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三维薄结构热传导问题分层二次元方程的多水平方法 预览
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作者 张申 肖映雄 郭瑞奇 《应用数学和力学》 CSCD 北大核心 2018年第6期700-713,共14页
在利用有限元法对三维薄结构进行分析时,为了减少单元数目,常采用六面体薄单元,相应的高阶单元在计算精度、抗畸变程度等方面具有明显优势.但与低阶元相比,高阶单元需要更多的计算机存储空间,离散化线性系统具有更高的计算复杂性,并且... 在利用有限元法对三维薄结构进行分析时,为了减少单元数目,常采用六面体薄单元,相应的高阶单元在计算精度、抗畸变程度等方面具有明显优势.但与低阶元相比,高阶单元需要更多的计算机存储空间,离散化线性系统具有更高的计算复杂性,并且系数矩阵是严重病态的,采用通常的求解方法其效率将大大降低.该文针对三维薄结构稳态热传导问题,利用局部块Gauss-Seidel光滑子和基于"距离矩阵"的DAMG法,为其分层二次元离散系统设计了一种具有更好计算效率和鲁棒性(robustness)的多水平方法.由于采用了分层基,程序实现中不再需要建立判定未知数变量指标与所属几何节点类型对应关系的代数判据,网格转换算子的构造也变得非常简单,从而大大提高了运算效率.数值实验结果验证了该方法的有效性和鲁棒性. 展开更多
关键词 热传导问题 薄体结构 分层二次元 多水平方法 代数多重网格法
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The PDE-Constrained Optimization Method Based on MFS for Solving Inverse Heat Conduction Problems
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作者 Yongfu ZHANG Chongjun LI 《数学研究及应用:英文版》 CSCD 2018年第3期303-330,共28页
关键词 热传导问题 PDE 优化 MFS NEUMANN 边界条件 产生系统 数字测试
三维薄结构热传导问题Wilson元离散系统的DAMG法 预览
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作者 张申 肖映雄 郭瑞奇 《广西大学学报:自然科学版》 北大核心 2017年第4期1291-1298,共8页
对三维薄结构问题,在进行网格剖分时,为了减少单元数目,常采用六面体薄单元,相应的高阶单元在计算精度、抗畸变程度等方面具有明显优势,但也大大增加了计算复杂性。Wilson元通过在单元内部设置附加自由度的方式来提高完全多项式的次数,... 对三维薄结构问题,在进行网格剖分时,为了减少单元数目,常采用六面体薄单元,相应的高阶单元在计算精度、抗畸变程度等方面具有明显优势,但也大大增加了计算复杂性。Wilson元通过在单元内部设置附加自由度的方式来提高完全多项式的次数,具有计算精度高且自由度又少的优点,因而在实际计算中被广泛使用。但要提高这种非协调元分析效率还需为相应离散系统设计好的求解方法。本文针对一般变系数三维薄结构热传导问题,建立了Wilson元计算格式,并将DAMG法应用于与8节点三线性元谱等价的Wilson元离散系统的求解。数值实验结果表明,与常用方法相比,基于"距离矩阵"的代数多重网格(DAMG)法具有更好的计算效率和鲁棒性(robustness)。 展开更多
关键词 热传导问题 薄结构 WILSON元 距离矩阵 代数多重网格法
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绝热裂纹对热传导影响的近场动力学研究
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作者 Migbar Assefa Zeleke 刘立胜 +1 位作者 赖欣 廖洋 《轻工科技》 2017年第5期42-43,共2页
提出一种基于态的近场动力学(Peridynamics,PD)理论来解决带有不连续现象的热传导问题。本文首先发展了热传导的PD公式,接着进行相关的数值模拟工作。本文采用有限元的数值解证明了PD理论模型的有效性。结果表明,有限元法的数值模拟和... 提出一种基于态的近场动力学(Peridynamics,PD)理论来解决带有不连续现象的热传导问题。本文首先发展了热传导的PD公式,接着进行相关的数值模拟工作。本文采用有限元的数值解证明了PD理论模型的有效性。结果表明,有限元法的数值模拟和近场动力学的数值模拟结果吻合良好,证明近场动力学理论在描述热场中不连续问题的适用性。 展开更多
关键词 热传导问题 近场动力学 裂纹
A new algorithm of global tightly-coupled transient heat transfer based on quasi-steady flow to the conjugate heat transfer problem 预览
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作者 Fanchao Meng Sujun Dong +1 位作者 Jun Wang Dechun Guo 《力学快报:英文版》 CAS CSCD 2016年第5期233-235,共3页
Concerning the specific demand on solving the long-term conjugate heat transfer(CHT) problem,a new algorithm of the global tightly-coupled transient heat transfer based on the quasi-steady flow field is further put fo... Concerning the specific demand on solving the long-term conjugate heat transfer(CHT) problem,a new algorithm of the global tightly-coupled transient heat transfer based on the quasi-steady flow field is further put forward.Compared to the traditional loosely-coupled algorithm,the computational efficiency is further improved with the greatly reduced update frequency of the flow field,and moreover the update step of the flow field can be reasonably determined by using the engineering empirical formula of the Nusselt number based on the changes of the inlet and outlet boundary conditions.Taking a duct heated by inner forced air flow heating process as an example,the comparing results to the tightly-coupled transient calculation by Fluent software shows that the new algorithm can significantly improve the computational efficiency with a reasonable accuracy on the transient temperature distribution,such as the computing time is reduced to 22.8% and 40% while the duct wall temperature deviation are 7% and 5% respectively using two flow update time step of 100 s and 50 s on the variable inlet-flow rate conditions. 展开更多
关键词 耦合算法 共轭传 紧耦合 瞬态热传导 热传导问题 稳态流动 FLUENT软件 稳态流场
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Finite Element Method Formulation in Polar Coordinates for Transient Heat Conduction Problems
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作者 Piotr Duda 《热科学学报:英文版》 SCIE EI CAS CSCD 2016年第2期188-194,共7页
The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method(F... The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method(FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method. 展开更多
关键词 瞬态温度分布 有限元法 极坐标系 热传导问题 坐标系统 边界条件 文件显示 试验验证
Statistical second-order two-scale analysis and computation for heat conduction problem with radiation boundary condition in porous materials
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作者 杨志强 刘世伟 孙毅 《中国物理B:英文版》 SCIE EI CAS CSCD 2016年第9期189-197,共9页
This paper discusses a statistical second-order two-scale(SSOTS) analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configurat... This paper discusses a statistical second-order two-scale(SSOTS) analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configuration for the structure with random distribution is briefly characterized.Secondly,the SSOTS formulae for computing the heat transfer problem are derived successively by means of the construction way for each cell.Then,the statistical prediction algorithm based on the proposed two-scale model is described in detail.Finally,some numerical experiments are proposed,which show that the SSOTS method developed in this paper is effective for predicting the heat transfer performance of porous materials and demonstrating its significant applications in actual engineering computation. 展开更多
关键词 热传导问题 多孔材料 计算传 二阶分析 边界条件 统计 辐射 预测算法
热传导问题有限元线法平面高精度曲线曲边单元研究 预览 被引量:3
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作者 张俊哲 徐冰 高建岭 《北方工业大学学报》 2016年第3期85-88,29共5页
本文首次将3次B样条插值基函数引入到平面温度场的单元映射中,建立了有限元线法平面高精度曲线曲边单元;以平面高精度曲线曲边单元的单元映射及泛函变分为理论基础,运用FORTRAN语言进行相关程序TFEMOL3.0的开发;将程序计算得到的数值解... 本文首次将3次B样条插值基函数引入到平面温度场的单元映射中,建立了有限元线法平面高精度曲线曲边单元;以平面高精度曲线曲边单元的单元映射及泛函变分为理论基础,运用FORTRAN语言进行相关程序TFEMOL3.0的开发;将程序计算得到的数值解与解析解进行对比.结果表明:有限元线法平面高精度曲线曲边单元适用性良好,在解决不规则平面热传导问题上,单元划分较简单,具有较高的计算精度. 展开更多
关键词 热传导问题 有限元线法 平面高精度曲线曲边单元 三次样条
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Model of temperature field for the preparation process of melt-spun NdFeB powders
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作者 赖彬 李岩峰 +4 位作者 王会杰 李安华 朱明刚 李卫 张跃 《中国稀土学报:英文版》 SCIE EI CAS CSCD 2014年第6期514-520,共7页
Melt-spun ribbons which are the important raw material for hot-deformed magnets can be prepared by single-roller melt-spinning. In order to prepare well-structured ribbons, the model of temperature field for single-ro... Melt-spun ribbons which are the important raw material for hot-deformed magnets can be prepared by single-roller melt-spinning. In order to prepare well-structured ribbons, the model of temperature field for single-roller melt-spinning process was constructed in this work. The heat conduction in this process was simplified as one dimensional heat conduction problem. It was shown by modeling that, the temperature field in the melt-spinning before solidification in this model could be described as this equation T(x,t)=Tmoexp[–k(x–x0)–k2αt]+T0. The temperature T(x,t) of the alloy melts decreased with increased position x and cooling time t exponentially from the wheel-free surface to the wheel-side surface. The constant k determined the decrease speed of alloy temperature T(x,t), which was proportional to the interfacial heat transfer coefficient h and the interfacial area of heat conduction A0, but inversely proportional to the thermal conductivity K. x0 was the thickness of the alloy melt. With increased x0, the temperature difference between wheel-free surface and the wheel-side surface became larger, which would lead to larger difference in grain size. In experiments, the influence of melt-spinning process parameters on the temperature field model was discussed, such as cooling roller materials, wheel speed, and so on. Melt-spun ribbons prepared by single-roller melt spinning at different wheel speed were investigated and magnetic properties of die-upset magnets from melt-spun ribbons on different cooling roller were analyzed. The variation of grain size in the depth direction consisted with temperature field model. This model provided directions for the preparation of melt-spun ribbons with uniformly distributed fine grains, which were very necessary for producing hot-deformed magnets with high magnetic performance. 展开更多
关键词 温度场模型 制备工艺 钕铁硼粉末 熔纺 车轮速度 热传导问题 界面热传导 变形磁体
Fuzzy finite difference method for heat conduction analysis with uncertain parameters 预览 被引量:1
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作者 Chong Wang Zhi-Ping Qiu 《力学学报:英文版》 SCIE EI CAS CSCD 2014年第3期383-390,共8页
A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the physical parameters and initial/boundary conditions.In virtue of... A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the physical parameters and initial/boundary conditions.In virtue of the level-cut method,the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations.New stability analysis theory suited to fuzzy difference schemes is developed.Based on the parameter perturbation method,the interval ranges of the uncertain temperature field can be approximately predicted.Subsequently,fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem.Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems. 展开更多
关键词 模糊不确定性 热传导问题 有限差分法 不确定参数 边界条件 物理参数 数字技术 离散方程
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Sobolev方程的基于H^1-Galerkin混合方法的新分裂格式 被引量:2
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作者 王金凤 刘洋 +1 位作者 李宏 牟森 《高等学校计算数学学报》 CSCD 北大核心 2014年第1期32-48,共17页
Sobolev方程是一类重要的发展型偏微分方程,在流体穿过裂缝岩石的渗透理论、不同介质的热传导问题、土壤中湿气的迁移问题等物理方面都有着十分广泛应用.
关键词 SOBOLEV方程 分裂格式 混合方法 偏微分方程 热传导问题 渗透理论 流体 介质
复合材料板热传导问题的二阶双尺度算法 预览 被引量:1
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作者 曹俊英 王自强 《贵州科学》 2014年第3期17-20,共4页
给出了具有三维周期结构的复合材料板热传导问题的二阶双尺度算法.首先,从三维的复合材料板模型出发定义局部单胞函数.根据得到的局部单胞函数计算出等效的均匀化参数,进而得到均匀化方程.其次,利用温度的积分投影近似求解均匀化方程的... 给出了具有三维周期结构的复合材料板热传导问题的二阶双尺度算法.首先,从三维的复合材料板模型出发定义局部单胞函数.根据得到的局部单胞函数计算出等效的均匀化参数,进而得到均匀化方程.其次,利用温度的积分投影近似求解均匀化方程的均匀化解.最后,利用均匀化解和局部单胞函数构造出复合材料板热传导问题的二阶双尺度近似解. 展开更多
关键词 复合材料板 热传导问题 二阶双尺度算法 均匀化
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基于无网格自然邻接点Petrov-Galerkin法求解带源参数瞬态热传导问题 预览
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作者 李庆华 陈莘莘 《动力学与控制学报》 2014年第2期178-182,共5页
基于无网格自然邻接点Petrov-Galerkin法,本文建立了一种求解带源参数瞬态热传导问题的新方法。为了克服移动最小二乘近似难以准确施加本质边界条件的缺点,采用了自然邻接点插值构造试函数。在局部多边形子域上采用局部Petrov-Galerki... 基于无网格自然邻接点Petrov-Galerkin法,本文建立了一种求解带源参数瞬态热传导问题的新方法。为了克服移动最小二乘近似难以准确施加本质边界条件的缺点,采用了自然邻接点插值构造试函数。在局部多边形子域上采用局部Petrov-Galerkin方法建立瞬态热传导问题的积分弱形式。这些多边形子域可由Delaunay三角形创建。时间域则通过传统的两点差分法进行离散。最后通过算例验证了该数值算法的有效性和正确性。 展开更多
关键词 热传导问题 源参数 无网格法 局部Petrov-Galerkin法 自然邻接点插值
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The improved element-free Galerkin method for three-dimensional transient heat conduction problems 被引量:4
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作者 ZHANG Zan WANG JianFei +1 位作者 CHENG YuMin LIEW Kim Meow 《中国科学:物理学、力学、天文学英文版》 SCIE EI CAS 2013年第8期1568-1580,共13页
With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS a... With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study. 展开更多
关键词 无网格伽辽金法 热传导问题 三维瞬态 本质边界条件 瞬态热传导方程 偏微分方程 移动最小二乘 边界值问题
Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems
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作者 陈丽 马和平 程玉民 《中国物理B:英文版》 SCIE EI CAS CSCD 2013年第5期67-74,共8页
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 no... 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. 展开更多
关键词 有限元方法 热传导问题 瞬态 粒子 本质边界条件 边界值问题 计算效率 时间离散
带源参数热传导问题的基于滑动Kriging插值的MLPG法 被引量:3
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作者 王峰 林皋 +2 位作者 郑保敬 刘俊 李建波 《力学季刊》 CSCD 北大核心 2013年第2期175-180,共6页
利用基于滑动Kriging插值的无网格局部Petrov-Galerkin(MLPG)法来求解带源参数的二维热传导问题,推导了相应的离散方程。由于滑动Kriging插值法构造的形函数满足Kronecker Delta特性,因此可以直接施加本质边界条件。在离散过程中采用H... 利用基于滑动Kriging插值的无网格局部Petrov-Galerkin(MLPG)法来求解带源参数的二维热传导问题,推导了相应的离散方程。由于滑动Kriging插值法构造的形函数满足Kronecker Delta特性,因此可以直接施加本质边界条件。在离散过程中采用Heaviside分段函数作为局部弱形式的权函数,时间域则通过向后差分法进行离散,这一处理过程中刚度矩阵只涉及到边界积分,而没有涉及到区域积分。最后通过算例验证了本方法的有效性。 展开更多
关键词 滑动Kriging插值 无网格局部Petrov-Galerkin Heaviside分段函数 向后差分法 热传导问题 源参数
A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems
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作者 王启防 戴保东 栗振锋 《中国物理B:英文版》 SCIE EI CAS CSCD 2013年第8期238-244,共7页
On the basis of the complex variable moving least-square (CVMLS) approximation, a complex variable meshless local Petrov-Galerkin (CVMLPG) method is presented for transient heat conduction problems. The method is deve... On the basis of the complex variable moving least-square (CVMLS) approximation, a complex variable meshless local Petrov-Galerkin (CVMLPG) method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional (2D) problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method (FEM). This comparison illustrates the accuracy as well as the capability of the CVMLPG method. 展开更多
关键词 无网格局部PETROV-GALERKIN方法 热传导问题 瞬态 移动最小二乘 形状函数 函数近似 测试函数 试探函数
Hybrid graded element model for transient heat conduction in functionally graded materials 预览 被引量:1
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作者 Lei-Lei Cao Qing-Hua Qin Ning Zhao 《力学学报:英文版》 SCIE EI CAS CSCD 2012年第1期 128-139,共12页
This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials (FGMs). First, a Laplace transform approach is used to handle the time variable. Then, a fun... This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials (FGMs). First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest's algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method. 展开更多
关键词 功能梯度材料 瞬态热传导 元模型 混合 Laplace空间 拉普拉斯变换 时间变量 热传导问题
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A new complex variable meshless method for transient heat conduction problems 被引量:3
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作者 王健菲 程玉民 《中国物理B:英文版》 SCIE EI CAS CSCD 2012年第12期42-50,共9页
<正>In this paper,based on the improved complex variable moving least-square(ICVMLS) approximation,a new complex variable meshless method(CVMM) for two-dimensional(2D) transient heat conduction problems is prese... <正>In this paper,based on the improved complex variable moving least-square(ICVMLS) approximation,a new complex variable meshless method(CVMM) for two-dimensional(2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations,and the essential boundary conditions are imposed by the penalty method.As the transient heat conduction problems are related to time,the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization.Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained.In order to demonstrate the applicability of the proposed method,numerical examples are given to show the high convergence rate,good accuracy,and high efficiency of the CVMM presented in this paper. 展开更多
关键词 热传导问题 无网格方法 复变量 瞬态 移动最小二乘 本质边界条件 时间离散 边界值问题
SOLVING THE BACKWARD HEAT CONDUCTION PROBLEM BY DATA FITTING WITH MULTIPLE REGULARIZING PARAMETERS
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作者 Qun Chen Jijun Liu 《计算数学:英文版》 SCIE CSCD 2012年第4期418-432,共15页
我们为向后的热传导问题建议一个新重建计划。由使用特徵函数扩大,这个提出病的问题被一个优化问题实质上解决,它是为有两个的吵闹的输入数据的一个调整计划为是的最后的数据的截断术语和近似精确性的数字多重调整参数。取决于象特徵... 我们为向后的热传导问题建议一个新重建计划。由使用特徵函数扩大,这个提出病的问题被一个优化问题实质上解决,它是为有两个的吵闹的输入数据的一个调整计划为是的最后的数据的截断术语和近似精确性的数字多重调整参数。取决于象特徵函数的计算精确性一样选择调整参数的策略的集中率分析被给。数字实现被介绍显示出这个新计划的有效性。 展开更多
关键词 热传导问题 数据拟合 正则参数 反向 求解 本征函数 优化问题 规范参数
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