Effects of attached straight pipes on finite element limit analysis for pipe bends

The effect of the length of an attached straight pipe on the plastic limit load of a 90° pipe bend under combined pressure and bending is quantified, based on finite element (FE) limit analyses using elastic–perfectly plastic materials with the small geometry change option. Systematic FE limit analyses of pipe bends with various lengths of the attached pipe are performed. It is shown that the effect of the length of the attached straight pipe on plastic limit loads can be significant, and the limit loads tend to decrease with decrease of the length of the attached straight pipe. In the limiting case of no attachment, the limit loads are found to be close to existing analytical solutions.     

Plastic limit pressures for cracked pipes using finite element limit analyses

Based on detailed finite element (FE) limit analyses, the present paper provides approximations for plastic limit pressure solutions for plane strain pipes with extended inner axial cracks; axi-symmetric (inner) circumferential cracks; axial through-wall cracks; axial (inner) surface cracks; circumferential through-wall cracks; and circumferential (inner) surface cracks. In particular, for surface crack problems, the effect of the crack shape, semi-elliptical or rectangular, on the limit pressure is quantified. Comparisons with existing analytical and empirical solutions show a large discrepancy for short circumferential through-wall cracks and for surface cracks (both axial and circumferential). Being based on detailed 3D FE limit analysis, the present solutions are believed to be accurate, and thus to be valuable information not only for plastic collapse analysis of pressurised piping but also for estimating non-linear fracture mechanics parameters based on the reference stress approach.     

Transient conjugated heat transfer in thick walled pipes with convective boundary conditions

Transient conjugated heat transfer for laminar flow in the thermal entrance region of pipes is investigated by considering two dimensional wall and axial fluid conduction. The problem is handled for an initially isothermal, infinitely long, thick-walled and two-regional pipe for which the upstream region is insulated and solved numerically by a finite difference method for hydrodynamically developed flow with a step change in the ambient fluid temperature in the heated downstream region. A parametric study is done to analyse the effects of five defining parameters namely, wall thickness ratio, wall-to-fluid conductivity ratio, wall-to-fluid thermal diffusivity ratio, the Peclet number and the Biot number.     

Thermo-mechanical modelling of a single-bead-on-plate weld using the finite element method

This work describes a three-dimensional thermo-mechanical finite element analysis of a single weld bead-on-plate of austenitic stainless steel performed as part of the NeT programme. The overall aim is to validate the use of finite element (FE) weld simulations to accurately predict residual stress states for use in the assessment of welded components. Here, the final residual stresses in the plate are predicted, which can later be verified through comparison with measured distributions. A one-way coupled analysis is carried out with the thermal and mechanical problems solved in sequence. For the thermal analysis, two approaches are adopted to simulate the welding process. In one case sections of the weld bead's elements are sequentially deposited, while in the other the whole bead is deposited simultaneously. A moving heat source is used to simulate the torch traversal over the weld bead in both cases. Predicted thermal profiles, residual stresses and equivalent plastic strains, due to the welding process are presented at certain locations in the plate.     

Implementation of boundary conditions in pressure-based finite volume methods on unstructured grids

In this study, the implementation of boundary conditions for the Navier–Stokes and the energy equations, including the pressure and pressure correction equations, are presented in the context of finite volume formulation on cell-centered, colocated unstructured grids. The implementation of boundary conditions is formulated in terms of the contribution of boundary face of a cell to the coefficients of the discretized equation for either Dirichlet- or Neumann-type boundary conditions. Open boundaries through which the flow is not fully developed are also considered. In this case, a data reconstruction method is proposed for finding the boundary values of the variables at the correction stage. The validity of implementations is checked by comparing the results with some well-known benchmark problems.     

基于边界元法的二维变截面管道内部噪声传播分析

利用二维边界元计算程序,分别研究了扩张和收缩两种变截面管道内部噪声传播规律。结果表明:采用二次单元边界元方法进行计算时,单元尺寸小于1/6波长可使计算相对误差达到1%以下;变截面腔室长度为半波长整数倍时,变截面腔室前后的声压分布相同,且此时的传递损失最小;变截面管道的收缩比越小或者扩张比越大,对应的传递损失也越大,其消声特性越强;变截面管道的起始变化点对于消声特性没有影响,但透射声压会随之周期性产生峰值点。     

Quasi-steady state temperature distribution in finite regions with periodically-varying boundary conditions

Reed and Mullineux applied in [3] a semi-numerical procedure for determining the quasisteady state solution of periodically varying phenomena. In the present study this problem is reduced to a system of matrix equations without using any approximation. The numerical results are compared with those of [3].     

Large scale multi-zone creep finite element modelling of a main steam line branch intersection

A number of papers detail the non-linear creep finite element analysis of branch pieces. Predominately these models have incorporated only a single material zone representing the parent material. Multi-zone models incorporating weld material and heat affected zones have primarily been two-dimensional analyses, in part due to the large number of elements required to adequately represent all of the zones. This paper describes a non-linear creep analysis of a main steam line branch intersection using creep properties to represent the parent metal, weld metal, and heat affected zone (HAZ), the stress redistribution over 100,000 h is examined. The results show that the redistribution leads to a complex stress state, particularly at the heat affected zone. Although, there is damage on the external surface of the branch piece as expected, the results indicate that the damage would be more widespread through extensive sections of the heat affected zone. This would appear to indicate that the time between damage indications on the surface using techniques such as replication and full thickness damage may be more limited then previously expected.     

The transient heat transfer analysis of solids with radiative boundary condition using finite element analysis

In this work, the system of equations to obtain the temperature distribution within a solid are derived using the finite element analysis. These nonlinear set of algebraic equations are solved using the Gauss-Seidel iteration technique. The results indicate that this method can be a valuable tool in the study of heat transfer process in the metallurgical or other related industries.     

Effects of thermal boundary conditions on natural convection flows within a square cavity

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁵ and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Effect of convection on boundary layer structures in finite thermoelasticity

Abstract

Till now, all of the research on boundary layer structures in thermoelasticity has focused on conduction as the primary mode of heat transfer. In this article, we investigate the additional effect of convection on the deformation field boundary layer structures formed within a thin infinite slab made of a neo-Hookean material. We find that additionally introducing convection in finite thermos-elasticity shifts the boundary layer vertically, while retaining its shape.     

Implementation of boundary conditions and global mass conservation in pressure-based finite volume method on unstructured grids for fluid flow and heat transfer simulations

Proper boundary condition implementation can be critical for efficient, accurate numerical simulations when a pressure-based finite volume methodology is used to solve fluid flow and heat transfer problems, especially when an unstructured mesh is used for domain discretization. This paper systematically addresses the relationships between the flow boundary conditions for the discretized momentum equations and the corresponding conditions for the (Poisson type) pressure-linked equation in the context of a cell-centred finite volume formulation employing unstructured grids and a collocated variable arrangement. Special attention is paid to the treatment of the outflow boundary where flow conditions are either known to be fully developed (if a long enough channel is used) or unknown prior to solution (if a truncated channel is used). In the latter case, due to the singularity of the coefficient matrix of the pressure-linked equation, no pressure or pressure corrector solution can exist without explicitly enforcing global mass conservation (GMC) during each iteration. After evaluating published methods designed to ensure GMC, two new methods are proposed to correct for global mass imbalance. The validity of the overall methodology is demonstrated by solving the evolving flow between two parallel plates and the laminar flow over a backward-facing step on progressively truncated domains. In the latter case, our methodology is shown to handle situations where the outflow boundary passes through a recirculation zone.     

An analytical study of heat transfer in a finite tissue region with two blood vessels and general Dirichlet boundary conditions

Vessel–vessel and vessel–tissue heat transfer rates are defined and explicitly quantified, for the first time, for a uniformly heated, finite, circular tissue region with two arbitrarily imbedded circular vessels and general Dirichlet boundary conditions. These heat transfer rates are obtained using an exact analytical solution for the tissue temperature field that is derived herein. Based on these heat transfer rates two different types of Poisson conduction shape factors (PCSFs) are defined. One is related to the vessel–vessel heat transfer rate (VVPCSF) and the other is related to the vessel–tissue heat transfer rates (VTPCSF). Two, conventional, alternative formulations for the VTPCSFs are studied; one is based on the difference between the average vessel wall and tissue boundary temperatures, and the other on the difference between the average vessel wall and the average tissue matrix temperatures. The effects of the angularly varying, non-uniform boundary conditions, the source term and the diameters and locations of the two vessels on these heat transfer rates and PCSFs are studied for the typical case of vessels cooling a tissue; i.e., when the average vessel wall boundary temperatures are lower than the average tissue boundary temperature. Results show that first, the effects of vessel wall temperature fluctuations on both the vessel–vessel and the vessel–tissue heat transfer rates are significant. Second, unlike the vessel wall temperature fluctuations, fluctuations at the outer tissue boundary affect only the vessel–tissue heat transfer rates. They do not affect the vessel–vessel heat transfer rates. Third, when strong fluctuations are present on the vessel walls and outer tissue boundary the shape factors are dependent on the shape of the fluctuations, and are thus very problem specific. Further, the analytical solution procedure used to derive the solution for the temperature field and the methodology developed to quantify the heat transfer rates are general and can be extended for the case of ‘N’ arbitrarily located vessels.     

Adaptive finite element analysis of axisymmetric freezing

The paper describes an adaptive finite element analysis of the transient axisymmetric freezing process. Adaptivity schemes are applied to both space and time tessellations. Error equidistribution adjusts the nodal positions and Taylor series analysis of time truncation error selects the time step. In implicit time integration, the location of the freezing front and the nodal temperatures at the next time is solved by full Newton all at once. The method appears to be accurate; in cases for which closed-form solutions are available, it agrees well with them. It also avoids the problem found in the Modified Isotherm Migration Method where the freezing front tends to retrogress when solid just forms on the outer surface cooled by convection.     

机车复轨器的有限元分析

复轨器是救援脱轨机车车辆的专用必备装置.在救援过程中,它能引导脱轨机车车辆的轮对滚动到钢轨顶部,复位到钢轨上,从而达到救援排障的目的,此间复轨器须承受较大的载荷.为了达到既满足强度和刚度的要求,又能减轻重量、节约材料等目的,对复轨器作较为精确的应力、位移等分析具有一定的实用价值.本文利用有限元分析软件ANSYS对某公司生产制造的人字型复轨器进行有限元计算分析,并且根据计算分析结果为以后此类复轨器的改进或重新设计提供重要的理论参考和工程实例.人字型复轨器由左"人"右"入"两个单件组成,其结构和组成如图1所示.     

基于参数化有限元分析方法的装配型架优化

装配型架的设计对飞机产品的制造与装配具有重要意义.基于参数化的型架有限元分析法能很好地克服现有装配型架设计方法工作效率低下的弱点.基于飞机装配型架设计的基本原理,在模型简化原则的基础上,将参数化设计与有限元相结合,通过改变型架参数自动生成分析模型,并完成型架有限元分析,从而实现型架骨架的界面优化.该方法在一定程度上提高了型架分析的效率,可缩短实际生产工作周期,避免了大量人力物力的浪费.     

Finite element simulation of welding residual stresses in martensitic steel pipes

Abstract

Finite element (FE) simulations of the welding of two high grade steel pipes are described. The first is a P91 steel pipe welded with a similar P91 weld consumable, and the second is a P92 steel pipe welded with dissimilar nickel–chromium based weld consumables. Both welds are multipass circumferential butt welds, having 73 weld beads in the P91 pipe and 36 beads in the P92 pipe. Since the pipes and welds are symmetric around their axes, the FE simulations are axisymmetric, allowing high FE mesh refinement and residual stress prediction accuracy. The FE simulations of the welding of the P91 and P92 pipes comprise thermal and sequentially coupled structural analyses. The thermal analyses model the heat evolution produced by the welding arc, determining the temperature history throughout the FE models. Structural analyses use the computed temperature history as input data to predict the residual stress fields throughout the models. Post-weld heat treatment (PWHT) of both pipes has also been numerically simulated by assuming that the FE models obey the Norton creep law during the hold time period at 760°C. The residual stresses presented here have all been validated by corresponding experimental measurements. Before PWHT, it has been found that, at certain locations in the weld region and heat affected zone (HAZ) in the pipes, tensile hoop and axial residual stresses approach the tensile strength of the material, presenting a high risk of failure. It has also been found that PWHT substantially reduces the magnitude of residual stresses by varying degrees depending on the material.     

基于显式有限元的机车碰撞模型研究

结合DF8B型机车,利用ANSYS/LS-DYNA软件分别建立了考虑转向架结构和考虑转向架质量的机车以10m/s的速度正面碰撞刚性墙的仿真模型,并对两种模型的仿真分析结果进行了比较。结果表明,考虑转向架实际结构的机车碰撞刚性墙有限元模型,能更准确地模拟机车的正面碰撞过程。