Plastic limit loads of defective pipes under combined internal pressure and axial tension

In this paper, a finite element mathematical programming formulation is presented for the statical limit analysis of 3-D perfectly plastic structures. 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 pipes under combined internal pressure and axial tension. 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 pipes are investigated and evaluated.     

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.     

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。     

Lateral crushing of square and rectangular tubes by non-orthogonally placed narrow width indenters

A study of the collapse behaviour of square or rectangular tubes subjected to transverse loading by narrow width indenters, placed in orthogonal and non-orthogonal positions is presented. Experiments were conducted on as-received aluminium tubes, wherein the tubes were compressed in an unsymmetrical and a symmetric arrangement. Typical load-compression curves and histories of the deforming specimens are presented. Based on experimental observations, an analysis which considers the energy absorbed in stationary and rolling plastic hinges is developed for typical cases of the two modes of tube collapse. Computed results of the hinge locations, deforming tube geometry and load-compression curves are presented in each case. These results show good agreement with the experimental observations.     

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.     

Denting of pressurised pipelines under localised radial loading

This paper examines quasi-static denting of buried pipelines under lateral loading from excavator machinery fitted with rectangular cross-section bucket teeth. A semi-analytical solution for the load-deflection response under this loading case is presented. Finite-deflection limit analysis is used to describe the plastic behaviour, while standard elastic shell theory is used to describe the elastic response of a pipeline. When calibrated against numerical results, the combination of these two analytical methods enables the entire load deflection history of a pipeline indentation to be described. This method is verified by comparison with finite element results and with experiment. For the range of geometries examined here, the accuracy of the analytical procedure exceeds that of currently available methods.     

Rapid analysis of plate collapse by live-energy minimisation

An efficient method is developed for the accurate collapse analysis of thin steel plates subjected to in-plane compression. The numerical technique is based on a variational principle in which a particular energy function is minimised within a Rayleigh-Ritz type of procedure. The stress-strain behaviour of the material is calculated from a plastic flow theory. The method is presented, verified, and compared with previous theoretical work. Preliminary results for the biaxial loading case are reported.     

Elastic–plastic beam-on-foundation under quasi-static loading

An elastic–plastic discrete spring model is developed to represent the mechanical behavior of an elastic–plastic beam-on-foundation (BoF) system, and an analytical procedure of analyzing the BoF under general quasi-static loading is formulated. The paper describes a detailed numerical simulation and analysis for the case of a BoF subjected to a concentrated force at the mid-span, and various plastic collapse mechanisms of BoFs are identified. Two peculiar phenomena, i.e. the migration of plastic hinge in the beam and the successive propagation of plastic zone in the foundation, are demonstrated. It is found that any elastic, perfectly plastic BoF system can be characterized merely by three non-dimensional parameters, but the limit state of a rigid, perfectly plastic BoF is determined by a single non-dimensional parameter only. The non-dimensional relative rigidity of BoF and the ratio of the maximum elastic deformation energies dissipated in the beam and foundation both play important roles in governing the deformation scenario of an elastic–plastic BoF system.     

Flat-topped conical shell under axial compression

Based on experimental observations of a grid-domed textile composite under axial compression, the large deformation mechanisms of a flat-topped conical shell are identified. Accordingly, both elastic model and rigid-plastic model are proposed to describe the collapse process and predict the load–displacement characteristics. In the rigid-plastic analysis, the energies dissipated in bending along plastic hinge lines and in stretching of the thin-wall segments between the plastic hinge lines are taken into account. Analytical expressions describing the load–displacement and energy–displacement relationships during the large deformation process are derived. Illustrated by typical numerical examples, the effects of apical angle of a flat-topped conical shell on its energy absorption capacity are revealed. The respective strain distributions on the conical shell resulted from bending deformation and membrane deformation are presented. A good agreement is shown between the theoretical predictions and experimental results.     

Experimental and theoretical studies on buckling of thin spherical shells under axial loads

In this paper we present experiments, simulation as well as analysis of the collapse behaviour of thin spherical shells under quasi-static loading. Various aluminium spherical shells with variation in geometrical parameters were manufactured by spinning. Experiments were performed on these shells in a universal testing machine and their load–compression histories were obtained on the machine chart recorder. Three-dimensional numerical simulations were carried out for all the specimens tested under quasi-static loading using ANSYS^®. All the stages of collapse of the shell including non-symmetrical lobe formation were simulated. Material, geometric and contact nonlinearities were incorporated in the analysis. The stress–strain curves of standard samples made from the material were used as input. Piecewise linearity was taken in the plastic region of the material curve. Results thus obtained compared with the experiments well.An analysis was also carried out to study the behaviour of shells under axial compression based on the formation of rolling and stationary plastic hinges. These hinges were also simulated numerically and results match the experiments well.     

A denting mechanism for orthogonally stiffened cylinders

A plastic mechanism analysis is derived for an orthogonally stiffened cylindrical shell with lateral line loading at mid-span. In the analysis the shell is assumed to act as a series of rings and longitudinal beams. At finite deflections the beams contain membrane tension forces as well as plastic hinges under the load and at the rings. Several modes of behaviour are identified as the ring frames progressively collapse. The method is correlated with test results for models of three bays length.     

含缺陷自增强厚壁圆筒塑性极限载荷分析

基于有限元理论,建立内壁含椭球形凹坑的厚壁圆筒有限元模型,模拟厚壁圆筒自增强过程的应力应变。采用三种不同的方法计算含凹坑缺陷的自增强厚壁圆筒的结构极限载荷,给出不同尺寸缺陷对极限载荷的影响规律。通过对比自增强与非增强条件下的极限载荷,表明自增强技术不能有效提高厚壁圆筒的极限承载能力,但在结构极限载荷下,含凹坑缺陷的自增强厚壁圆筒存在一个缺陷尺寸相对不敏感区,对提高结构的安全性是有利的。     

The influence of plastic-strain-induced anisotropy modeled as combined isotropic-kinematic hardening in the tension-torsion straining problem (I)

In order to express the plastic-strain-induced anisotropy at finite deformation of ductile metals, a combined isotropic-kinematic hardening model which is a particular form of anisotropic hardening, is an appropriate model because of its simple and convenient mathematical formulation. This paper examines the applicability of the model in the computation of general straining problems by performing a numerical tension-torsion test. The anisotropy generated by plastic flow is expressed by back stress. The evolution equation contains form invariant isotropic functions of plastic strain rate and back stress and also involves the spin associated with induced anisotropy. A numerical fitting procedure allowed us to show that circules modeled as combined isotropic-kinematic hardening around the loading nose are in good agreement with the experimental yield loci taken from the nonproportional straining. The measure of checking the applicability of combined isotropic-kinematic hardening by analyzing the total stress history has also been demonstrated by simulating an extrusion process using the finite-element method. From the computed results. the angle variations between the principal stress direction and the material direction, initially axial, were observed if they are small enough in the active plastic deformation region to ensure that the stress point will move along the part of the yield locus exhibiting nearly uniform curvature. This indicated that stress and deformation can be predicted with combined isotropic-kinematic hardening as long as the loading is not reversed.     

Advanced applications of BEM to three-dimensional problems of monotonic and cyclic plasticity

An advanced formulation of the boundary-element method (BEM) has been developed for three-dimensional inelastic analysis under both monotonic and cyclic loading. The analysis uses isoparametric shape functions to model complex geometries and rapid functional variations accurately. The numerical integration of the kernels are carried out by devising suitable automatic sub-segmentation which controls the error in the integration. The formulation has been applied to a number of three-dimensional elastoplastic problems involving monotonic and cyclic loading to demonstrate that it can be used for realistic engineering plasticity problems.     

A probe for in situ, remote, detection of defects in buried plastic natural gas pipelines

Several techniques are available to determine the integrity of in situ metal pipeline but very little is available in the literature to determine the integrity of plastic pipelines. Since the decade of the 1970s much of the newly installed gas distribution and transmission lines in the United States are fabricated from polyethylene or other plastic. A probe has been developed to determine the in situ integrity of plastic natural gas pipelines that can be installed on a traversing mechanism (pig) to detect abnormalities in the walls of the plastic natural gas pipeline from the interior. This probe has its own internal power source and can be deployed into existing natural gas supply lines. Utilizing the capacitance parameter, the probe inspects the pipe for flaws and records the data internally which can be retrieved later for analysis.     

The effect of doubly tapered strut morphology on the plastic yield surface of cellular materials

Although the literature on the mechanics of cellular materials is vast, there is no theoretical model to account for the effects of axial yielding of struts aligned to the applied loading direction on the plastic yield surface under multiaxial loading conditions. An anisotropic hexagonal model having tapered strut morphology is developed to show these effects on the plastic yield surface under multiaxial tensile loading condition. This model covers several types of cellular structure such as two-dimensional (2D) hexagonal and square cellular materials, and three-dimensional (3D) hexagonal and rhombic cellular materials of rod-like columnar structure. A tetrahedral element with tapered strut morphology is also used for a foam model to illustrate these effects on the yield surface under axisymmetric loading condition. Plastic collapse due to bending moment in the inclined struts is a dominant mode. However, under multiaxial tensile loading, the collapse due to axial yielding of struts parallel to the loading direction is found to be an important mode. The shape of plastic yield surface was found to depend not only on relative density but also on the strut morphology.     

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.     

Upper-bound limit analysis of a rigid-plastic body with frictional interfaces

A finite element formulation of the upper-bound theorem for rigid-plastic solids, generalized to include interfaces with finite friction, is described. As proved by Collins [J. Mech. Phys. Solids 17, 323 (1969)], the usual definition of a kinematically admissible velocity field is unnecessarily restrictive when the upper-bound theorem is applied to many practical problems. This paper shows that a relaxed inequality can be used successfully to derive upper bounds in the presence of Coulomb friction on interfaces, provided one considers a wide enough class of “admissible” velocity fields.One of the major advantages of using a numerical formulation of the upper-bound theorem is that both complex loading geometry and inhomogeneous material behaviour can be easily dealt with. Using a suitable linear approximation of the yield surface, the application of the necessary boundary conditions, the plastic flow rule and the yield criterion lead to a large linear programming problem. The numerical procedure uses constant-strain triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the finite element mesh. During the solution phase, an active set algorithm is used to solve the linear programming problem.     

Effect of cyclic loading on the yield surface evolution of 18G2A low-alloy steel

Experimental analysis is presented of the plastic properties of 18G2A steel (notation according to Polish Standards) in the as-received state, and of the same material subjected to cyclic predeformation in different directions of the two-dimensional stress space (σ_xx, τ_xy). The analysis was made by studying the position in stress space and by determination of typical dimensions of the yield surfaces. The initial yield surface has been determined using a number of specimens which were loaded up to the plastic range along different stress directions, and this surface was used as the starting point for comparative studies of yield surfaces of the cyclic prestrained material. Cyclic predeformations were induced by loading at ambient temperature. After predeformation, yield surfaces were determined by the technique of sequential probes of the single specimen. The anisotropic yield condition due to Szczepiński was shown to model the experimental results well. Prior cyclic loading induced the softening effect observed during subsequent monotonic loading of the steel in the plastic strain range considered.     

Analysis on collapse strength of casing wear

Carrying capacity of the casing will reduce after the casing is worn, which seriously affects the subsequent well drilling, well completion, oil extraction and well repair. A lot of researches on calculation of casing wear collapse strength have been done, but few of them focus on collapsing failure mechanism, and influencing factors and law of collapse strength. So, significant difference between estimated value and actual value of collapse strength comes into being. By theoretical analysis, numerical simulation and actual test, the collapsing failure mechanism of casing wear as well as the influencing factors and laws of collapse strength are investigated, and the investigation results show that collapse of crescent casing wear belongs to "three hinged" instability. The severely-worn position on the casing is yielded into the plastic zone first then deformed greatly, which causes the plastic instability of the whole structure. The casing wear collapse strength presents changes of exponent, power function and linear trend with the residual casing wall thickness, wear radius and axial load, respectively. When the flexibility is less than 10°/30 m, the borehole bending has less impact on casing collapse strength. Thus, the computation model for the casing wear collapsing strength is established by introducing wear radius coefficient and casing equivalent yield strength, at the same time, the model is tested. The test results show that the relative error for the computation model is less than 5%. The research results provide a basis for design of the casing string strength and evaluation of down-hole safety.