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.     

Limit moment of local wall thinning in pipe under bending

In engineering practice, pipe containing local wall thinning may be subjected to bending load. The existence of local wall thinning on pipe surface impairs the load-carrying capacity of pipe. In order to maintain the integrity of the pipe containing local wall thinning, it is very important to develop a method to evaluate such a pipe with local wall thinning under bending. In this paper, the limit moment of local wall thinning pipe under pure bending is computed employing 3D elastic–plastic finite element analysis. The results show that the limit moment of pipe is affected not only by the width of defect but also by the longitudinal length of defect. When the longitudinal length of defect overpasses some critical value, the results from net-section collapse criterion (NSC) are in very reasonable agreement with the results from finite element analysis. Therefore, the NSC formula can conservatively be used to assess the limit load-carrying capability of local wall thinning pipe under bending.     

On the shakedown analysis of nozzles using elasto-plastic FEA

The performed shakedown calculations of a dished end with a nozzle in the knuckle region with varying internal pressure load, and two cylinder–cylinder intersections with constant moment load and varying internal pressure load are example cases for the application of the check against progressive plastic deformation as stated in the new European UFPV standard, Annex 5.B: “Direct route for design by analysis” (DBA). To calculate the shakedown limits, Melan's (lower bound) shakedown theorem is used. In this context, the usage of the deviatoric maps of stress states to obtain proper self-equilibrating stress fields is shown. Furthermore, some problems and corresponding possible solutions for performing the shakedown check using a finite element model with shell elements are stated and shown in the examples.     

Shakedown limit loads for elbows under internal pressure and cyclic in-plane bending

This paper presents elastic, shakedown and plastic limit loads for 90° elbows under constant internal pressure and cyclic in-plane bending, via finite element (FE) analysis. Effects of the elbow geometry (the bend radius to mean radius ratio and the mean radius-to-thickness ratio) and of the large geometry change are systematically investigated. By normalizing the in-plane bending moment by the plastic limit load solution of Calladine, the shakedown diagram is found to be close to unity up to a certain value of normalized pressure (normalized with respect to the limit pressure) and then to decrease almost linearly with increasing normalized pressure. The value up to which shakedown limit loads remain constant depends on the elbow geometry and the large geometry change effect. Effects of the elbow geometry and the large geometry change on shakedown diagrams are discussed.     

Parametric survey of upper and lower bound limit in-plane bending moments for single mitred pipe bends of various geometries

The problem of limit analysis for a cylinder–cylinder intersection forming a single mitred pipe bend subject to in-plane bending has been investigated. Lower bound analysis with new equations of force and moment equilibrium together with a higher number of parameters resulted in more stability as compared to a previous analysis of the same problem [PhD Thesis, The University of Manchester, 1991]. Concurrently, abaqus finite element plastic collapse moments were obtained as upper bounds to the problem. Two sets of results were compared, showing good agreement with each other. It could be finally concluded that the true limit moments are bounded in between.     

Plastic collapse of pipe bends under combined internal pressure and in-plane bending

Plastic collapse of pipe bends with attached straight pipes under combined internal pressure and in-plane closing moment is investigated by elastic–plastic finite element analysis. Three load histories are investigated, proportional loading, sequential pressure–moment loading and sequential moment–pressure loading. Three categories of ductile failure load are defined: limit load, plastic load (with associated criteria of collapse) and instability loads. The results show that theoretical limit analysis is not conservative for all the load combinations considered. The calculated plastic load is dependent on the plastic collapse criteria used. The plastic instability load gives an objective measure of failure and accounts for the effects of large deformations. The proportional and pressure–moment load cases exhibit significant geometric strengthening, whereas the moment–pressure load case exhibits significant geometric weakening.     

Limit loads for thin-walled piping branch junctions under internal pressure and in-plane bending

The present work presents plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on detailed three-dimensional (3-D) finite element (FE) limit analyses using elastic–perfectly plastic materials. To assure reliability of the FE limit loads, modelling issues are addressed first, such as the effect of kinematic boundary conditions and branch junction geometries on the FE limit loads. Then the FE limit loads for branch junctions under internal pressure and in-plane bending are compared with existing limit load solutions, and new limit load solutions, improving the accuracy, are proposed based on the FE results. The proposed solutions are valid for ratios of the branch-to-run pipe radius and thickness from 0.4 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 10.0 to 20.0.     

A comparison of plastic collapse and limit loads for single mitred pipe bends under in-plane bending

This paper presents a comparison of the plastic collapse loads from experimental in-plane bending tests on three 90° single un-reinforced mitred pipe bends, with the results from various 3D solid finite element models. The bending load applied reduced the bend angle and in turn, the resulting cross-sectional ovalisation led to a recognised weakening mechanism. In addition, at maximum load there was a reversal in stiffness, characteristic of buckling. This reversal in stiffness was accompanied by significant ovalisation and plasticity at the mitre intersection. Both the weakening mechanism and the post-buckling behaviour are only observable by testing or by including large displacement effects in the plastic finite element solution. A small displacement limit solution with an elastic-perfectly plastic material model overestimated the collapse load by more than 40% and could not reproduce the buckling behaviour.     

Plastic limit loads of nozzles in cylindrical vessels under out-of-plane moment loading

The purpose of this paper is to study the plastic limit moment of nozzles in cylindrical vessels with different d/D ratios under out-of-plane moment loading. Three full size test models were designed and fabricated. A 3D nonlinear finite element numerical simulation was also performed. A twice-elastic-slope plastic moment on the nozzles was obtained approximately by use of load–displacement and load–strain curves. The results show that plastic loads determined by test and numerical simulation methods are in good agreement. The results can serve as a basis for developing an advanced design guideline by limit analysis for cylindrical vessels with a nozzle under external loads.     

A numerical method for lower bound limit analysis of 3-D structures with multi-loading systems

The determination of lower bound limit load of 3-D structures is by no means an easy task, especially for complex configurations and loading systems. In our previous work, a numerical method of upper bound limit analysis for 3-D structures with multi-loading systems was proposed. This method combines FEM and mathematical programming technique in an iterative procedure. In the present article, on the basis of the nature of the iterative procedure for upper bound limit analysis, the statically admissible stress fields, which satisfies the equilibrium equation and boundary conditions, are constructed using some intermediate variables obtained by upper bound limit analysis procedure. Moreover, a mathematical programming formulation is set up for the static limit analysis of 3-D structures under multi-loading systems and a direct iterative algorithm used to determine the lower bound limit load multiplier is proposed, which depends on the static theorem of plasticity. The numerical examples are given to demonstrate the applicability of the procedure.     

Moment resistance of steel pipes subjected to combined loads

The first part of this paper provides a review of recent investigations on steel pipes subjected to combined loads. Attention is given to studies involving both numerical and experimental components aimed at quantifying the modified moment resistance of pipes subjected to internal pressure and axial force. The comparison of experimental and finite element results indicate that the nonlinear shell finite element analysis is a reliable tool for predicting moment capacities of pipes. The second part of the paper reports two additional full-scale tests recently conducted at the University of Ottawa aimed at expanding the existing experimental database to pipes subjected to more complex load combinations involving twisting moment and shear (in addition to axial force, internal pressure, and bending). The finite element analysis for both tests is shown to provide excellent predictions of pipe moment capacity. The third part of the paper is a systematic parametric study based on the FEA model verified in previous and present investigations, aimed to assess the ability of pipe sections to attain their modified elastic and/or plastic moment resistance as predicted by analytically derived interaction equations. The parameters investigated are the applied torsion, internal pressure, axial force, and the diameter-to-thickness ratio of the pipe.     

Limit loads for piping branch junctions under internal pressure and in-plane bending—Extended solutions

The authors have previously proposed plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on finite element (FE) limit loads resulting from three-dimensional (3-D) FE limit analyses using elastic–perfectly plastic materials [Kim YJ, Lee KH, Park CY. Limit loads for thin-walled piping branch junctions under internal pressure and in-plane bending. Int J Press Vessels Piping 2006;83:645–53]. The solutions are valid for ratios of the branch-to-run pipe radius and thickness from 0.4 to 1.0, and for the mean radius-to-thickness ratio of the run pipe from 10.0 to 20.0. Moreover, the solutions considered the case of in-plane bending only on the branch pipe. This paper extends the previous solutions in two aspects. Firstly, plastic limit load solutions are given also for in-plane bending on the run pipe. Secondly, the validity of the proposed solutions is extended to ratios of the branch-to-run pipe radius and thickness from 0.0 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 5.0 to 20.0. Comparisons with FE results show good agreement.     

Studies on gasketed flange joints under bending with anisotropic Hill plasticity model for gasket

The behavior of a gasketed flange joint under bending loads has been studied by three dimensional finite element analysis (FEA) and experiments. The in-plane and bending stiffness of spiral wound gaskets are considered using anisotropic Hill plasticity material model. The variation in bolt axial force of joints under bending load predicted by the finite element analysis compares well with the experimental results. The contact stress distribution obtained have significant variation in the pattern from the previous material models and consistent with the results of Bouzid [1] regarding flange rotation.     

GEOMETRICALLY LINEAR ANALYSIS OF THE THERMAL STRESSES IN ONE-SIDED COMPOSITE REPAIRS

This article presents an explicit solution of the thermal stresses in a one-sided composite patch repair, with the patch being orthotropic in both mechanical and thermal properties. The emphasis is placed on the analysis of the bending deformation of the reinforced structure resulting from thermal loading. The reinforced region is represented by an equivalent inclusion that undergoes a combination of in-plane extension and out-of-plane extension. Explicit formulae are derived for the thermal expansion coefficients as well as the bending stiffness and the in-plane extensional stiffness of the equivalent inclusion. The Eshelby inclusion analogy is first extended by postulating uniform bending curvatures and mean strains throughout the inclusion. The correctness of this conjecture is then proved by the satisfaction of force, bending moment, and displacement continuity conditions. Explicit solutions are finally derived for the bending and membrane stresses resulting from thermal loading of an isotropic plate reinforced by a circular patch. It is shown that the present solutions correlate well with the numerical results obtained using fully three-dimensional finite element analysis.     

Plastic collapse moment of 90° long radius elbows with internal circumferential surface crack at intrados under in-plane bending

Piping elbows under in-plane bending moment are vulnerable to cracking. The crack initiates at the surface and eventually reaches through the thickness and may lead to failure. The structural integrity assessment requires knowledge of the limit load. Limit load solutions for elbows with through-wall crack configurations are available in the open literature. But solutions for surface crack are not available. This paper presents a closed form expression for the plastic collapse moment (PCM) of 90°, long radius elbows with circumferential surface cracks at the intrados, under in-plane bending moment. The expression is derived, based on the results of non-linear (geometric and material) FE analyses covering a wide range of geometries and crack sizes. These plastic collapse moments evaluated herein will help in structural integrity assessment.     

A global limit load solution for plates with surface cracks under combined end force and cross-thickness bending

A global limit load solution for rectangular surface cracks in plates under combined end force and cross-thickness bending is derived, which allows any combination of positive/negative end force and positive/negative cross-thickness moment. The solution is based on the net-section plastic collapse concept and, therefore, gives limit load values based on the Tresca yielding criterion. Solutions for both cases with and without crack face contact are derived when whole or part of the crack is located in the compressive stress zone. From the solution, particular global limit load solutions for plates with extended surface cracks and through-thickness cracks under the same loading conditions are obtained. The solution is consistent with the limit load solution for surface cracks in plates under combined tension and positive bending due to Goodall & Webster and Lei when both the applied end force and bending moment are positive. The solution reduces to the limit load solution for plain plates under combined end force and cross-thickness bending when the crack vanishes.     

On nonlinear bending and instability of imperfect cylindrical tubes

In this paper, the nonlinear bending and instability of initial geometrical imperfect cylindrical tubes subjected to pure bending load are studied. The imperfection is assumed to be a small ovality expressed as Timoshenko initial noncircularity function. A set of new nonlinear differential equations is developed, through a virtual work principle with a Lagrange multiplier, and solved asymptotically by means of a perturbation method. The asymptotical expressions for a nonlinear moment–curvature relationship and a critical moment are obtained. The effect of the noncircularity on the bending and instability are examined. The results of numerical calculations are presented by curves and compared with available theoretical and experimental data.     

Reference stress method for evaluation of failure assessment curve of cracked pipes in nuclear power plants

In order to obtain a precise failure assessment curve (FAC) in the R6 defect assessment procedure, it is necessary to evaluate the J-value of cracked components. The reference stress method can be used for estimating J-values. However, the accuracy of estimation depends on the limit load used for evaluating the reference stress. In this study, the applicability of several limit load solutions was investigated through comparison with the results of elastic-plastic finite element analyses (FEA). A pipe containing a circumferential surface crack was analyzed under pure bending load. Six materials used in nuclear power plants were assumed. It was shown that the reference stress method is valid for FAC evaluation. The maximum non-conservativeness caused by using the reference stress method is less than 20% compared to the results obtained by FEA.     

碳纤维复合芯导线输电线路风振响应时域分析

针对碳纤维复合芯导线(ACCC)输电线路的风振响应,采用数值模拟建立输电线路体系有限元模型进行分析,并将得到的位移、弯矩和轴力响应与传统钢芯铝绞线(ACSR)进行对比。结果表明,ACCC导线的抗风性能优于ACSR导线,更适用于高温运行环境和风灾严重地区、大跨越输电线路等频繁承受大风荷载作用的输电线路。     

Simulations and experiments on a 12 kW direct driven PM synchronous generator for wind power

A direct driven permanent magnet (PM) synchronous generator has been designed and constructed and results from the first experimental tests are presented. The generator has been designed using the finite element method (FEM) and dynamic simulations have been performed to study the generator. The simulations are performed by using an electromagnetic model, which is described by a combined field and circuit equation model and is solved in a finite element environment. The stator winding of the generator consists of circular cables and the rotor has surface mounted, arched PMs. A complete experimental setup has been constructed consisting of a motor, a frequency converter, a gearbox and electrical loads. Oscilloscopes are used to measure the voltage and the current for each phase. Measurements have been performed for both full load and no load at rated speed. The harmonic content of the voltage is analyzed and compared to results from simulations. Furthermore, the generated electric power has been calculated from knowing the voltage and current and is compared to the simulated power. The agreement between experimental results and results from simulations based on finite element calculations is very high, especially considering harmonics. Several sources of error are suggested that could cause the small differences between the simulated results and the measured data for the constructed generator.