三维断裂弹性动力学的改进无单元Galerkin法

为提高断裂弹性动力学问题数值计算的精度,避免出现病态或奇异方程组,基于改进的移动最小二乘法建立三维弹性动力学问题的积分弱形式,采用罚函数法施加位移边界条件,引入隐式时间积分并且结合三维断裂力学的形函数考虑裂纹尖端的奇异性,探究将改进的无单元Galerkin(improved element-free Galerkin,IEFG)法用于断裂弹性动力学问题的数值计算.通过悬臂梁、柱和矩形板等3个算例,讨论节点分布、影响域比例参数、罚因子和时间步长等参数对计算精度的影响,证明IEFG法用于求解三维断裂弹性动力学问题的正确性和有效性.     

飞机起降过程中机场道面的动力响应

利用改进的Kantorovich法分析了飞机起降过程中机场道面板的动力响应问题.在分析中把机场道面板简化成Winkler地基上四边自由的矩形弹性薄板,通过引入两端自由的梁函数,采用改进的Kantorovich法将机场道面板的动力微分方程化简成为常微分方程,然后利用Duhamel积分求得问题的精确解.文中还通过具体算例,分析了移动载荷的速度、加速度、道面板厚度和地基基床系数对板的动力响应的影响.计算结果表明：移动载荷的速度和地基的基床系数对道面板的动力响应有较大影响;而飞机起降时的加速度、减速度及道面板厚度对机场道面动力响应的影响不大.     

基于比例边界问断谱元法的无穷域亚音速圆柱绕流数值模拟

将比例边界坐标插值方法引入谱元法,构成比例边界谱单元;为了增加计算的稳定性,将节点布置在单元内部;用若干无限谱元离散计算域,用间断有限元方法对无穷域Euler方程亚音速圆柱绕流问题进行了数值模拟;计算结果的误差很小,显示了计算方法的可行性.     

机场地基反应模量动态识别仿真研究

机场道面是由多块道面板连接在一起共同工作的,Kelvin粘弹性地基上有限尺寸矩形板系统为基础,建立了运动荷载作用下四边弹性支撑的道面板的运动方程,利用变分法、功互等定理等方法求得道面板系统的弯沉解析解.进而根据最小二乘方准则,采用Matlab编程拟合实测动挠度和理论动挠度,从而识别出地基反应模量K.实例计算表明所得结果具有较好的精度.研究结果可为机场道面的板厚设计、参数识别和质量评价等提供理论依据.     

势问题的复变量无单元Galerkin方法

为提高无单元Galerkin(Element-Free Galerkin, EFG)方法的计算效率,将复变量移动最小二乘法与EFG方法结合,利用控制方程的积分弱形式并采用Lagrange乘子法引入边界条件,提出势问题的复变量无单元Galerkin(Complex Variable EFG,CVEFG)方法,并推导相关公式.与传统的EFG方法相比,该方法采用复变量移动最小二乘法可以减少试函数中的待定系数,从而减少计算量、提高计算效率. 最后,给出数值算例验证该方法的有效性.     

平面正交各向异性体材料参数识别的新方法

为有效确定平面正交各向异性体的材料参数,提出一种基于比例边界有限元法(Scaled Boundary Finite Element Method,SBFEM)和混合粒子群算法的识别方法.该方法以测量位移与SBFEM计算相应的位移之差的平方和最小为基础,采用粒子群优化（Particle Swarm Optimization, PSO)算法全局搜索材料参数.为加快收敛速度和提高反演识别精度,在PSO算法中引入自然选择的机制.采用SBFEM进行正分析问题计算时,只需对计算域边界进行数值离散,大大减少计算量.相对于边界元法,SBFEM不需要基本解.数值算例表明所提出的方法有效.     

加权无标度网络的级联失效模型

在加权的无标度网络中,为了抵抗网络的级联失效,增强网络的鲁棒性,提出了一种参数可调的级联失效模型.该模型从全局和局域的角度,将节点介数、节点度、节点权重和邻居节点权重相结合构建节点的初始负载,并建立节点容量与初始负载的比例关系,当节点失效后,通过结合失效节点邻居的容量来制定负载重分配规则,进而通过对网络级联失效的分析,推导负载参数的演化过程,得出模型中的参数对网络鲁棒性的影响.最后,通过实验验证了所提方法的有效性.     

基于波前法的参数曲面有限元网格生成算法

为克服参数曲面有限元网格生成中的单元形状映射畸变问题,提出一种曲面有限元网格自动生成算法.该算法由弹性矢量确定曲面上新节点的生成方向和空间位置,利用相应的参数域网格进行新单元拓扑相容性判断.在生成闭曲面网格时,通过添加参/虚边界棱边对闭曲面边界进行调整,确保闭曲面边界信息相对其参数域的完整性;在给出闭曲面极点初始化方法和适当设置单元边线段相等条件的基础上,该算法适用于各种不同形式闭曲面的网格自动生成.实验算例表明,文中算法可生成质量良好的参数曲面和组合面有限元网格.     

热传导方程的无网格Galerkin方法数值模拟研究

为了更好地数值模拟热传导方程,将无网格Galerkin( EFG)方法引入热传导问题的求解中,时间导数采用θ加权方法离散,同时与有限元(FE)方法的数值结果进行了比较,并研究了EFG方法中若干参数的选取对数值结果的影响.计算结果表明:相对于有限元方法,EFG方法能更好地吻合微分方程的解析解,EFG方法在节点布置较稀疏时,也可以获得很高的计算精度;θ≥1/2,EFG方法无条件稳定,且θ=1时数值解精度最高;算例中影响半径取为1.2h≤r＜2.8h,EFG方法可获得较为理想的计算结果.     

改进神经网络对机场刚性道面损伤参数的识别

机场道面使用性状对于飞机安全起降具有重要意义。由于路面有损伤,要求在实际工程中快速识别机场刚性道面性状,但传统解析法缺乏快速有效性。为了提高识别的快速性,提出采用主成分分析(PCA)的神经网络理论自动识别系统的检测方法,通过ANSYS仿真对损伤参数进行研究,确定神经网络输入参数,对采用人工神经网络进行道面性状检测的网络形式与训练函数的选择等问题进行讨论,并考虑实际检测过程中噪声的影响,最终建立PCA—BP神经网络。经过仿真验证,PCA—BP神经网络在一定噪声影响的情况下的检测结果可靠适用,可用于实际工程,证明提出的方法也为刚性道面理论研究提供了新的思路。     

气辅成型首次气体穿透的无网格模拟

基于气体穿透机理的研究分析,精确描述气辅成型中气体穿透推进过程,将三明治成型理论应用到气辅成型中。以矩形平板型腔为例,结合Hele-Shaw流动模型,引入合理简化和假设,建立气体辅助注射成型首次气体充填过程的压力控制方程和气/液交界面运动方程,并应用无网格Galerkin法做数值模拟。得到了不同时刻气体的穿透情况以及不同节点的压力随时间的变化曲线。数值表明:三明治成型理论应用于气辅成型所建的数学模型能准确反应气体穿透推进过程,无网格Galerkin法能较好的追踪气/液界面的动态演化过程。     

A framework combining meshfree analysis and adaptive kriging for optimization of stiffened panels

Structural and Multidisciplinary Optimization - A framework is developed for structural optimization using an Element Free Galerkin (EFG) method for analyzing the structure, a kriging for surrogate...     

Nonlinear Galerkin methods for a system of PDEs with Turing instabilities

We address and discuss the application of nonlinear Galerkin methods for the model reduction and numerical solution of partial differential equations (PDE) with Turing instabilities in comparison with standard (linear) Galerkin methods. The model considered is a system of PDEs modelling the pattern formation in vegetation dynamics. In particular, by constructing the approximate inertial manifold on the basis of the spectral decomposition of the solution, we implement the so-called Euler–Galerkin method and we compare its efficiency and accuracy versus the linear Galerkin methods. We compare the efficiency of the methods by (a) the accuracy of the computed bifurcation points, and, (b) by the computation of the Hausdorff distance between the limit sets obtained by the Galerkin methods and the ones obtained with a reference finite difference scheme. The efficiency with respect to the required CPU time is also accessed. For our illustrations we used three different ODE time integrators, from the Matlab ODE suite. Our results indicate that the performance of the Euler–Galerkin method is superior compared to the linear Galerkin method when either explicit or linearly implicit time integration scheme are adopted. For the particular problem considered, we found that the dimension of approximate inertial manifold is strongly affected by the lenght of the spatial domain. Indeeed, we show that the number of modes required to accurately describe the long time Turing pattern forming solutions increases as the domain increases.     

Optimized meshfree methods for acoustics

When the Helmholtz equation is solved by numerical methods as, e.g., the finite element method (FEM), the solution suffers from the so-called pollution effect. The pollution is mainly caused by the dispersion, meaning that the numerical wave number disagrees with the wave number of the exact solution. This leads to inaccurate results, especially for high wave numbers. In order to obtain acceptable results also for higher wave numbers, either a high element resolution or elements of a higher order can be used. For either option the consequence is an increased computation time and memory capacity.Meshfree methods as the element free Galerkin method (EFGM) and the radial point interpolation method (RPIM) are not dispersion-free either, but it has been shown that meshfree methods are able to reduce the dispersion significantly. Both methods offer several parameters, which can be modified in order to obtain optimal results with respect to the dispersion effect. This work presents an exhaustive parameter study on both the EFGM and the RPIM. It is shown, that the methods can be significantly improved if certain parameters as, e.g., weighting functions, shape parameters, size of the influence domain, are chosen appropriately.     

Collocation and galerkin finite element methods for viscoelastic fluid flow—II. Die swell problems with a free surface

The die swell problem occurs when a fluid flows down a capillary and is emitted into a gas which exerts negligible shear and normal forces on the jet. The die swell problem is solved for Newtonian and viscoelastic fluids. The viscoelastic fluids use a nonlinear Maxwell model but we report calculations for only a small elastic component. Both Galerkin and collocation Finite Element Methods are used and compared. The role of natural boundary conditions in the Galerkin method is compared to the pointwise satisfaction of boundary conditions in the collocation method.     

Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations

We consider a Galerkin Finite Element approximation of the Stokes-Darcy problem which models the coupling between surface and groundwater flows. Then we propose an iterative subdomain method for its solution, inspired to the domain decomposition theory. The convergence analysis that we develop is based on the properties of the discrete Steklov-Poincaré operators associated to the given coupled problem. An optimal preconditioner for Krylov methods is proposed and analyzed.     

Parallel solvers for linear and nonlinear exterior magnetic field problems based upon coupled FE/BE Formulations

An efficient parallel algorithm for solving linear and nonlinear exterior boundary value problems arising, e.g., in magnetostatics is presented. It is based upon the domaindecomposition-(DD)-coupling of Finite Element and Galerkin Boundary Element Methods which results in a unified variational formulation. In this way, e.g., magnetic field problems in an unbounded domain with Sommerfeld's radiation condition can be modelled correctly. The problem of a nonsymmetric system matrix due to Galerkin-BEM is overcome by transforming it into a symmetric but indefinite matrix and applying Bramble/Pasciak's CG for indefinite systems. For preconditioning, the main ideas of recent DD research are being applied. Test computations on a multiprocessor system were performed for two problems of practical interest including a nonlinear example.     

机场净空区CAD系统设计

针对机场净空区设计、计算以及人工出图工作繁重等问题,在三维地形模型的基础上提出机场净空区设计专用CAD系统的功能框架,采用参数化设计方法开发相应的集成CAD系统．采用ARX（AutoCAD Runtimee Xtension）和VC＋＋对AutoCAD进行二次开发,在AutoCAD中实现该专用CAD系统的各项重要功能,给出三维地形三角网格的数据结构以及净空区各限制面的建模方法;通过构建和比较分析机场实地三维模型和机场净空立体模型,直观地显示出机场净空障碍物的分布,自动生成包含净空区地形的平面图和剖面图．某机场的实例表明,该专用CAD系统可简化繁重的计算和出图工作,对促进机场净空区设计具有参考价值．