传热与接触两类问题耦合作用的有限元分析

考虑传热接触耦合作用的热力学分析问题大量存在于工程中,分析的难点是必须考虑热与可移动接触边界间的耦合作用。针对这类问题的求解,该文给出了接触边界上热交换与温度边界条件,并在此基础上建立了两类变分方程,一类是热力学变分泛函,其考虑了接触区域对结构热传导的影响;另一类是二维热弹性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。文中给出有限元分析的离散公式,并进一步给出两类问题耦合分析的迭代算法,其中接触分析的惩罚因子是可以消除的,数值结果验证了该文的理论与算法。     

电磁对偶有限元及在波导计算中的应用

力学中的Hamilton体系采用对偶变量描述问题。电磁场采用电场和磁场两类变量描述问题。将力学中的Hamilton体系引入到电磁场问题中，电场变量和磁场变量构成对偶变量，把频域电磁场的基本方程导向对偶方程形式，建立电磁场有限元所需的对偶变量变分原理，由此推导出电磁对偶有限元。将电磁对偶有限元应用于电磁波导计算中，可确定电磁波导的传播常数。文中给出了用电磁对偶有限元方法，计算矩形波导不同模式对应的传播常数的数值计算结果。     

基于Hamilton体系的辛半解析法在各向异性电磁波导中的应用

力学中的Hamilton体系使用对偶变量来描述问题,而电磁场正好有电场和磁场这一对对偶变量。本文将力学中的Hamilton体系应用到电磁波导问题。根据电磁波导的Hamilton体系理论,辛几何可用于任意各向异性材料。将横向的电场和磁场构成对偶向量,基于Hamilton变分原理做半解析横向离散,并保持结构辛体系。本文以各向异性材料电磁波导为例,求解了问题的辛本征值,得到了镜像线的色散曲线。     

MAGNETO-THERMO-ELASTIC COUPLED DYNAMICS EQUATIONS OF AXIALLY MOVING CARRY CURRENT PLATE IN MAGNETIC FIELD

针对磁场环境中轴向运动载电流导电板磁热弹性耦合动力学建模问题进行研究. 考虑几何非线性和热效应条件下, 给出薄板运动的动能、应变能以及外力虚功的表达式.应用哈密顿变分原 理, 推得力、运动、电、磁和热效应相互作用下轴向运动导电板的非线性磁热弹性耦合振动方程.基于麦克斯韦电磁场方程, 考虑相应的电磁本构关系和电磁边界条件, 推得磁场环境中轴向运动载电流导电板满足的电动力学方程和所受电磁力表达式, 并给出焦耳热作用下耦合形式的热传导方程. 算例表明, 磁场等参量对动力学系统分岔特性有明显影响.所得结果可为此类问题的进一步求解和分 析提供理论参考.     

应用云纹干涉法测量力电耦合作用下铁电陶瓷的破坏行为

本文采用云纹干涉系统对的电陶瓷在力电耦合载荷作用下裂纹尖端的力学行为进行全场实时非接触动态细观测量,采用三点弯实验获取裂纹尖端区域在力电耦合作用下与电场集中有关的电致伸缩位移场,应变场,通过分析实验取得的云纹图得到了裂尖区域的位移场,应变场,发现裂尖区域就变随着与裂尖距离的增加衰减的速率比没有电场作用下的理论计算结果要快。     

旋转运动导电圆板电磁弹性耦合振动方程

针对磁场环境中旋转运动导电圆板的电磁弹性耦合振动理论建模问题进行研究。在考虑几何非线性效应下,给出了旋转运动圆板的形变势能、动能及变分表达式。应用哈密顿变分原理,推得磁场中旋转运动导电圆板的磁弹性耦合非线性振动方程。根据麦克斯威尔电磁场方程及相应的电磁本构关系,并基于磁弹性基本假设,推得磁场环境中旋转运动圆板所受的电磁力表达式和磁弹性二维电动力学方程。通过算例,分析了横向磁场中旋转运动圆板的轴对称振动问题,得到了圆板的固有振动频率随转速、磁感应强度的变化规律,并对结果进行了分析。     

一类Signorini问题的边界变分不等式

本文讨论了一类简化的Signorini问题。首先将原问题和一个边值问题建立联系，其次将原问题的解分解为不带不等边界条件的变分方程的解和一个变分不等式的解。然后利用边值问题的边界积分方程将变分不等式等价地化解为边界变分不等式。这样原求区域上的第一类椭圆变分不等式问题化解为求一个区域上的变分方程和一个边界变分不等式。最后说明了边界变分不等式解的存在唯一性。文末计算了柱面和半无限刚性基础的摩擦接触问题。结论表明文中方法具有较好的精度。     

考虑损伤累积的热弹塑性问题变分原理及其有限元方法

本文基于连续介质损伤力学中有效应力的概念，研究建筑结构抗火分析中遇到的热弹塑性问题与损伤的耦合，并运用参变量变分原理，建立起用于热弹塑性损伤问题结构分析的变分原理。本文给出了原理应用的有限元列式。具有明确的物理意义，表达形式规范，便于数值手段实现。     

电磁场?渗流场耦合作用下离子液体多孔介质流动模型

离子液体是一类可调控、多功能的绿色环保材料, 具有良好的电磁场响应, 有望应用于调控水驱油路径. 在分析离子液体在毛细管中电磁场响应机理的基础上, 建立了电磁场?渗流场耦合作用下离子液体多孔介质流动模型. 通过理论推导与数值分析发现: 电磁场?渗流场耦合作用下毛细管流量大小主要由离子液体电导率与黏度的比值(内因)、电磁场强度与压力梯度(外因)两方面决定; 电磁场产生的洛伦兹力对离子液体施加一个电磁驱动压强, 形成一个类似压力梯度的电磁驱动等效压力梯度, 从而改变离子液体的流量, 当电磁场强度为2.0 × 104 V/m·T时, 电磁场在电导率为0.5 S/m的离子液体上可形成10 kPa/m电磁驱动等效压力梯度. 通过调整电磁场方向即可控制离子液体在多孔介质中的流动方向, 解决常规注水利用压力差难以控制流动路径的难题, 为离子液体智能驱油提供理论依据, 且电磁场产生的热效应会影响离子液体的流动能力及潜在驱油效率.      

一种化学-力学耦合连续介质理论与数值格式

对化学驱动的连续介质化学-力学耦合系统进行研究,从热力学定律和化学势角度出发,推导了等温过程的化学-力学耦合本构关系和控制方程,利用变分方法建立了化学-力学耦合系统的能量泛函,得到化学-力学耦合控制方程的等效积分形式和相应的有限元列式. 结合算例,对连续介质的化学-力学耦合行为进行了数值计算,数值结果反映了化学与力学系统的相互耦合作用,即浓度变化能引起介质的变形,同样力学作用也能引起浓度重分布. 从全新的角度建立了描述连续介质的化学-力学耦合行为的基本理论和数值方法,能够较好地反映一类连续介质的化学-力学耦合行为.      

On electromagnetic forming processes in finitely strained solids: Theory and examples

The process of electromagnetic forming (EMF) is a high velocity manufacturing technique that uses electromagnetic (Lorentz) body forces to shape sheet metal parts. EMF holds several advantages over conventional forming techniques: speed, repeatability, one-sided tooling, and most importantly considerable ductility increase in several metals. Current modeling techniques for EMF processes are not based on coupled variational principles to simultaneously account for electromagnetic and mechanical effects. Typically, separate solutions to the electromagnetic (Maxwell) and motion (Newton) equations are combined in staggered or lock-step methods, sequentially solving the mechanical and electromagnetic problems.The present work addresses these issues by introducing a fully coupled Lagrangian (reference configuration) least-action variational principle, involving magnetic flux and electric potentials and the displacement field as independent variables. The corresponding Euler-Lagrange equations are Maxwell's and Newton's equations in the reference configuration, which are shown to coincide with their current configuration counterparts obtained independently by a direct approach. The general theory is subsequently simplified for EMF processes by considering the eddy current approximation.Next, an application is presented for axisymmetric EMF problems. It is shown that the proposed variational principle forms the basis of a variational integration numerical scheme that provides an efficient staggered solution algorithm. As an illustration a number of such processes are simulated, inspired by recent experiments of freely expanding uncoated and polyurea-coated aluminum tubes.     

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.     

多孔介质的热-电-化-力学耦合理论及应用

本文针对自然界中不同种类的多孔介质,评述了包含化学效应的多场耦合力学问题的国外内研究现状.介绍了研究多场耦合问题的理论架构,并基于唯象理论和热力学理论,建立了一般性的热-电-化-力学多场耦合理论,在此基础上简化为化学-力学耦合理论,利用相应的控制方程和本构关系, 给出了线性耦合系统的变分原理,并证明了化学-力学耦合理论架构的封闭性. 基于所提出的化-力耦合模型,通过数值算例解释了多孔介质中的化学-力学耦合现象.最后对多孔介质,特别是对活体生物软组织中的多场耦合研究中存在的问题进行了讨论,并展望了本领域的未来发展趋势.     

Metal-forming problems with combined hardening

A class of quasi-steady metal-forming problems under nonlocal contactand Coulomb’s friction boundary conditions is considered with an incompressible,rigid-plastic,strain-rate dependent,isotropic,and kinematic hardening material model.Acoupled variational formulation is derived,the convergence of a variable stiffness parame-ter method with time retardation is proved,and the existence and uniqueness results areobtained.     

Inelastic deformation of conductive bodies in electromagnetic fields

Inelastic deformation of conductive bodies under the action of electromagnetic fields is analyzed. Governing equations for non-stationary electromagnetic field propagation and elastic–plastic deformation are presented. The variational principle of minimum of the total energy is applied to formulate the numerical solution procedure by the finite element method. With the proposed method, distributions of vector characteristics of the electromagnetic field and tensor characteristics of the deformation process are illustrated for the inductor–workpiece system within a realistic electromagnetic forming process.     

Simulation of two‐phase flow with moving immersed boundaries

A two‐dimensional multi‐phase model for immiscible binary fluid flow including moving immersed objects is presented. The fluid motion is described by the incompressible Navier–Stokes equation coupled with a phase‐field model based on van der Waals' free energy density and the Cahn–Hilliard equation. A new phase‐field boundary condition was implemented with minimization of the free energy in a direct way, to specifically improve the physical behavior of the contact line dynamics for moving immersed objects. Numerical stability and execution time were significantly improved by the use of the new boundary condition. Convergence toward the analytical solution was demonstrated for equilibrium contact angle, the Lucas–Washburn theory and Stefan's problem. The proposed model may be used for multi‐phase flow problems with moving boundaries of complex geometry, such as the penetration of fluid into a deformable, porous medium. Copyright © 2010 John Wiley & Sons, Ltd.     

Plotting isoclinics for hybrid photoelasticity and finite element analysis

Displacement-based finite element method formulations are coupled with stress-based photoelasticity analysis. As the stress field is discontinuous at the interelement boundaries, the introduced smoothing procedure enables the generation of high-quality digital images acceptable for hybird experimental-numerical techniques. The proposed methods are applicable for the analysis of static and dynamic results of experimental photoelasticity.