Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems

In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.

Increment-Dimensional Scaled Boundary Finite Element Method for Solving Transient Heat Conduction Problem

An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method.

Adaptive mixed least squares Galerkin/Petrov finite element method for stationary conduction convection problems

An adaptive mixed least squares Galerkin/Petrov finite element method （FEM） is developed for stationary conduction convection problems. The mixed least squares Galerkin/Petrov FEM is consistent and stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. Using the general theory of Verfiirth, the posteriori error estimates of the residual type are derived. Finally, numerical tests are presented to illustrate the effectiveness of the method.

Radiation heat transfer model for complex superalloy turbine blade in directional solidification process based on finite element method

For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

Numerical Analysis on the Static Performance of Gas Journal Bearing by Using Finite Element Method

In this paper,finite element method is used to calculate the static performance of gas journal bearing,in which rotation speed term is introduced into the stiffness matrix of linear triangular element to realize the performance calculation of the bearing with rotation speed.The results indicate that the average gas film thicknesses corresponding to the maximum load capac-ity and stiffness,and the minimum attitude angle increase with the growth of orifice diameter.Load capacity and stiffness significantly improved with the increase of rotation speed,eccentricity ratio and supply pressure when the bearing has thin average gas film thickness.Attitude angle increases with the growth of rotation speed,while the growth rate slows down or even decreases at high speed.The most effective way of reducing attitude angle is to increase supply pressure.It can be found that rotation speed affects attitude angle through changing gas pressure difference between two orifices,while other parameters have the same effect by changing gas pressure at orifice outlet.

Damage prediction for magnesium matrix composites formed by liquid-solid extrusion process based on finite element simulation

A damage prediction method based on FE simulation was proposed to predict the occurrence of hot shortness crocks and surface cracks in liquid-solid extrusion process. This method integrated the critical temperature criterion and Cockcroft ＆ Latham ductile damage model, which were used to predict the initiation of hot shortness cracks and surface cracks of products, respectively. A coupling simulation of deformation with heat transfer as well as ductile damage was carried out to investigate the effect of extrusion temperature and extrusion speed on the damage behavior of Csf/AZ91D composites. It is concluded that the semisolid zone moves gradually toward deformation zone with the punch descending. The amplitude of the temperature rise at the exit of die from the initial billet temperature increases with the increase of extrusion speed during steady-state extrusion at a given punch displacement. In order to prevent the surface temperature of products beyond the incipient melting temperature of composites, the critical extrusion speed is decreased with the increase of extrusion temperature, otherwise the hot shortness cracks will occur. The maximum damage values increase with increasing extrusion speed or extrusion temperature. Theoretical results obtained by the Deform^TM-2D simulation agree well with the experiments.

CRITERIA FOR FINITE ELEMENT ALGORITHM OF GENERALIZED HEAT CONDUCTION EQUATION

To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation, the author and Xiao have put forward two new concepts of monotonies and have derived and proved several criteria. This idea is borrowed here to deal with generalized conduction equation and finite element criteria for eliminating oscillation and overbounding are also presented. Some new and useful conclusions are drawn.

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.

Finite Element Analysis of Push-Out Test of SiC Fiber Reinforced Titanium Matrix Composites

Based on the interphase layer model and the spring layer model, an improved interface model was developed to evaluate the interfacial shear strength of Titanium matrix composites(TMCs) and to analyze the effects of various parameters on the interfacial properties. The results showed that the improved interface model is more suitable for calculating the interfacial properties of SiC fiber reinforced titanium matrix composites. The interfacial shear strength of SiC/Timetal-834 predicted is 500 MPa. In addition, in order to better understand the interfacial properties of composites, some push out phenomenon were analyzed.

An AMR Capable Finite Element Diffusion Solver for ALE Hydrocodes

We present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffu- sion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L2 norm.

Finite Element Analysis of the Material’s Area Affected during a Micro Thermal Analysis Applied to Homogeneous Materials

Micro-thermal analysis (μ-TA), with a miniaturized thermo-resistive probe, allows topographic and thermal imaging of surfaces to be carried out and permits localized thermal analysis of materials. In order to estimate the effective volume of material thermally affected during this localized measurement, simulations, using finite element method were used. Several parameters and conditions were considered. So, thermal conductivity was found to be the driving physical parameter in thermal exchanges. Indeed, the evolution of the heat affected zone (HAZ) versus thermal conductivity can well be described by a linear interpolation. Therefore it is possible to estimate the HAZ before experimental measurements. This result is an important progress especially for accurate interphase characterization in heterogeneous materials.

基于Lagrange-Galerkin有限元方法的焊接热循环轻量化求解

焊接热循环的干扰因素多、变化速度快、影响范围广,常需要对其进行即时预测与控制,以保证焊接质量。以焊缝中心温度分布与变化为研究对象,将其简化为一维焊接热循环瞬态热传导问题,并基于Lagrange-Galerkin有限元方法,进行算域离散与插值。开发了一种轻量化的焊接热循环求解算法,研究不同时刻下焊缝中心温度分布曲线与变化曲线的即时变化。以镍基Inconel 718合金2 mm薄板对接接头为例,进行数值模拟实例演算,结果表明计算耗时约0.41~0.72 s,满足数据与轻量化计算的要求。

地—井瞬变电磁三维各向异性响应特征研究

地—井瞬变电磁法由于抗干扰能力强、响应信号明显等优势而应用广泛。在深部矿产资源调查和地质构造勘查等任务中,多个油气储存在层理发育的沉积岩地区大多数情况下表现为电各向异性,但是目前地—井瞬变电磁反演算法均基于各向同性模型,传统反演成像技术不再适用。为了分析地层电导率各向异性对地—井瞬变电磁勘探结果的影响,对各向异性介质模型研究其电磁响应特性。基于各向异性介质的电导率张量,提出了一种基于有限元方法的三维分析模型,采用PARDISO求解器进行求解。针对多个各向异性角度的情况模拟了各向异性介质的瞬变电磁响应,分析介质各向异性对电磁波传播规律的影响,探讨了各向异性瞬变电磁响应特征。研究结果表明:在垂直各向异性介质中,电磁波传播方向垂直于电导率最大的方向时,电磁响应变化最明显;电磁波传播方向平行于电导率最大的方向时,电磁响应变化最弱。在水平各向异性介质中,电磁波垂直于电导率最小的方向时,电磁响应变化最明显;电磁波平行于电导率最小的方向时,响应变化较弱。最后,针对地—井瞬变电磁方位测井,分析了发射源沿不同方向条件下各向异性地层和异常体模型的电磁响应,结果表明其瞬变电磁响应特征与发射源的方向有关,且对于主轴各向异性异常体,发射源方向的选择直接影响对异常体各向异性方向的判断。该研究结论对油气开发地球物理勘探方法的研究具有一定的参考价值。

基于声电类比的低频消音结构优化设计

基于声电类比,设计了与电滤波器性能相似的低频消音结构,并结合传递矩阵法和模拟退火法,构造了声学结构的优化设计策略。首先,采用归一化方法,以四阶切比雪夫高通电滤波器为基准,设计了电学带阻滤波器;然后,基于声电类比,将电路中的电感电容转换为声学结构中的细管和圆柱腔,构造了消音结构原型,并利用传递矩阵法,建立其数学模型,推导声波传递损失表达式;最后,结合声学结构的数学模型和模拟退火法,以有效衰减带宽最大为目标,以消音结构的尺寸参数为变量,对原型结构进行优化设计。结果表明:基于声电类比,能获得合理的消音结构原型,克服了仅依靠经典消音结构进行设计的局限;结合推导的传递损失数学模型和模拟退火法,对消音结构原型进行参数优化,能显著提高其消音效果,表现在传递损失超过20 dB的带宽拓宽至410~2 165 Hz,是优化前带宽的202%,特别是优化后的结构克服了原型结构在466~537 Hz频率内不能实现有效消音的缺陷,获得了连续的大跨度有效带宽,且传递损失曲线平均增幅达22.8%。

磁矢量势的全球电磁感应时间域三维有限元正演计算方法

全球电磁感应测深方法能获得地球深部电导率结构分布,目前被广泛应用于地球内部结构与热状态研究.地磁台站与地磁卫星观测的电磁感应数据为时间序列信号,在时间域分析全球电磁感应数据,特别是分析频谱极宽的磁暴脉冲响应,具有天然的优势.然而,当前的全球电磁感应数据解释技术一般在频率域进行,缺少时间域中的研究成果.为了弥补缺少时间域全球电磁感应数据解释方法的问题,本文开发了一种基于磁场矢量势的全球电磁感应时间域三维有限元并行正演求解方法,具备高精度快速计算源于地球外部时变电流源的地球感应电磁场时间序列的能力,特别适合于计算与分析频谱极宽的磁暴脉冲电磁感应时变响应.首先,建立基于磁场矢量势的全球电磁感应时间域微分控制方程,结合磁层外部电流源的物理属性建立边界条件和初始条件,从而构建出全球电磁感应时间域初始边界值问题.然后,利用四面体矢量有限元技术和无条件稳定的隐式后退欧拉公式,分别实现磁场矢量势的空间域和时间域离散,进而获得不同时刻的实系数大型有限元线性方程组,借助于高性能并行直接求解器,快速高精度地求解不同时刻的磁场矢量势与感应磁场.最后,利用理论模型验证本文算法的正确性.利用Dst磁暴环电流指数建立的时间域电流源与真实地球三维电性模型,研究"澳科一号"后续卫星200 km轨道对中国和澳大利亚下方地幔转换带高导体的探测能力,结果表明这些地幔转换带异常体在200 km卫星轨道高度能产生明显异常.综上所述,本文开发的时间域全球电磁感应方法不仅具备精确快速计算全球感应电磁场时间序列响应的能力,还能为反演与解释"澳科一号"等我国地磁卫星观测数据提供技术支持.

Thermal residual stresses and stress distributions under tensile and compressive loadings of short fiber reinforced metal matrix composites

The thermal residual stresses and the stress distributions of short fiber reinforced metal matrix composite under tensile and compressive loadings were studied using large strain axisymmetric elasto plastic finite element method. It is demonstrated that the thermal residual stresses can result in asymmetrical stress distributions and matrix plasticity. The thermal residual stresses decrease the stress transfer in tension and enhance the stress transfer in compression. The fiber volume fraction has more important effects on the thermal residual stresses and the stress distributions under tensile and compressive loadings than the fiber aspect ratio and the fiber end distance. [

基于综合优化法的矮塔斜拉桥成桥索力优化

为确定矮塔斜拉桥合理成桥索力,提出一种索力综合优化法。该方法以影响矩阵法为基础,采用数据标准化法将2种或以上不同类型的离散数据变为无量纲的统一化数据,以结构控制截面位移及弯矩综合最小为目标进行索力求解。以南京地铁宁句线矮塔斜拉桥为算例,采用最小弯曲能量法、刚性支承连续梁法和综合优化法对成桥状态的索力进行计算,将计算结果与原设计成桥索力进行对比。结果表明:对于矮塔斜拉桥,在恒载作用下,采用综合优化法计算得到的索力及主梁弯矩分布最为合理;在运营阶段,综合优化法计算得到的索力与原设计索力相比,主梁上、下缘最大压应力分别降低3.3%、3.8%,并且主梁应力分布更优。

高压电力电缆土壤导热系数的反演与计算

温度和载流量是电缆运行状态及热稳定极限的重要指标参数,精确的土壤导热系数是电缆温度场准确计算的前提和基础。土壤导热系数受多种因素影响,呈现较大差异性和不确定性。为精确计算高压电力电缆实际运行工况下的温度场和载流量,本文提出了电力电缆实时土壤导热系数逆问题的数学模型和计算方法。开发了电缆表皮温度测量的分布式光纤测温系统,基于电缆表面采样点实时温度构建了分层土壤实时导热系数反演数学模型,并提出逆问题求解的改进遗传算法。实例计算结果表明,应用本文成果计算的实时或动态载流量比标称载流量高出38.08%。

Numerical well test for well with finite conductivity vertical fracture in coalbed

A new well test model is developed for the hydraulic fractured well in coalbed by considering the following aspects： methane desorption phenomena, finite conductivity vertical fractures, and asymmetry of the fracture about the well. A new parameter is introduced to describe the storage of the fracture, which is named as a combined fracture storage. Another new concept called the fracture asymmetry coefficient is used to define the asymmetry of the fracture about the well. Finite element method （FEM） is used to solve the new mathematical model. The well test type curves and pressure fields are obtained and analyzed. The effects of the combined fracture storage, desorption factor, fracture conductivity, and fracture asymmetry coefficient on the well test type curves are discussed in detail. In order to verify the new model, a set of field well test data is analyzed.