非定常Navier-Stokes方程基于两重网格离散的有限元并行算法

基于两重网格离散和区域分解技巧，提出三种求解非定常Navier-Stokes方程的有限元并行算法.算法的基本思想是在每一时间迭代步，在粗网格上采用Oseen迭代法求解非线性问题，在细网格上分别并行求解Oseen、Newton、Stokes线性问题以校正粗网格解.对于空间变量采用有限元离散，时间变量采用向后Euler格式离散.数值实验验证了算法的有效性.     

基于像差特征分析的变焦光学系统装调

提出了一种基于像差特征分析的变焦系统共轴性装调方法。针对某型20倍变焦光学系统的装调，在分析变焦光学系统装调要求的基础上，通过采用光学定心加工技术，提高变焦系统各镜组内光学元件的同轴度；采用Zygo干涉仪，检测变焦系统在长短焦位置的像差特性分布；借助CodeV软件仿真计算各光学元件在系统中的公差灵敏度分布，并确定产生像差影响的敏感光学元件；在中心偏测量仪上，完成最终光学系统像质的调整。此外，还设计了一种变焦光学系统各动组间同轴度调试装置，对变焦相机主镜筒机械内孔轴线与直线导轨的平行性进行了精确测量，保证了动组组元光轴的同轴精度。装调结果表明:变焦系统成像质量有明显改善，像面一致性得到保证，长短焦轴上传递函数值分别优于技术要求值0.45和0.55，长短焦轴外0.7视场传递函数值优于0.25和0.35，实现了高精度装调，验证了该方法的可靠性。     

Investigation on the effect of density ratio on the convergence behavior of partitioned method for fluid–structure interaction simulation

In order to investigate the effect of density ratio of fluid and solid on the convergence behavior of partitioned FSI algorithm, three strong-coupling partitioned algorithms (fixed-point method with a constant under-relaxation parameter, Aitken’s method and Quasi-Newton inverse least squares (QN-ILS) method) have been considered in the context of finite element method. We have employed the incompressible Navier–Stokes equations for a Newtonian fluid domain and the total Lagrangian formulation for a non-linear motion of solid domain. Linear-elastic (hyper-elastic) model has been employed for solid material with small (large) deformation. A pulsatile inlet-flow interacting with a 2D circular channel of linear-elastic material and a pressure wave propagation in a 3D flexible vessel have been simulated. Both linear-elastic and hyper-elastic (Mooney–Rivlin) models have been adopted for the 3D flexible vessel. From the present numerical experiments, we have found that QN-ILS outperforms the others leading to a robust convergence regardless of the density ratio for both linear-elastic and hyper-elastic models. On the other hand, the performances of the fixed-point method with a constant under-relaxation parameter and the Aitken’s method depend strongly on the density ratio, relaxation parameter selected for coupling iteration, and degree of deformation. Although the QN-ILS of this work is still slower than a monolithic method for serial computation, it has an advantage of easier parallelization due to the modularity of the partitioned FSI algorithm.     

基于改进格林元的压裂水平井动态分析方法

以建立高效的动态分析方法为出发点，以边单元作为求解点，改进传统的格林元方法，减少未知数和求解矩阵维度；并提出基于改进格林元的加密网格加密方法，保证考虑复杂裂缝网络的压裂水平井动态模拟的早期精度.退化模型与半解析解、数值模拟结果进行对比，验证本文基于加密网格的改进格林元方法的准确性和动态分析的高效性.最后进行动态响应的敏感性分析，结果表明：①格林元方法是一种高精度的动态模拟方法，将求解节点设置在网格的边上可以提高压裂水平井动态模拟的速度；②改进格林元方法的加密基于叠加原理，不需要通过插值近似，其求解精度高.在相同加密网格条件下，基于本文改进格林元方法的加密效果比有限差分加密效果更佳；③复杂裂缝导流能力、改造区渗透率提高倍数、改造区大小等参数对压裂水平井动态特征影响较大，在动态分析和参数反演时，应着重考虑这些因素的影响.     

梁柱简化模型在自立塔塔线体系动态响应中的适用性研究

对输电塔进行合理简化可以提高塔线体系动力学仿真的效率。本文给出自立塔梁柱简化模型的计算方法，并提出利用梁柱简化模型计算方法建立自立塔塔线体系整体模型，同时采用桁梁混合模型建立精细化塔线体系整体模型，对两种模型塔线体系静力特性及振型和固有频率等动力特性进行对比分析。以脱冰工况为例，采用生死单元技术将施加在输电线节点上的集中质量单元杀死来模拟脱冰，实现对塔线体系动力学响应的有限元模拟，研究塔线体系简化模型在动态响应中的适用性。结果表明，两种模型弯曲变形误差小，低阶的振型相同，固有频率值误差小，动力特性基本相同；脱冰工况下，自立塔节点位移和塔材内力时程曲线一致，在提高计算效率的情况下，能有效保证计算精度。     

Design of a tuned vibration absorber for a slender hollow cylindrical structure

Abstract

In this paper, details of the design work for a tuned vibration absorber to be used on a hollow cylindrical structure is presented. The vibration problem is of resonant type and the tuned vibration absorber is designed to suppress the displacement vibration response of the free end of the slender hollow structure dominated by the contribution of its lowest transverse vibration modes. The structure is modeled using a commercial finite element software. Finite element model of the structure is verified using experimentally obtained frequency response functions and modal parameters. Effective parameters of the tuned vibration absorber design are then determined based on finite element analysis simulations of the vibration suppression performance of the tuned vibration absorber as it is used on the structure. Details of the tuned vibration absorber design are determined and a prototype is fabricated. Prototype tuned vibration absorber is then characterized experimentally both as a standalone system and also as it is used on the main structure. Vibration reduction performance of the physical prototype of the tuned vibration absorber is also compared with its vibration reduction performance estimated from finite element analysis simulations so that the analysis based design process can be validated.

Communicated by Dumitru Caruntu.     

Spectral analysis of Pk Finite Element matrices in the case of Friedrichs–Keller triangulations via Generalized Locally Toeplitz technology

In the present article, we consider a class of elliptic partial differential equations with Dirichlet boundary conditions and where the operator is div(?a( x )?·), with a continuous and positive over $\stackrel{￣}{\mathrm{\Omega }}$, Ω being an open and bounded subset of ${\mathbb{R}}^d$, d≥1. For the numerical approximation, we consider the classical ${\mathbb{P}}_k$ Finite Elements, in the case of Friedrichs–Keller triangulations, leading, as usual, to sequences of matrices of increasing size. The new results concern the spectral analysis of the resulting matrix‐sequences in the direction of the global distribution in the Weyl sense, with a concise overview on localization, clustering, extremal eigenvalues, and asymptotic conditioning. We study in detail the case of constant coefficients on Ω=(0,1)² and we give a brief account in the more involved case of variable coefficients and more general domains. Tools are drawn from the Toeplitz technology and from the rather new theory of Generalized Locally Toeplitz sequences. Numerical results are shown for a practical evidence of the theoretical findings.     

基于SWT方法的钢绞线索微动疲劳特性分析

为得到钢绞线索丝间接触区的应力场分布并预测微动疲劳裂纹萌生位置和微动疲劳寿命，本文利用参数化方法建立了精细化的钢绞线拉索有限元模型，包括整索模型和不同层丝间接触区域的局部精细化子模型．分析了钢绞线索在两种交变荷载工况下的应力场变化情况，并基于多轴疲劳SWT(Smith-Watson-Topper)临界平面法进行了疲劳特性分析和疲劳寿命预测．主要结论如下：钢绞线索内接触区边缘处的微动幅值较大，中心处几乎没有相对滑动，微动疲劳的初始裂纹萌生点位于接触区域边缘；经不同区域子模型分析比较，在轴向循环荷载作用下，外层钢丝的接触区域比内层钢丝更易发生微动疲劳损伤；在横向位移循环荷载作用下，同层钢丝因位置角度不同而产生了较大的疲劳特性差异，且相比轴向循环拉伸，该工况下最不利单丝的微动疲劳寿命更低；与非接触区域相比，接触区的疲劳寿命大幅降低，微动现象对钢绞线索的抗疲劳性能有明显降低作用．     

A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.