Effects of boundary conditions on testing of pipes and finite element modelling

The design of many submarine pipelines, especially for operating in deep water, relies on accurate test results for the local buckling collapse of pipes subjected to bending loading. Recent test results have shown apparently anomalous values of axial tensile and compressive strains in comparison to the values that would be expected on the basis of simple bending theory. This could have important consequences for the efficacy of the design factors derived using these anomalous results. Examples of anomalous test results are given in the paper and the cause of the differences between the strain values obtained in the tests and those expected on the basis of simple bending theory are explained using finite element modelling.The major point is that the general application of the simplified engineering theory of bending can be erroneous when ovalisation is imposed or, on the contrary, the boundary conditions of the section are restrained from ovalising deformations.This is a crucial limit state for the design of onshore and offshore pipelines.     

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.     

Efficient and reliable analysis of structural collapse by using a DQFEM along with a GSR-based accelerated equilibrium iteration procedure

The differential quadrature finite element method which uses the differential quadrature techniques to the finite element discretization is used to analyze the static linear or non-linear elastic–plastic collapse of structural problems. The incremental loading procedure in conjunction with the use of equilibrium iteration is used to update the response history. The equilibrium iteration can be carried out by using the global secant relaxation-based accelerated constant stiffness iteration procedure which is efficient and reliable even the load stage is up to the near collapse level. Sample problems are analyzed. Numerical results demonstrate the algorithm.     

Uncoupled/coupled buckling response of piezothermoelastic composite plates

A geometric nonlinear finite element formulation for piezothermoelastic composite laminates using first-order shear deformation theory (FSDT) is presented to solve mechanically and self-strain loaded smart composite plate buckling problems. Green–Lagrange strain–displacement equations consistent with von Kármán geometric nonlinearity are used. Mixed finite elements using hierarchic Lagrangian interpolation functions are used for the membrane/bending displacements and electric potential variations; transverse shear stress resultants at the Gauss quadrature points use standard Lagrangian functions. Eigenvalue analysis is used to determine the laminate buckling load magnitudes and corresponding mode shapes. A primary purpose of this investigation on the buckling behavior of smart composite plates is to demonstrate the impact of the direct piezoelectric effect. Thermal buckling study includes rectangular and circular plate geometries.     

Effects of composite fiber orientation on wind turbine blade buckling resistance

This paper utilized the inherent directional properties of composite materials to increase the critical buckling load of a 70 m carbon/glass hybrid wind turbine blade. The effect of changing the fiber orientations of the less stiff, off‐axis glass fiber plies (referred to as stability plies in this paper) was studied via nonlinear finite element buckling simulations. The orientation of the stability plies was found to influence the onset of the Brazier effect, which further influenced blade stability and buckling failure location. Although both blade weight and laminate thickness remained constant, an increase in critical buckling load of 8% was achieved with a negligible change in bending stiffness. The more stable blade allowed for removal of material leading to a decrease in maximum laminate thickness and a drop in blade mass of 3.3%. Modifications to the ply stacking sequence and carbon fiber usage were also considered and were found to affect the buckling load but not necessarily the optimum fiber orientation of the stability plies. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

A strain hardening failure assessment diagram derived from carbon-manganese steel compact tension specimens

A failure assessment diagram is derived from carbon-manganese steel compact tension specimens. The diagram has been determined from an elastic-plastic finite element analysis of a compact tension specimen geometry. The diagram has been validated by using experimental fracture toughness data obtained on the same steel and specimen geometry modelled in the finite element analysis. The plastic collapse load has been determined empirically for this geometry.It is shown that a non-work-hardening failure assessment diagram is not a good representation of the experimental data and that the computed failure assessment diagram is more appropriate for describing the behaviour of the carbon-manganese steel specimens.     

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.     

Limit and plastic collapse loads for un-reinforced mitred bends under pressure and bending

Approximate limit and plastic collapse load solutions for un-reinforced mitred bends under internal pressure and under bending are proposed in this paper, based on three-dimensional finite element analysis and approximate solutions for smooth bends. Solutions are given for single- and multi-mitred bends (mainly for single and double segmented bends) with the pipe mean radius-to-thickness ratio (r/t) ranging from r/t = 5 to r/t = 50, and the bend radius-to-mean radius ratio (R/r) from R/r = 2 to R/r = 4. Internal pressure, in-plane bending and out-of-plane bending loads are considered, but not their combination. It is found that the essential features of limit and plastic collapse loads for mitred bends are similar to those for smooth bends, and thus existing solutions for smooth elbows can be used to construct limit loads and plastic collapse for mitred bends.     

开孔和补强对圆柱壳轴压屈曲的影响分析

  [目的]  早期的圆柱壳轴压屈曲试验结果与理论偏差较大,导致差异的因素较多,其中初始几何缺陷是产生差异的主要因素。  [方法]  文章采用一种专用的轴压屈曲试验平台,可以利用激光位移传感器扫描壳体三维实际形貌。屈曲试验轴压采用液压装置,轴压数据通过称重传感器读取。  [结果]  试验结果表明:开孔降低了圆柱壳轴压屈曲临界载荷,在开孔处插入圆管补强件,提高了圆柱壳轴压屈曲临界载荷。基于壳体形貌实测数据建立了有限元模型,利用Abaqus对圆柱壳、开孔圆柱壳和补强圆柱壳进行非线性屈曲有限元分析。  [结论]  模拟得到的规律与试验规律一致,壳体轴向载荷均是先呈线性增大后减小,开孔圆柱壳轴压屈曲临界载荷最小,含补强件圆柱壳轴压屈曲临界载荷次之,未开过孔的圆柱壳轴压屈曲临界载荷最大。对不同壳体的临界载荷模拟值与试验值进行了比较,其中最小的相对误差只有13.8%。说明运用此方法可以预测壳体轴压屈曲临界载荷,对壳体屈曲设计具有参考价值。     

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.     

The influence of side-grooving on pre-cracked Charpy specimens in bending

Fatigue pre-cracked Charpy specimens are sometimes used to measure the fracture toughness of steels. For most steels the dimensions of the Charpy specimens are insufficient to prevent significant plastic yielding ahead of the crack during a test. A feature of the tests is that stable crack growth results in significant crack front curvature. Side-grooving compact tension specimens has been found to inhibit crack front curvature and promote straight fronted crack growth. This paper investigates the effect of side-groove depth on the fracture behaviour of pre-cracked Charpy specimens.Elastic three-dimensional finite element analyses have been performed to assess the effect of side-groove depth on the compliance, stress state and stress intensity factor.The load displacement behaviour of Charpy specimens has been measured to determine the effect of side-groove depth on the limit load and fracture resistance.Using the finite element and experimental results an expression is derived for calculating the fracture resistance of side-grooved Charpy specimens. The expression is used to determine the critical fracture resistance of 1CrMoV steel at two temperatures using Charpy specimens with and without side-grooves.     

Effect of reinforcement on plastic limit loads of branch junctions

This paper provides effects of reinforcement shape and area on plastic limit loads of branch junctions under internal pressure and in-plane/out-of-plane bending, via detailed three-dimensional finite element limit analysis assuming elastic-perfectly plastic material behaviour. It is found that reinforcement is most effective when (in-plane/out-of-plane) bending is applied to the branch pipe. When bending is applied to the run pipe, reinforcement is less effective when bending is applied to the branch pipe. The reinforcement effect is the least effective for internal pressure.     

Evaluation of local thinned pressurized elbows

Erosion, corrosion or mechanical damage may cause local thinned areas (LTA) in piping and degrade its integrity. Acceptability criteria for LTA are available for straight pipes. However, for elbows, there are few studies. In this paper, the finite element method (FEM) is used to calculate the collapse load of a local thinned pressurized elbow and to analyse the factors influencing the collapse load. Based on the solution of the collapse load of LTA straight pipe, the stress level in an elbow without defects, and finite element analysis results, an analytical solution of the collapse load of LTA pressurized elbow is presented. A method to assess the acceptability of LTA in an elbow is given and compared with FEM results.     

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.     

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.     

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.     

Development of DKT Finite Element Formulation for Thermal Bending of Thin Plate

The finite element formulation for thermal bending analysis of a thin plate due to the temperature gradient through its thickness is presented. The formulation is developed for the Discrete Kirchhoff Triangle (DKT) element to analyze the plate bending behavior under the thermal loading. The finite element load vector is derived in closed-form expressions so that the numerical integration is not required. Solution accuracy of the developed DKT finite element is evaluated by several examples. Performance of the developed DKT finite element is also compared with the effective nonconforming triangular element (BCIZ element). Results show that the developed DKT finite element formulation provides high solution accuracy for analysis of plate bending problem under thermal loading.     

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.     

基于解析位移形函数的改进风力机叶片梁单元

为提高空间梁单元在风力机叶片结构计算方面的精度,提出一种基于解析位移形函数的改进空间梁单元.首先考虑叶片截面偏心的影响,从空间Timoshenko梁的平衡方程出发,构建弯曲位移的解析解插值函数.根据弯曲位移与横向位移和剪切变形的关系,得到横向位移和剪切角的形函数.采用有限元理论,得到改进风力机叶片梁单元的刚度矩阵和质量...