电磁接触问题的变分原理与有限元求解

电磁接触耦合作用的力学分析的难点是必须考虑电磁场以及由此引起的电磁力与可移动接触边界间的耦合作用，属于强非线性问题。本文给出接触面区域电磁场分析的处理条件，并进一步建立了两类变分方程，一类是电磁分析的变分泛函，其考虑了接触区域对结构电磁场的影响；另一类是二维电磁力学接触分析的参数变分原理，可以方便地对接触问题进行求解。数值结果验证了本文的理论与算法。     

基于约束函数法的热力耦合有限元分析

分析了滑移接触条件下热力耦合现象,建立了热力耦合的有限元分析连续模型,提出了系统动力学平衡方程和热力学平衡方程。对系统中物体间的接触条件进行了分析,得到了物体间接触条件的数学表达式,在此基础上,用约束函数表示接触约束条件。应用变分原理对约束函数进行变分,与系统平衡方程组成非线性方程组对热力耦合问题进行求解。实例表明,用约束函数法求解热力耦合问题,收敛性较好,算法稳定,计算结果能反映实际。     

耦合热弹性接触问题的变分原理

本文给出了考虑库伦摩擦力的热弹性接触问题的一个变分原理，该变分原理在约束条件Ｐｎ≥０和－μＰｎ≤Ｐｔ≤μＰｎ下，在接触边界上自动给出导热条件及剩余互补条件等。从它出发将接触弹性体离散后可直接进行二次规划求解。文中特地引进了因子β，它计及了接触问题中的热量散失和功率损耗     

应用变域变分有限元法解平面叶栅反命题

反命题作为一种可变(未知)边界问题近年来得到了广泛的研究。本文给出了亚声速平面叶栅反命题计算的势函数变域变分有限元解法。变域变分通过把可变边界结合在变分泛函中，使其与求解流场的控制方程结合起来，从而使可变边界求解和流场分析可以完全耦合进行。本文针对亚声速平面叶栅的反命题，根据泛函的驻值必要条件，介绍了变域变分有限元方法的求解过程，最后给出了两个数值算例。这两个算例均采用四节点矩形单元的插值基函数，第一个算例用于检验程序的可靠性，第二个算例设计了一个给定叶面马赫数分布的叶型，并与试验结果进行对照。     

弹性接触问题的变分原理及参数二次规划求解

本文给出了平面与空间接触问题的带参变量的变分极值原理。接触是考虑库伦摩擦的。参变量二次规划可以用于精确求解,并且通过数例说明了计算方法。     

耦合热弹性接触问题的有限元分析

对于受热的互相接触的弹性体的热负荷分析,需要在接触边界上同时考虑复杂接触传热条件及弹性接触条件,并计及耦合影响.本文对此提出了一个有效的解法——有限元混合法.计算表明:对求解这类复杂的非线性边界条件问题,该法在计算速度和机器存贮上仅比求解一般线性连续体的热负荷问题的花费略有增加以致相当。     

正交各向异性弹塑性摩擦接触问题的数值求解

采用正交各向异性摩擦定律对三维弹塑性摩擦接触问题进行分析,基于参变量变分原理,经过有限元离散,将问题化为线性互补问题模型,之后给出一个求解互补问题的非内点光滑化算法．对三维接触问题,滑动方向的确定一直是个难点,为此,该文采用作者提出的组合规划法和迭代法对各向异性摩擦本构模型进行分析,数值结果说明了模型与算法的正确性。     

自适应无网格热弹塑性接触模型研究

提出一种自适应无网格热弹塑性接触求解模型,求解接触问题的线性规划-增量初应力法与基于应变能梯度的自适应无网格法相结合,给出了模型计算理论和算法实现.通过圆柱体与弹塑性平面热弹塑性接触算例对模型进行验证.对是否考虑材料应变硬化,是否考虑摩擦力和热输入,是否考虑材料屈服强度温度相关等情况的两种算例进行了讨论.结果表明,该模型能有效地求解考虑不同情况下的热弹塑性接触问题,在较真实地模拟接触状况的同时,具有较高的计算精度和计算效率.     

参变量变分原理的提出、发展与应用

参变量变分原理及其参数二次规划算法是由钟万勰院士1985年针对弹性接触边界非线性问题首次提出来的,经过将近40年的不断发展,目前参变量变分原理已经成功应用于各个领域,其中包括弹塑性分析、接触问题、润滑力学、岩土力学、变刚度杆系结构、先进材料性能分析、材料的蠕变与损伤、柔性结构力学和LQ最优控制等各个工程领域。本文首先回顾了参变量变分原理的起源,介绍了参变量变分原理的基本概念,然后以弹塑性分析问题为例,阐明建立参变量变分原理的理论模型以及实现数值参数二次规划求解原理,最后详细回顾了参变量变分原理的基本理论与相应数值算法在各个领域的发展及其工程应用,展示了参变量变分原理在求解各类非线性问题的特色与优势。     

第二类抛物型变分不等式中的MRM方法

本文讨论了第二类抛物型变分不等式中的MRM(多重互易方法)方法。首先采用时间项半离散和隐格式方法将抛物型变分不等式化解为一个椭圆变分不等式，然后利用MRM-边界积分方程，将其化解为MRM-边界混合变分不等式，并给出了MRM-边界混合变分不等式解的存在唯一性。说明了该MRM-边界混合变分不等式与常规边界积分方程得到的边界混合变分不等式是一致的，并且具有更容易编程实现。这为使用MRM边界元方法数值求解抛物型变分不等式提供了方法和理论依据。文末给出了数值算例。     

A finite element model for numerical simulation of thermo-mechanical frictional contact problems

Two kinds of variational principles for numerical simulation of heat transfer and contact analysis are respectively presented. A finite element model for numerical simulation of the thermal contact problems is developed with a pressure dependent heat transfer constitutive model across the contact surface. The numerical algorithm for the finite element analysis of the thermomechanical contact problems is thus developed. Numerical examples are computed and the results demonstrate the validity of the model and algorithm developed. The project supported by the National Key Basic Research Special Foundation (G1999032805), the National Natural Science Foundation of China (50178016, 10225212) and the Foundation for University Key Teacher by the Ministry of Education of China     

瞬态耦合热弹塑性接触有限元分析方法

在弹性接触问题有限元混合法的基础上,把材料非线性和表面非线性两种迭代过程耦合,在瞬态温度场分析中将伽辽金法和向后差分法结合,并用混合法进行热接触迭代,把瞬态温度场分析和弹塑性接触分析耦合。提出了一种瞬态耦合热弹塑性接触有限元分析方法,并已成功地用于核容器的密封分析。     

Coupled problems of heat and mass transfer in a viscous fluid when a phase transition occurs

The investigation of heat and mass transfer processes involves, as a rule, solution of coupled problems of mathematical physics in which the coupling is realized through contiguous boundaries. In some cases, when the conditions at the contiguous boundaries can be specified in the form of simple correlation connections the overall problem can be analyzed by means of successive approximation by separate parametric solution of each problem separately; this is the case, for example, for the problem of a boundary layer on a wall that is not thermally insulated. When the correlation connections are complicated or the successive approximations do not converge (cases near equilibrium) or the contiguous boundaries themselves cannot be determined in advance, the problems do not separate and it is necessary to solve them simultaneously. Of this type is the considered problem of the flow and heat transfer of a fluid when a phase transition occurs. Problems of this kind arise in particular in the case of internal cooling of a shell by the heats of phase transitions of energy-bearing substances. In the present paper, analytic solutions are obtained for problems of the flow and heat transfer of a liquid (or gas) formed as a result of the phase transition of a solid when strongly heated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 46–50, March–April, 1984.     

Efficient solution algorithms for thermomechanical contact problems based on a domain/boundary decomposition method

An efficient domain/boundary decomposition method is presented for fully coupled thermomechanical problems with contact boundaries. The whole domain is regarded as a union of subdomains, an interface, and contact interfaces. Penalized variational formulations are performed to connect the interface or contact interfaces with the neighboring subdomains that satisfy continuity constraints on the displacement and temperature fields. As a result, non-linear finite element computations due to the contact boundaries can be localized within a few subdomains or contact interfaces. Therefore, the computational efficiency can be enhanced considerably by devising suitable solution algorithms. A variety of numerical examples were tested to confirm the important features of the new algorithms presented.     

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.     

A note for analysis of thermo-mechanical contact problems

A discussion about the bifurcation and non-uniqueness of solutions in the analysis of thermo-mechanical contact problems with initial gap is given. Without loss of generality, a mechanical contact problem coupled with steady heat transfer is studied and an example of non-uniqueness of solutions caused by the thermo-mechanical mechanism is presented. The important work is that the non-uniqueness of solutions, which is different from that found in the analysis of the traditional frictional contact problems, is studied in detail. The possible oscillation and non-convergence problems in the iteraction process of the numerical computation are discussed, and an enhanced algorithm is put forward to overcome the difficulties. Project sypported by the National Natural Science Foundation of China (Nos. 50178016, 10225212 and 19872016), the National Key Basic Research Special Foundation (No. G1999032805) and the Foundation for University Key Teacher by the Ministry of Education.     

Natural convection in a porous medium coupled across an impermeable vertical wall with film condensation

This paper presents a theoretical study of thermofluid interaction between natural convection in fluid-saturated porous medium and film condensation, coupled through an impermeable vertical wall. The two heat transfer modes are analyzed separately. The solutions are matched on the wall. The complexion of this two-fluid problem is governed by a dimensionless interaction parameter which relates the heat transfer effectiveness of the two heat transfer mechanisms. The effect of this parameter on the flow and heat transfer is documented. Results regarding the overall heat transfer coefficient are obtained for a wide range of the independent parameters. Received on 19 January 1998     

固体－气幕－液体耦合系统广义变分原理

基于驻值势能原理，本文建立了固体－气幕－液体耦合系统的广义变分原理．本文进一步根据薄气幕层的特性，将广义变分原理的相关项适当组合，得出结论，在薄气幕层情况下，固体－气幕－液体三介质耦合问题可以化为在气泡振动方程、速度与压力连续条件限制下的流－固两介质耦合问题来进行数值计算．     

An analytical solution to the heat transfer problem in thick-walled hunt flow

The flow of a liquid metal in a rectangular duct, subject to a strong transverse magnetic field is of interest in a number of applications. An important application of such flows is in the context of coolants in fusion reactors, where heat is transferred to a lead-lithium eutectic. It is vital, therefore, that the heat transfer mechanisms are understood. Forced convection heat transfer is strongly dependent on the flow profile. In the hydrodynamic case, Nusselt numbers and the like, have long been well characterised in duct geometries. In the case of liquid metals in strong magnetic fields (magnetohydrodynamics), the flow profiles are very different and one can expect a concomitant effect on convective heat transfer. For fully developed laminar flows, the magnetohydrodynamic problem can be characterised in terms of two coupled partial differential equations. The problem of heat transfer for perfectly electrically insulating boundaries (Shercliff case) has been studied previously (Bluck et al., 2015). In this paper, we demonstrate corresponding analytical solutions for the case of conducting hartmann walls of arbitrary thickness. The flow is very different from the Shercliff case, exhibiting jets near the side walls and core flow suppression which have profound effects on heat transfer.