有限变形时材料性质张量的选取

在有限变形时导出了用欧拉观点描述的与用拉格朗日观点描述的材料性质张量之间用矩阵形式表达的转换关系，指出正确应用这个关系时将到唯一的计算结果，与计算方法无关，建立在连续体力学中应将材料性质实验结果与欧拉观点描述的材料性质张量相对应。     

棒材通过锥形模静液挤压成形的无网格法分析

建立了一种基于初始构形及有限变形的粘塑性弹性本构关系，并由空间描述的Galerkin能量弱变分原理，经一致转换得一整体拉格朗日方程描述下的动量平衡方程．同时经线性化处理给出了显示中心差分法求解格式，以棒材通过锥形模的静液挤压成形为例进行了全面的EFG法数值模拟，从而证明了有限变形粘塑性EFG法对实际成形工艺分析、优化及设计的有效性。     

THE PARAMETRIC VARATIONAL PRINCIPLE AND NON-LINEAR FINITE ELEMENT METHOD FOR ANALYSIS OF ASTROMESH ANTENNA STRUCTURES

针对大型周边桁架式索网天线由拉索拉压模量不同引起的本构非线性和结构大变形引起的几何非线性问题，给出了基于参变量变分原理的几何非线性有限元方法. 首先针对含预应力索单元拉压模量不同分段描述的本构关系，通过引入参变量，导出了基于参变量及其互补方程的统一描述形式，避免了传统算法需要根据当前变形对索单元张紧/松弛状态的预测，提高了算法收敛性. 然后利用拉格朗日应变描述索网天线结构大变形问题，结合几何非线性有限元法，建立了基于参变量的非线性平衡方程和线性互补方程；并给出了牛顿-拉斐逊迭代法与莱姆算法相结合的求解算法. 数值算例验证了本文提出的算法比传统算法具有更稳定的收敛性和更高的求解精度，特别适合于大型索网天线结构的高精度变形分析和预测.     

极端变形问题的物质点法研究进展

物质点法采用了拉格朗日和欧拉双重描述,将物体离散为一组在固定于空间的网格(欧拉描述)中运动的质点(拉格朗日描述),有效地综合了拉格朗日法和欧拉法的优点,是分析冲击爆炸等极端变形问题的一种有效方法. 本文系统总结了本课题组近年来针对冲击、爆炸和流固耦合等极端变形问题在物质点法算法方面的研究进展,并简要介绍了开发的三维显式并行物质点法数值仿真软件MPM3D及其在超高速碰撞、侵彻、爆炸、边坡失效、金属切削和流固耦合等问题中的应用.     

Application of generalized variational principle for solving assembly stress of rod system

利用拉格朗日乘数法建立广义变分原理以求解有误差杆件结构装配应力. 引入拉格朗日乘数并结合静力平衡方程，构造无条件广义变分原理的新泛函，求解新泛函的极值问题，获得超静定的变形协调方程，从而计算有误差杆件结构的装配应力. 结果表明：该方法求解装配应力的通用性较强，不但克服传统几何方法建立变形协调方程的缺陷，而且具有计算过程简洁以及便于掌握等优点.     

力电耦合偏场理论：回顾、比较与展望

力电耦合固体的非线性连续介质理论最早出现于20世纪50年代，而成熟于70年代.80年代末、90年代初则因智能材料与结构的兴起而又得到了新的发展，引起了较为广泛的关注，但应用上以线性分析为主.21世纪初以来，力电耦合软材料因其潜在的应用前景激发了众多的研究兴趣.由于牵涉到大变形，必须在一般非线性连续介质力学的框架内进行问题的建模和开展定量分析，因此力电耦合固体的非线性理论重新得到了大家的重视，出现了很多新版本.本文旨在阐述力电耦合固体非线性连续介质理论一般框架的基础上，采用3个构型的表述方式，较为详细地给出拉格朗日描述和更新拉格朗日描述下的力电耦合偏场理论，甄别不同理论表述版本之间的异同，以廓清目前文献中的混乱现象，为今后的相关研究提供理论指导.最后，本文讨论和展望了力电耦合偏场理论在不同研究领域的若干研究重点及其未来发展趋势.     

索网天线的参变量变分及非线性有限元方法

针对大型周边桁架式索网天线由拉索拉压模量不同引起的本构非线性和结构大变形引起的几何非线性问题,给出了基于参变量变分原理的几何非线性有限元方法.首先针对含预应力索单元拉压模量不同分段描述的本构关系,通过引入参变量,导出了基于参变量及其互补方程的统一描述形式,避免了传统算法需要根据当前变形对索单元张紧/松弛状态的预测,提高了算法收敛性.然后利用拉格朗日应变描述索网天线结构大变形问题,结合几何非线性有限元法,建立了基于参变量的非线性平衡方程和线性互补方程;并给出了牛顿--拉斐逊迭代法与莱姆算法相结合的求解算法.数值算例验证了本文提出的算法比传统算法具有更稳定的收敛性和更高的求解精度,特别适合于大型索网天线结构的高精度变形分析和预测.     

贮腔类三维自由液面动力学问题数值研究

讨论了贮腔类三维自由液面动力学问题的数值研究,将任意的拉格朗日-欧拉运动学描述关系引入到系统的控制方程中,采用任意的拉格朗日-欧拉描述跟踪自由液面,推导了自由面上结点的法向矢量计算公式。采用Galerkin余量法推导了Navier-Stokes方程的空间离散有限元方程,采用三维自由液面上微分几何理论推导了表面张力计算公式。数值研究中考虑了接触角效应,最后进行了三维数值算例分析。     

空间桁架结构大位移问题的有限元分析方法

本文基于总体拉格朗日坐标描述法，采用Ｋｉｒｃｈｏｆｆ应力张量和Ｇｒｅｅｎ应变张量定义，导出了严格意义下的杆单元增量列式，计算表明本文方法可以有效用于空间桁架结构大位移问题分析。     

单杆柔性机械臂的控制仿真研究

本文应用模态控制理论，对柔性机械臂的主动控制问题中的动力学模型进行了研究。在小变形假设的前提下，考虑由于横向变形而引起的轴向位称位的影响，采用拉格朗日方程建立了计及动力刚化项的动力学模型，并将ＰＤ控制理论和方法应用于刻模型。最后，对一单杆柔性机械臂的振动控制进行了计算机仿真．     

Prediction of extrudate swell in polymer melt extrusion using an Arbitrary Lagrangian Eulerian (ALE) based finite element method

Accurate prediction of extrudate (die) swell in polymer melt extrusion is important as this helps in appropriate die design for profile extrusion applications. Extrudate swell prediction has shown significant difficulties due to two key reasons. The first is the appropriate representation of the constitutive behavior of the polymer melt. The second is regarding the simulation of the free surface, which requires special techniques in the traditionally used Eulerian framework. In this paper we propose a method for simulation of extrudate swell using an Arbitrary Lagrangian Eulerian (ALE) technique based finite element formulation. The ALE technique provides advantages of both Lagrangian and Eulerian frameworks by allowing the computational mesh to move in an arbitrary manner, independent of the material motion. In the present method, a fractional-step ALE technique is employed in which the Lagrangian phase of material motion and convection arising out of mesh motion are decoupled. In the first step, the relevant flow and constitutive equations are solved in Lagrangian framework. The simpler representation of polymer constitutive equations in a Lagrangian framework avoids the difficulties associated with convective terms thereby resulting in a robust numerical formulation besides allowing for natural evolution of the free surface with the flow. In the second step, mesh is moved in ALE mode and the associated convection of the variables due to relative motion of the mesh is performed using a Godunov type scheme. While the mesh is fixed in space in the die region, the nodal points of the mesh on the extrudate free surface are allowed to move normal to flow direction with special rules to facilitate the simulation of swell. A differential exponential Phan Thien Tanner (PTT) model is used to represent the constitutive behavior of the melt. Using this method we simulate extrudate swell in planar and axisymmetric extrusion with abrupt contraction ahead of the die exit. This geometry allows the extrudate to have significant memory for shorter die lengths and acts as a good test for swell predictions. We demonstrate that our predictions of extrudate swell match well with reported experimental and numerical simulations.     

Some issues regarding spectral element meshes for moving journal bearing systems

This paper concerns the modelling of dynamically loaded journal bearing systems using a moving spectral element method. The moving grid method employed in this paper is the arbitrary Lagrangian–Eulerian (ALE) method. The ALE methodology is compared with a quasi‐Eulerian approach in the context of dynamically loaded journal bearings and the advantages of adopting the ALE formulation are highlighted. A comparison with the predictions of lubrication theory is also presented and the limitations of the lubrication approximation are demonstrated when inertial effects are significant. A comprehensive set of results is presented illustrating the salient features of the spectral element mesh generation schemes described in the paper and the way in which these impinge on the efficiency of the iterative solution of the discrete equations at each time step. Copyright © 2005 John Wiley & Sons, Ltd.     

ALE方法在爆炸数值模拟中的应用

本文以ALE（Arbitrary Lagrange—Euler）理论为基础，结合非线性动力学的相关理论，推导了ALE方法描述的控制方程组。最后采用ALE描述方法针对集团装药在半无限土质中爆炸进行了数值模拟，并将模拟计算结果与现有实验研究成果进行了对比。在模拟给出的最大压力时程曲线和爆腔发展时程曲线的基础上，对空腔的形成和发展规律以及次生波的形成等问题进行了研究。通过对比，证明ALE算法综合了Lagrange和Euler法的优点，能够有效地用于对爆炸过程进行数值模拟。     

An arbitrary Lagrangian Eulerian (ALE) formulation for free surface flows using the characteristic‐based split (CBS) scheme

An arbitrary Lagrangian Eulerian (ALE) method for non‐breaking free surface flow problems is presented. The characteristic‐based split (CBS) scheme has been employed to solve the ALE equations. A simple mesh smoothing procedure based on coordinate averaging (Laplacian smoothing) is employed in the calculations. The mesh velocity is calculated at each time step and incorporated as part of the scheme. Results presented show an excellent agreement with the available experimental data. Copyright © 2005 John Wiley & Sons, Ltd.     

A swept‐intersection‐based remapping method in a ReALE framework

A complete reconnection‐based arbitrary Lagrangian–Eulerian (ReALE) strategy devoted to the computation of hydrodynamic applications for compressible fluid flows is presented here. In ReALE, we replace the rezoning phase of classical ALE method by a rezoning where we allow the connectivity between cells of the mesh to change. This leads to a polygonal mesh that recovers the Lagrangian features in order to follow more efficiently the flow. Those reconnections allow to deal with complex geometries and high vorticity problems contrary to ALE method. For optimizing the remapping phase, we have modified the idea of swept‐integration‐based. The new method is called swept‐intersection‐based remapping method. We demonstrate that our method can be applied to several numerical examples representative of hydrodynamic experiments.Copyright © 2012 John Wiley & Sons, Ltd.     

A fully discrete ALE method over untwisted time–space control volumes

In this paper, a fully discrete high‐resolution arbitrary Lagrangian–Eulerian (ALE) method is developed over untwisted time–space control volumes. In the framework of the finite volume method, 2D Euler equations are discretized over untwisted moving control volumes, and the resulting numerical flux is computed using the generalized Riemann problem solver. Then, the fluid flows between meshes at two successive time steps can be updated without a remapping process in the classic ALE method. This remapping‐free ALE method directly couples the mesh motion into a physical variable update to reflect the temporal evolution in the whole process. An untwisted moving mesh is generated in terms of the vorticity‐free part of the fluid velocity according to the Helmholtz theorem. Some typical numerical tests show the competitive performance of the current method. Copyright © 2016 John Wiley & Sons, Ltd.     

An improved MUSCL treatment for the SPH‐ALE method: comparison with the standard SPH method for the jet impingement case

In the present work, a new implementation of the Monotone Upwind‐centered Scheme for Conservation Laws (MUSCL) ‐ Hancock scheme has been developed for the SPH‐Arbitrary Lagrangian Eulerian (ALE) method. The resulting method was tested at various benchmark cases and then it was used to simulate the jet impingement on a flat plate for several different impingement angles, in comparison with the standard SPH method and results from literature. The SPH‐ALE method proves to produce higher quality results than the standard SPH method in all cases, while the MUSCL treatment tends to remedy the issues of the numerical viscosity, inherent to the method, up to a point. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparisons of some difference forms for compressible flow in cylindrical geometry on arbitrary Lagrangian and Eulerian framework

The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical symmetry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian (ALE) method. Numerical results are presented to compare three discrete configurations, i.e., the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometrical source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.     

Sigma transformation and ALE formulation for three‐dimensional free surface flows

In this paper we establish a link between the sigma transformation approach and the arbitrary Lagrangian–Eulerian (ALE) approach. For that purpose we introduce the ALE‐sigma (ALES) approach, which consists in an ALE interpretation of the sigma transformation. Taking advantage of this new approach, we propose a general ALES transformation, allowing for a great adaptability of the vertical discretization and therefore overcoming some drawbacks of the classical sigma transformation. Numerical results are presented, showing the advantages of this general coordinate system, as, for example, a better representation of horizontal stratifications. Copyright © 2008 John Wiley & Sons, Ltd.     

An extended finite element method for the simulation of particulate viscoelastic flows

We present an extended finite element method (XFEM) for the direct numerical simulation of the flow of viscoelastic fluids with suspended particles. For moving particle problems, we devise a temporary arbitrary Lagrangian–Eulerian (ALE) scheme which defines the mapping of field variables at previous time levels onto the computational mesh at the current time level. In this method, a regular mesh is used for the whole computational domain including both fluid and particles. A temporary ALE mesh is constructed separately and the computational mesh is kept unchanged throughout the whole computations. Particles are moving on a fixed Eulerian mesh without any need of re-meshing. For mesh refinements around the interface, we combine XFEM with the grid deformation method, in which nodal points are redistributed close to the interface while preserving the mesh topology. Our method is verified by comparing with the results of boundary fitted mesh problems combined with the conventional ALE scheme. The proposed method shows similar accuracy compared with boundary fitted mesh problems and superior accuracy compared with the fictitious domain method. If the grid deformation method is combined with XFEM, the required computational time is reduced significantly compared to uniform mesh refinements, while providing mesh convergent solutions. We apply the proposed method to the particle migration in rotating Couette flow of a Giesekus fluid. We investigate the effect of initial particle positions, the Weissenberg number, the mobility parameter of the Giesekus model and the particle size on the particle migration. We also show two-particle interactions in confined shear flow of a viscoelastic fluid. We find three different regimes of particle motions according to initial separations of particles.