力管道的应力分析

应用有限元分析方法并结合压力管道分析设计标准,分析研究某输油管管道在受腐蚀情况下的承载能力和应力分布。通过腐蚀深度与强度标准的数据比对,得出腐蚀深度与达到较大塑性破坏的关系,为管道工程焊接和运营过程中裂纹与腐蚀应力破坏实际控制提供了理论依据。     

内压及扭矩载荷下无缺陷弯管的塑性极限载荷

弯管在管线中通常是承受应力较大的元件，极限载荷相应较低。为充分发挥结构的塑性极限承载能力，对弯管的塑性极限载荷进行理论分析，利用von Mises屈服准则，推导出内压和扭矩联合载荷作用下等厚弯管、非均匀壁厚椭圆弯管的塑性极限压力。实验验证了理论分析的正确性。     

周向裂纹管道在含扭转各种组合变形时的极限载荷分析

到目前为止，还没有文献给中向裂纹管道在非对称弯曲及扭转组合变形时的塑性极限载荷计算公式。文中根据净截面垮塌准则用沙堆比拟法分别求出埋藏裂纹、外表面裂纹、内表面裂纹、穿透裂纹管道发生扭转变形时的塑性极限扭矩；给出含周向裂纹薄壁管道横截面上的剪应力分布规律，其塑性极限扭矩等于一个闭口薄壁截面与一个开口薄壁截面圆环的塑性极限扭矩之和，闭口薄壁截面的壁厚为管道壁厚减裂纹深度；开口薄壁截面的壁厚为裂纹的深度。推导了各种周向裂纹管在内压、轴力、扭矩及非对称弯矩共同作用时的塑性极限载荷关系式，并由此给出其他一些组合变形时的极限载荷计算公式。本文结果可供管道安全评价时参考。     

Analysis of wave propagation in fluid-filled viscoelastic pipes

This paper describes the investigation of the propagation wave speed and wave attenuation in viscoelastic fluid-filled pipes. Relatively predictable for metal pipes, these are largely unknown for plastic pipes, since they depend on the pipe wall properties. Wave number measurements, encompassing both wave speed and wave attenuation, were carried out on different water-filled plastic pipes using three hydrophones. The frequency-dependent wave speed and attenuation were calculated from the transfer function between three pressure measurements. Experimental results for different pipe wall materials, particularly those with applications in water supply installations, are presented. The purpose of this paper is to present a method of analysis in the frequency domain that can be used to determine the acoustical properties of fluid-filled plastic pipes.     

Safety and collapse of elastic–plastic beams against dynamic loads

The dynamic load-bearing capacity of elastic–plastic beam structures is analysed by the apparatus of shakedown theory. The reduced kinematic formulation for bending beams, which is equivalently deduced from Koiter’s kinematic theorem, combined with the plastic collapse’s method of hinge mechanisms appears effective in solving practical problems. The safety limits on the quasiperiodic dynamic loads as well as respective collapse mechanisms for a number of practical beams are determined.     

Elastic moduli and plastic collapse strength of hexagonal honeycombs with plateau borders

The theoretical analysis for the elastic moduli and plastic collapse strength of hexagonal honeycombs with Plateau borders is proposed and presented here. The variation of cell edge thickness in real honeycombs is taken into account in deriving their elastic moduli and plastic collapse strengths. A repeating element, composed of three cell edges connected at a vertex with Plateau borders of constant radius of curvature and width, is employed to calculate the elastic moduli and plastic collapse strength of hexagonal honeycombs. Results suggest that both the elastic moduli and plastic collapse strength of hexagonal honeycombs with Plateau borders depend on their relative density and the volume fraction of solid contained in the Plateau border region. Meanwhile, effects of solid distribution on the elastic moduli and plastic collapse strength of hexagonal honeycombs are investigated, providing a guideline for the optimal microstructure design of honeycombs.     

Shakedown theory for elastic-perfectly plastic bodies revisited

Yield criteria for elastic-perfectly plastic solids, in particular, the Mises and Tresca ones, permit unlimited hydrostatic stresses, leading to some singularity in the classical Melan–Koiter shakedown theory. Classical shakedown theory is re-examined regarding this problem. It is shown that the complete proofs of both static and kinematic theorems require restrictions on the hydrostatic stresses. A modified shakedown kinematic theorem using a fictitious material that can yield in bulk tension and compression has been constructed for subsequent treatment of real engineering materials, which cannot yield but fail under high hydrostatic stresses. The kinematic theorem should have vanishing hydrostatic plastic strain rate solution for the safety of the body against hydrostatic fracture. In this way, the modified kinematic formulation including the limits on hydrostatic stresses are suggested for application. The modifications are also naturally added into the plastic limit theory, which is a limiting case of the shakedown one. Also in the paper, the kinematic approach is used to deduce some simplified estimates for specific non-shakedown collapse modes of elastic plastic structures.     

防止承压设备总体塑性变形的5%最大主应变准则

提出了按5%应变确定塑性载荷的最大主应变准则。该准则可以用来防止承压设备的总体塑性变形。5%最大主应变准则只需要经过弹塑性分析,求出承压设备在载荷作用下产生的最大主应变,当最大主应变达到5%时,作用在承压设备上的载荷就是塑性载荷。与其它已有确定塑性载荷的准则相比较,5%最大主应变准则不需要预先画出载荷—变形(应变)曲线,因而,就不需要选择变形参数(选择变形点的位移,或者容器体积的变化等)。例子分析给出了5%最大主应变得到的塑性载荷,并与应力分类方法、两倍弹性斜率准则和双切线准则作了比较。     

Hardening-softening behaviour of circular pipes under bending and tension

A theoretical analysis, based on plastic shell theory and utilizing extremum and variational principles combined with numerical approaches, has been conducted to investigate the quasi-static flexural behaviour of mild steel circular pipes. Attention is focused on the hardening-softening relations between the bending moment and the curvature of pipes which, according to observations in pipe-whip experiments, governs the deformation process and can lead to localization. As the study is concerned with free pipe-whip behaviour of the high pressure piping system, in the theoretical analysis the circular pipe is assumed to be subjected to a bending moment as well as a relatively small tension force in the axial direction. In addition to numerical examples for various cases, a quasi-static four-point bending test was carried out to verify the hardening-softening moment vs curvature relation of pipes predicted by the present theory in the case of pure bending. A simpler, approximate procedure which predicts the moment-curvature relationship with reasonable accuracy is also described.     

Plastic limit load of plane frames with frictional contact supports

On the basis of the bipotential theory, published in previous contributions, the objective of the work presented in this paper is to establish an extended formulation of limit analysis theory for frames in presence of the unilateral contact with Coulomb's dry friction at supports. The kinematic and static approaches are formulated by the calculation of the total dissipation power of the frame. As it will be shown, on account of the presence of contact with friction, the two approaches are coupled in the sense that the kinematic limit analysis contains static variables and converse. To deal with, an iterative algorithm, based on successive approximations method, will be described here. The study of a simple example, consisting of a rectangular frame, demonstrates that the coefficient of friction value affects the plastic limit state and therefore the limit load and the collapse mechanism taking place too.     

Elastic–plastic response of unpressurised pipes subjected to axially-long radial indentation

Elastic–plastic force-deflection analysis of unpressurised pipes with long axial indentations are carried out. Solutions from an analytical method are compared to the corresponding finite element solutions and experimental test results. The analytical method is based on a simple energy-based approach developed to predict the initial gradients of the force-deflection curves and the limit loads of the indented rings using linear beam bending theory and upper bound theories. A comprehensive finite element study of indented unpressurised pipes is performed to study their sensitivities to the elastic–plastic responses. The finite element analysis covers six different materials, four different geometries and two different boundary conditions, and is compared with the corresponding analytical solutions. The results presented in this paper indicate that by using the analytical solutions for limit loads incorporating a representative flow stress as the average value of the yield stress and ultimate tensile stress, it is possible to obtain reasonably accurate predictions for the peak loads.     

内压载荷作用下含纵向穿透裂纹弯头的塑性极限载荷

弯头是管道系统中最薄弱、最容易失效的管件。研究含缺陷弯头的塑性承载能力在整个压力管道系统安全评定中占有重要地位。利用求取直管极限载荷的鼓胀系数法建立不考虑直管影响的含缺陷弯头的塑性极限载荷估算式。采用三维弹塑性有限元技术,对内压载荷作用下含纵向穿透裂纹弯头的塑性极限载荷进行系统分析。结果表明,裂纹削弱系数（PL／P LO）与厚径比（t／rm）无关,在实际工程应用中可忽略厚径比对裂纹削弱系数的影响。裂纹对长半径弯头的塑性极限承载能力影响程度明显大于对短半径弯头的。     

The plastic collapse and energy absorption capacity of egg-box panels

The plastic collapse response of aluminium egg-box panels subjected to out-of-plane compression has been measured and modelled. It is observed that the collapse strength and energy absorption are sensitive to the level of in-plane constraint, with collapse dictated either by plastic buckling or by a travelling plastic knuckle mechanism. Drop weight tests have been performed at speeds of up to 6 ms⁻¹, and an elevation in strength with impact velocity is noted. A 3D finite element shell model is needed in order to reproduce the observed behaviours. Additional calculations using an axisymmetric finite element model give the correct collapse modes but are less accurate than the more sophisticated 3D model. The finite element simulations suggest that the observed velocity dependence of strength is primarily due to strain-rate sensitivity of the aluminium sheet, with material inertia playing a negligible role. Finally, it is shown that the energy absorption capacity of the egg-box material is comparable to that of metallic foams.     

Plastic deformation modes of regular hexagonal honeycombs under in-plane biaxial compression

A limit analysis approach is employed to identify the plastic deformation modes of regular hexagonal honeycombs with relatively large wall-thickness-to-length ratios under in-plane biaxial compression. An infinite block of honeycomb material is considered and a representative block consisting of four hexagonal cells is defined when assuming the kinematic admissibility of the modes and a periodic repeatability of the representative block in both spatial directions. In general, three plastic collapse modes are found to be preferable depending on the direction of loading, and in some particular cases they are similar to the modes that occur elastically under stress or strain controlled in-plane biaxial compression. It is shown that the critical forces at the onset of the plastic collapse depend on the assumed constraints for the deformation of the representative block. The results obtained from the theoretical analysis and the numerical simulations are compared and discussed.     

Experimental Study of the Scattering Fields of Elastically and Plastically Bent Steel Pipes in Earth's Magnetic Field

All components of the scattering field of ferromagnetic steel pipes and their crosssection-average magnetization under elastic and plastic bending in Earth's magnetic field have been measured. An analysis of the results obtained on the basis of taking all the components of stresses and induced magnetoelastic increments of magnetization into account has shown that we can determine both the dimensions of plastic strain zones (PSZs) and strengthening zones (under large de ections) and the maximum stresses acting in bending by measuring the scattering field.     

Upper- and lower-bounds for rectangular plates transversely loaded

A new technique, the ‘end-fixity coefficients method’, is developed for the prediction of upper- and lower-bound loads to cause the plastic collapse of thin, uniformly loaded rectangular plates of rigid-perfectly plastic material, which is assumed to flow according to the Johansen yield criterion, re-deriving some well-known results and extending the analysis to other cases of loaded plates. The proposed theory has unified application for the analysis of plate bending, under various boundary conditions, taking into consideration the clamping conditions of plate sides.