Stochastic transient analysis of thermal stresses in solids by explicit time-domain method

Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years. The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses. Therefore, it is reasonable to consider the variability of thermal environments while conducting thermal analysis. However, for ambient thermal excitations, only stationary random processes have been investigated thus far. In this study, the highly efficient explicit time-domain method(ETDM) is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems. The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body. Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses. A numerical example involving non-stationary stochastic internal heat generation rate is investigated. The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.     

一种求解瞬态热传导方程的无条件稳定方法

瞬态热传导问题普遍存在于航空航天、土木和冶金等领域中, 对这类问题精确、高效的数值求解方法一直备受关注. 为此, 本文提出了一种无条件稳定的单步时间积分方法. 在所提出的方法中, 拉格朗日插值函数被用来近似真实的温度场及其一次导数场, 之后, 加权残量法被用来建立二者之间的关系. 通过对算法参数的巧妙设计, 本文提出的方法具有二阶精度和L型数值耗散, 其中, L型耗散使得本文方法能够快速过滤掉虚假的高频振荡. 多数现有时间积分方法仅对线性系统具有无条件稳定性, 对非线性系统则是条件稳定的. 为此, 本文改进了Hughes针对一阶非线性热传导问题提出的时间积分方法稳定性评估理论, 并将改进的理论用于方法的参数设计中. 理论分析的结果表明本文方法对线性和非线性热传导系统均是无条件稳定的. 即使对于著名的Crank-Nicolson方法失稳的非线性热传导问题, 本文方法仍能给出稳定且精确的预测. 数值测试结果显示, 所提出的方法相较于当前流行的方法具有明显的精度、耗散和稳定性优势.      

带源参数的二维热传导反问题的无网格方法

利用无网格有限点法求解带源参数的二维热传导反问题,推导了相应的离散方程. 与 其它基于网格的方法相比,有限点法采用移动最小二乘法构造形函数,只需要节点信息,不 需要划分网格,用配点法离散控制方程,可以直接施加边界条件,不需要在区域内部求积分. 用有限点法求解二维热传导反问题具有数值实现简单、计算量小、可以任意布置节点等优点. 最后通过算例验证了该方法的有效性.     

PRECISE INTEGRAL ALGORITHM BASED SOLUTION FOR TRANSIENT INVERSE HEAT CONDUCTION PROBLEMS WITH MULTI-VARIABLES

IntroductionIHCPs (InverseHeatConductionProblems)arecloselyassociatedwithmanyengineeringaspects,andwelldocumentedintheliteratures,coveringtheidentificationsofthermalparameters[1,2 ],boundaryshapes[3],boundaryconditions[4 ]andsource_relatedterms[5 ,6 ]etc .Howeveritseemsthatonlylittleworkisdirectlyconcernedwithmulti_variablesidentificationsbyauthors’knowledge.Tsengetal.presentedanapproachtodeterminingtwokindsofvariables[7],butonlygavefewnumericalexamplestodeterminethemsimultaneously .Thesol…     

二阶非定常多宗量热传导反问题的正则解

引入Bregman距离函数及其加权函数作为正则项,应用Tikhonov正则 化方法,对二阶非定常多宗量热传导反问题进行求解. 利用测量信息和计算信息构造最小二 乘函数,将多宗量反演识别问题转化为一个优化问题. 空间上采用8节点等参元进行离散, 时域上采用时域精细算法进行离散,建立了二阶非定常多宗量热传导问题的有限元正/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,而且也便于正反演问题的敏度分析, 可对导热系数和边界条件等宗量进行有效的单一和组合识别. 给出了相关的数值验证,对信 息测量误差以及不同正则项的计算效率作了探讨. 数值结果表明,该方法能够对二阶非定常 多宗量热传导反问题进行有效的求解,并具有较高的计算精度.     

多宗量瞬态热传导反演识别

引入Bregman距离加权函数,建立了多宗量瞬态热传导反演的一种求解模式.时域上采用精细算法,分别建立了便于敏度分析的有限元正/反演模型,应用同伦算法进行反问题求解,对导热系数和边界条件等宗量进行有效的组合识别.对信息误差和计算效率作了探讨,并给出了相应的数值验证.     

二阶非定常热传导反问题的多宗量辨识

引入Bregman距离构造同伦函数,建立了二阶非定常多宗量热传导反问题的一种求解模式,可对导热系数和边界条件等宗量进行识别。时域上采用精细算法,建立了便于敏度分析的有限元正/反演模型,对各宗量进行有效的组合识别。对信息测量误差和初值选取作了初步探讨,数值验证取得了满意的结果。     

New analytic solutions to 2D transient heat conduction problems with/without heat sources in the symplectic space

The two-dimensional (2D) transient heat conduction problems with/without heat sources in a rectangular domain under different combinations of temperature and heat flux boundary conditions are studied by a novel symplectic superposition method (SSM). The solution process is within the Hamiltonian system framework such that the mathematical procedures in the symplectic space can be implemented, which provides an exceptional direct rigorous derivation without any assumptions or predetermination of the solution forms compared with the conventional inverse/semi-inverse methods. The distinctive advantage of the SSM offers an access to new analytic heat conduction solutions. The results obtained by the SSM agree well with those obtained from the finite element method (FEM), which confirms the accuracy of the SSM.     

基于物理信息神经网络的功能梯度材料稳态/瞬态热传导分析

采用物理信息神经网络PINN(Physics-informed Neural Networks)求解稳态和瞬态功能梯度材料(FGMs)热传导问题。该方法利用控制方程、边界及初始条件的残差构造损失函数,在无任何响应数据的情况下得到了更具泛化能力的神经网络模型,同时避免了传统数值方法在求解计算力学问题时所需的微分、积分公式推导以及繁重的建模和划分网格等前处理工作。本文探究了PINN及其域分解的扩展物理信息神经网络XPINN(eXtended Physics-informed Neural Networks)在求解稳态和瞬态FGMs热传导问题时的适用性,讨论了网络结构对预测结果的影响。研究结果表明,PINN/XPINN在解决几何复杂的稳态和瞬态FGMs热传导问题时仍具有较高的可靠性和简洁的求解流程,同时,为极端环境下求解复杂多场耦合和夹杂等问题提供了新思路。     

Inverse approach and sensitivity analysis for identification of ingot-mould thermal resistance in continuous casting of metals

The problem of appropriate location of the sensors for identification of ingot – mould thermal resistance during continuous casting of metals is the subject of the paper. Analysed problem belongs to the group of inverse problems. The present work shows also the method of identification of unknown thermal resistance using the temperature measurements at the number of sensors located in the wall of the mould. The influence of the location of the sensors on the results of identification is analysed. The best location of the sensors results from the sensitivity analysis for the steady-state inverse heat conduction problem. Validation of the proposed inverse method is realized by comparison of the results taken from solution of inverse and direct problems. Several numerical examples are presented and analysed.     

基于数据驱动模型求解热传导反问题

热传导反问题求解在工程领域具有重要的应用价值.本文发展数据驱动模型识别了管道内壁几何形状和皮肤肿瘤生长参数等热传导反问题.在管道内壁几何形状识别问题中,首先采用随机生成模型结合有限元法求解热传导正问题,并采用有效导热系数转化的思想,建立机器学习模型,求解了测点温度与有效导热系数之间的抽象映射关系,进而实现管道内壁几何形...     

粗糙表面之间接触热阻反问题研究

当两个固体表面相互接触时,由于接触面粗糙度的影响,界面间就形成了非一致接触,这种接触导致热流收缩,进而产生接触热阻. 目前的理论研究主要集中在正问题研究,对反问题的研究相对较少. 接触热阻反问题研究是通过研究部分边界温度、热流和部分测量点的温度来反演得到界面上的接触热阻. 反问题研究在很多工程领域都有应用,如航空航天、机械制造、微电子等,是工程中确定接触热阻一种快速有效的方法. 本文采用边界元法和共轭梯度法研究了二维空间随坐标变化的接触热阻反问题. 为了验证方法的准确性和可行性,假定在已知部分测量点温度和真实接触热阻的情况下,反演计算得到界面的温度和热流,进而得到接触热阻,并与真实接触热阻进行比较. 结果表明采用边界元法和共轭梯度法在无测量误差的情况下,可以准确反演获得界面的真实接触热阻. 若存在测量误差,反演计算结果对测量误差极其敏感,反演结果误差会由于测量误差的引入而被放大. 为处理这种不适定性, 采用最小二乘法对反演计算结果进行校正,结果表明采用最小二乘法能够避开反问题中一些偏离实际值较大的测量点,显著提高反演计算结果的准确性.      

Extension of the virtual fields method to elasto-plastic material identification with cyclic loads and kinematic hardening

The virtual fields method (VFM) has been specifically developed for solving inverse problems from dense full-field data. This paper explores recent improvements regarding the identification of elasto-plastic models. The procedure has been extended to cyclic loads and combined kinematic/isotropic hardening. A specific attention has also been given to the effect of noise in the data. Indeed, noise in experimental data may significantly affect the robustness of the VFM for solving such inverse problems. The concept of optimized virtual fields that minimize the noise effects, previously developed for linear elasticity, is extended to plasticity in this study. Numerical examples with models combining isotropic and kinematic hardening have been considered for the validation. Different load paths (tension, compression, notched specimen) have shown that this new procedure is robust when applied to elasto-plastic material identification. Finally, the procedure is validated on experimental data.     

An inverse geometry problem in estimating frost growth on an evaporating tube

 When humid air comes into contact with a surface whose temperature is below the dew point of water vapor in air and also below the freezing point, frost deposition takes place over the surface. The phenomena of the frost growth are very complicated and therefore it is very difficult to model mathematically the behavior of frost growth and predict it. In the present study a transient inverse geometry heat conduction problem (shape identification problem) is solved using the conjugate gradient method (CGM) and boundary element method (BEM)-based inverse algorithm to estimate the unknown irregular frost thickness and shape. Results obtained by using the CGM to estimate the frost growth are justified based on the numerical experiments. It is concluded that the accurate frost shape can be estimated by the CGM except for the initial and final time. The reason and improvement of this singularity are addressed. Finally the effects of reducing the number of sensors and increasing the measurement errors on the inverse solutions are discussed. Received on 25 September 2000 / Published online: 29 November 2001     

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法, 建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型. 在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性. 研究结果表明: (1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下, 而其计算效率比有限元全阶模型提高2$\sim $3个数量级, 并且自由度数量(DOFs)愈大提高的幅度也愈加显著; (2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题, 即使是在DOFs比较小的时候也能够明显提高计算效率; (3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型, 并对其传热过程和温度场进行快速准确的分析与预测, 具有很好的工程应用价值.      

基于遗传算法的混凝土三维非稳态温度场反分析

大体积混凝土结构施工期间的合理温度控制问题非常重要，而精确进行温度计算所需的一些材料参数往往不易直接测得，需要根据一些易测得的量进行反求。本文基于三维瞬态温度场有限元求解理论与反问题理论，建立了混凝土三维瞬态温度场反问题求解数值模型。运用遗传算法寻求非线性反演问题全局最优解，只需要若干点温度实测值便可实现混凝土多个热学参数如绝热温升、导温、导热系数及热交换系鼓等的同时反演，算例对本文反演方法的反演精度及数值稳定性给出了满意的证明。     

正交各向异性稳态热传导问题的ICVEFG方法

本文将改进的复变量无单元Galerkin方法（Improved Complex Variable Element-free Galerkin method,ICVEFG）应用于求解正交各向异性介质中的稳态热传导问题,提出了正交各向异性稳态热传导问题的ICVEFG方法。采用罚函数法引入本质边界条件,推导了正交各向异性介质中的稳态热传导问题的Galerkin积分弱形式。采用改进的复变量移动最小二乘近似（Improved Complex Variable Moving least-squares approximation,ICVMLS）建立二维温度场问题的逼近函数,推导了相应的计算公式。编制了计算程序,对三个正交各向异性介质中的热传导问题进行了分析,说明了本文方法的有效性。     

共轭梯度法求解非线性多宗量稳态传热反问题

应用共轭梯度法求解非线性多宗量稳态热传导反问题。采用八节点的等参单元在空间上进行离散,建立了便于敏度分析的非线性正演和反演的有限元模型,可直接求导进行敏度分析。给出了相关的数值验证,对测量误差及测点数目的影响作了初步探讨,结果表明,采用的算法能够对非线性稳态热传导中导热系数和边界条件联合反问题进行有效的求解,并具有较高精度。     

Solution of non-linear inverse heat conduction problems using the method of lines

 Two space marching methods for solving the one-dimensional nonlinear inverse heat conduction problems are presented. The temperature-dependent thermal properties and the boundary condition on the accessible part of the boundary of the body are known. Additional temperature measurements in time are taken with a sensor located in an arbitrary position within the solid, and the objective is to determine the surface temperature and heat flux on the remaining part of the unspecified boundary. The methods have the advantage that time derivatives are not replaced by finite differences and the good accuracy of the method results from an appropriate approximation of the first time derivative using smoothing polynomials. The extension of the first method presented in this study to higher dimensions inverse heat conduction problems is straightforward. Received on 3 May 1999     

半无限介质瞬态热传导的同伦分析法

In the current work, transient heat conduction in a semi-infinite medium is considered for its many applications in various heat fields. Here, the homotopy analysis method （HAM） is applied to solve this problem and analytical results are compared with those of the exact and integral methods results. The results show that the HAM can give much better approximations than the other approximate methods： Changes in heat fluxes and profiles of temperature are obtained at different times and positions for copper, iron and aluminum.