瞬态热传导区间反演分析

基于区间有限元和矩阵摄动理论, 引入同伦技术, 建立了瞬态热传导不确定性区间参数反演识别的数值求解模式。利用测量信息和计算信息的区间残差构造同伦函数, 将反演识别问题转化为一个优化问题进行求解。时间域上, 引入时域精细算法进行离散, 空间上, 采用八节点等参元技术进行离散, 并结合区间有限元法, 建立了便于敏度分析的不确定性正反演数值模型。该模型不仅考虑了非均质和参数分布的影响, 而且也便于正演和反演问题的敏度分析, 可对导热系数和热边界条件等宗量的区间范围进行有效的单一和组合识别, 并给出了相关的数值算例。数值结果表明了所建数值模型的有效性和可行性, 并具有较高的计算精度。     

一个瞬态温度场区间上下界估计的数值方法

提出一种求解带有区间不确定性参数的瞬态热传导问题的数值方法。利用Taylor展开和区间分析技术,建立温度区间量与不确定参数区间量的确定性关系,然后采用时域分段自适应算法和有限元技术,递推计算温度场的区间半径及区间中值,以估算温度场不确定区间的上下界。自适应计算可根据时间步长的变化,使计算在各离散时段达到给定的计算精度,从而保证整个时域的计算精度。在算例分析中,通过与组合方法、概率方法的比较,说明了所提方法的有效性,并探讨了Taylor展开阶次与计算步长对计算结果的影响。     

区间参数空间结构的瞬态温度场数值分析

针对含有区间参数的空间薄壁圆管结构,基于区间分析理论,给出其在持续热流作用下瞬态温度场问题的区间分析方法。将结构所有物性参数均视为区间变量,建立了空间结构的瞬态热分析有限元模型,对该模型在空间域上利用有限元离散,在时间域上利用差分递推。基于区间扩张理论和Taylor级数展开,利用矩阵摄动方法求解,获得了区间参数结构的瞬态温度场响应的区间范围。通过算例的计算结果与参考文献结果的对比,显示了文中计算模型的合理性和方法的有效性。     

瞬态热传导问题的修正变分原理及其数值算法

本文采用拉格朗日乘子将本征边界条件引入到瞬态热传导问题的泛函方程,通过变分原理得到了其修正泛函.采用Galerkin无网格法在空间域内进行离散,得到瞬态热传导问题的半离散方程;在时间域上通过与Romberg积分相结合的精细积分法求解,并且推导了瞬态热传导方程中精细积分的普遍适应的公式,结合数值算例对方法的有效性和精确性进行了验证.     

基于区间分析的不确定性结构动力学模型修正方法

提出了一种基于区间分析的不确定性有限元模型修正方法。在区间参数结构特征值分析理论和确定性有限元模型修正方法基础上,假设不确定性与初始有限元模型误差均较小,采用灵敏度方法推导了待修正参数区间中点值和不确定区间的迭代格式。以三自由度弹簧-质量系统和复合材料板为例,采用拉丁超立方抽样构造仿真试验模态参数样本,开展仿真研究。结果表明,当仿真试验样本能准确反映结构模态参数的区间特性时,方法的收敛精度和效率均较高;修正后计算模态参数能准确反映试验数据的区间特性。所提出方法适用于解决试验样本较少,仅能得到试验模态参数区间的有限元模型修正问题。     

三维复杂区域瞬态热传导边界元分析

本文把狭缝面作为中面,细长圆形管道作为横截面中心的简单奇异源处理,用与时间相关的基本 三维复杂区域瞬态传导边界积分公式。     

基于区间法的发动机曲轴不确定性优化研究

该文基于非线性区间数规划方法和区间分析方法,针对某型发动机曲轴的不确定性优化问题进行了研究。载荷中的不确定参数采用区间描述,极限工况下的最大等效应力作为目标函数且通过有限元方法求解。非线性区间数规划方法用以处理不确定目标函数,区间分析方法用以快速求解目标函数在每一个设计矢量下的区间,隔代映射遗传算法作为优化求解器。应用算例说明了该文算法的有效性。     

含区间不确定性参数的机翼气动弹性优化

提出了一种具有区间不确定性的机翼颤振优化方法.采用拉丁超立方方法建立仿真试验表,基于MSC.Nastran平台进行颤振仿真分析.获得仿真数据之后,应用Kriging方法构造了包含区间不确定性参数的机翼颤振分析代理模型,并进行有效性检验.基于建立的代理模型并按照区间序数关系,将不确定性优化目标和约束条件转化为确定性表达形式,从面形成区间不确定性的结构优化设计方法.该方法将区间法优化和代理模型相结合,同时综合有限元仿真和遗传算法的优点,计算效率较高且应用范围较广.以某复杂机翼结构为例进行了含区间不确定性的颤振优化计算.分析结果表明了所提方法的正确性和可行性.     

对流换热边界下梯度功能材料板瞬态热传导有限元分析

用有限元法与有限差分法相结合的方法，对处在对流换热边界条件下的梯度功能材料板的瞬态热传导问题进行了分析，并且通过对ZrO2和Ti－6Al-4V组成的梯度功能材料板对本方法的正确性进行了检验，最后给出了对流换热边界下的瞬态温度场分布。数值计算结果表明：材料组成的分布形状系数M、环境介质温度和对流换热系数的变化对梯度功能材料板的瞬态温度场分布有明显的影响。本文结果为梯度功能材料的优化设计和进一步的热应力分析提供了理论计算依据。     

灵敏度的模态区间分析方法及其在不确定性参数识别中的应用EI北大核心CSCD

由于存在区间过估计及无法获知结构响应表达式的问题,区间灵敏度分析方法难以广泛地应用于实际复杂结构中。为此,提出一种基于响应面的灵敏度模态区间分析方法,该方法在区间响应面模型上分别对每个区间参数进行模态区间扩张得到响应区间,进而计算相对模态区间灵敏度,通过比较相对模态区间灵敏度即可判断结构响应对参数的敏感程度。通过数值算例探讨响应面形式对计算结果的影响,阐述灵敏度区间分析与灵敏度模态区间分析的优缺点。最后以钢板试验及钢筋混凝土拱桥不确定性参数识别算例来验证所提方法在复杂结构分析中的可行性。灵敏度分析结果表明该方法有效地解决区间过估计问题,提高了灵敏度分析的精度。对参数在多个范围内的灵敏度分析,所提方法具有较高的计算效率。参数识别结果表明将逆响应面与模态区间分析结合可避免区间优化过程,在保证精度的前提下,提高了参数识别效率。     

A meshless analysis of three-dimensional transient heat conduction problems

In this paper, we consider a numerical modeling of a three-dimensional transient heat conduction problem. The modeling is carried out using a meshless reproducing kernel particle (RKPM) method. In the mathematical formulation, a variational method is employed to derive the discrete equations. The essential boundary conditions of the formulated problems are enforced by the penalty method. Compared with numerical methods based on meshes, the RKPM needs only scattered nodes, rather than having to mesh the domain of the problem. An error analysis of the RKPM for three-dimensional transient heat conduction problem is also presented in this paper. In order to demonstrate the applicability of the proposed solution procedures, numerical experiments are carried out for a few selected three-dimensional transient heat conduction problems.     

Fuzzy interval perturbation method for uncertain heat conduction problem with interval and fuzzy parameters

This paper proposes a fuzzy interval perturbation method (FIPM) and a modified fuzzy interval perturbation method (MFIPM) for the hybrid uncertain temperature field prediction involving both interval and fuzzy parameters in material properties and boundary conditions. Interval variables are used to quantify the non‐probabilistic uncertainty with limited information, whereas fuzzy variables are used to represent the uncertainty associated with the expert opinions. The level‐cut method is introduced to decompose the fuzzy parameters into interval variables. FIPM approximates the interval matrix inverse by the first‐order Neumann series, while MFIPM improves the accuracy by considering higher‐order terms of the Neumann series. The membership functions of the interval temperature field are eventually derived using the fuzzy decomposition theorem. Three numerical examples are provided to demonstrate the feasibility and effectiveness of the proposed methods for solving heat conduction problems with hybrid uncertain parameters, pure interval parameters, and pure fuzzy parameters, respectively. Copyright © 2015 John Wiley & Sons, Ltd.     

Boundary element method analyses of transient heat conduction in an unbounded solid layer containing inclusions

The boundary element method (BEM) is used to compute the three-dimensional transient heat conduction through an unbounded solid layer that may contain heterogeneities, when a pointwise heat source placed at some point in the media is excited. Analytical solutions for the steady-state response of this solid layer when subjected to a spatially sinusoidal harmonic heat line source are presented when the solid layer has no inclusions. These solutions are incorporated into a BEM formulation as Greens functions to avoid the discretization of flat media interfaces. The solution is obtained in the frequency domain, and time responses are computed by applying inverse (Fast) Fourier Transforms. Complex frequencies are used to prevent the aliasing phenomena. The results provided by the proposed Greens functions and BEM formulation are implemented and compared with those computed by a BEM code that uses the Greens functions for an unbounded media which requires the discretization of all solid interfaces with boundary elements. The proposed BEM model is then used to evaluate the temperature field evolution through an unbounded solid layer that contains cylindrical inclusions with different thermal properties, when illuminated by a plane heat source. In this model zero initial conditions are assumed. Different simulation analyses using this model are then performed to evaluate the importance of the thermal properties of the inclusions on transient heat conduction through the solid layer.     

Simulation of transient heat conduction using one‐dimensional mapped infinite elements

Many engineering problems exist in physical domains that can be said to be infinitely large. A common problem in the simulation of these unbounded domains is that a balance must be met between a practically sized mesh and the accuracy of the solution. In transient applications, developing an appropriate mesh size becomes increasingly difficult as time marches forward. The concept of the infinite element was introduced and implemented for elliptic and for parabolic problems using exponential decay functions. This paper presents a different methodology for modeling transient heat conduction using a simplified mesh consisting of only two‐node, one‐dimensional infinite elements for diffusion into an unbounded domain and is shown to be applicable for multi‐dimensional problems. A brief review of infinite elements applied to static and transient problems is presented. A transient infinite element is presented in which the element length is time‐dependent such that it provides the optimal solution at each time step. The element is validated against the exact solution for constant surface heat flux into an infinite half‐space and then applied to the problem of heat loss in thermal reservoirs. The methodology presented accurately models these phenomena and presents an alternative methodology for modeling heat loss in thermal reservoirs. Copyright © 2010 John Wiley & Sons, Ltd.     

Gradient method for inverse heat conduction problem in nanoscale

An inverse heat conduction problem for nanoscale structures was studied. The conduction phenomenon is modelled using the Boltzmann transport equation. Phonon‐mediated heat conduction in one dimension is considered. One boundary, where temperature observation takes place, is subject to a known boundary condition and the other boundary is exposed to an unknown temperature. The gradient method is employed to solve the described inverse problem. The sensitivity, adjoint and gradient equations are derived. Sample results are presented and discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

稳态热传导结构非概率可靠性拓扑优化设计

研究具有区间参数的稳态热传导结构在散热弱度非概率可靠性约束下的拓扑优化设计问题。建立了以单元相对导热系数为设计变量,导热材料体积极小化为目标函数,满足散热弱度非概率可靠性为约束条件的稳态热传导结构的拓扑优化设计数学模型。基于区间因子法,推导出散热弱度的均值及离差的计算表达式。采用渐进结构优化法的求解策略与方法,并利用过滤技术消除优化过程中的数值不稳定性现象。通过算例验证文中模型及求解策略、方法的合理性和有效性。     

Three-step multi-domain BEM for solving transient multi-media heat conduction problems

In this paper, a three-step BEM analysis technique is proposed for solving 2D and 3D transient heat conduction problems consisting of multiple non-homogeneous media. The discretized boundary element formulation is written for each medium. The first step is to eliminate internal variables at the individual medium level; the second step is to eliminate boundary unknowns defined over nodes used only by the medium itself; and the third step is to establish the system of equations according to the continuity conditions of the temperature and heat flux at common interface nodes. Based on the central finite difference technique, an implicit time marching solution scheme is developed for solving the time-dependent system of equations. Three numerical examples are given to demonstrate the accuracy and effectiveness of the presented method.     

A Gaussian RBFs method with regularization for the numerical solution of inverse heat conduction problems

In this paper, a recursion numerical technique is considered to solve the inverse heat conduction problems, with an unknown time-dependent heat source and the Neumann boundary conditions. The numerical solutions of the heat diffusion equations are constructed using the Gaussian radial basis functions. The details of algorithms in the one-dimensional and two-dimensional cases, involving the global or partial initial conditions, are proposed, respectively. The Tikhonov regularization method, with the generalized cross-validation criterion, is used to obtain more stable numerical results, since the linear systems are badly ill-conditioned. Moreover, we propose some results of the condition number estimates to a class of positive define matrices constructed by the Gaussian radial basis functions. Some numerical experiments are given to show that the presented schemes are favourably accurate and effective.     

Effects of wall thickness and material property on inverse heat conduction analysis of a hollow cylindrical tube

In this study, we examined the effects of a hollow cylindrical tube’s thickness and material properties on estimated time delay and waveform distortion in a one-dimensional inverse heat transfer analysis model using the thermal resistance method and an input estimation algorithm. Results indicated a persistent time delay for various heat flux amounts applied to different tube thicknesses. As the tube thickness increased, the numerically determined temperature data also experienced a time delay, which affected the inverse heat transfer response curve. Results also indicated that the transient heat flux waveform estimated for different material properties showed higher levels of distortion for materials having relatively low thermal conductivity. These materials also exhibited greater time delays. To address these issues, we applied a Fourier number (a dimensionless number representing the tube’s thickness and material properties) and proposed an equation to calculate sharpness, which can subsequently be used to predict probable time delays and heat flux waveform distortion. In conclusion, a correction is required when a low Fourier number is used in inverse heat transfer analysis.