An adaptive algorithm of precise integration for transient analysis

This paper presents an improved precise integration algorithm for transient analysis of heat transfer and some other problems. The original precise integration method is improved by means of the inverse accuracy analysis so that the parameterN, which has been taken as a constant and an independent parameter without consideration of the problems in the original method, can be generated automatically by the algorithm itself. Thus, the improved algorithm is adaptive and the accuracy of the algorithm is not dependent on the length of the time step in the integration process. It is shown that the numerical results obtained by the method proposed are more accurate than those obtained by the conventional time integration methods such as the difference method and others. Four examples are given to demonstrate the validity, accuracy and efficiency of the new method. Project supported by the National Natural Science Foundation of China (No. 19872016, 19872017), the National Key Basic Research Special Foundation (G1999032805) and the Foundation for University Key Teachers by the Ministry of Education of China.     

A novel 3D geometrical reconstruction method for aluminum foams and FEM modeling of the material response

A novel method for modeling cellular materials is proposed based on MATLAB image processing and synchrotron X-ray computed tomography scanning to obtain an accurate calculation result of aluminum foam based on finite element model. The maximum entropy algorithm is employed to obtain the binarization image, and the median filtering algorithm is used to reduce the noise after binarization. The external contour and internal pores boundary is extracted by the “edge” function in MATLAB, and the geometrical model is reconstructed. A two-step mesh algorithm is adopted to mesh the reconstructed geometrical model. Accordingly, the finite element model of aluminum foam is established by the proposed method based on reconstruction geometrical model. The compression behavior of aluminum foam is obtained at 25°C, 100°C, 200°C by ABAQUS, and good agreements with experiments are achieved by applying the present reconstruction algorithm and modeling method.     

残损航空器搬移拖车悬臂的拓扑优化

首先,采用导重准则法对在固定载荷下以位移为约束的拓扑优化问题进行计算,运用一种新的插值模型推导了在单工况作用下的最小质量拓扑优化迭代算法,并通过一个算例验证了该算法的可行性。然后,将该算法应用于残损航空器搬移拖车悬臂的拓扑优化设计中,将由此获得的悬臂的拓扑形貌与结构优化软件Optistruct得到的拓扑结果进行对比。结果表明,二者的迭代速度差别不大,且导重准则法的优化效果更好。作为概念设计,所得的拓扑形貌为以后悬臂结构的优化设计提供了有效参考。     

Symmetric Gauss-Seidel multigrid solution of the Euler equations on structured and unstructured grids

The efficient symmetric Gauss-Seidel (SGS) algorithm for solving the Euler equations of inviscid, compressible flow on structured grids, developed in collaboration with Jameson of Stanford University, is extended to unstructured grids. The algorithm uses a nonlinear formulation of an SGS solver, implemented within the framework of multigrid. The earlier form of the algorithm used the natural (lexicographic) ordering of the mesh cells available on structured grids for the SGS sweeps, but a number of features of the method that are believed to contribute to its success can also be implemented for computations on unstructured grids. The present paper reviews, the features of the SGS multigrid solver for structured gr0ids, including its nonlinear implementation, its use of “absolute” Jacobian matrix preconditioning, and its incorporation of multigrid, and then describes the incorporation of these features into an algorithm suitable for computations on unstructured grids. The implementation on unstructured grids is based on the agglomerated multigrid method developed by Sørensen, which uses an explicit Runge-Kutta smoothing algorithm. Results of computations for steady, transonic flows past two-dimensional airfoils are presented, and the efficiency of the method is evaluated for computations on both structured and unstructured meshes.     

Parameter identification for improved viscoplastic model considering dynamic recrystallization

The successful application of viscoplastic model considering dynamic recrystallization depends on how well the parameters are identified. However, it is difficult to obtain satisfactory parameters using conventional parameter identification methods. The reasons are due to difficulties in obtaining homogeneous deformation, high complexity of physical process described by the model and large number of parameters. In this paper, the material parameters are identified by inverse analysis. Global information on objective function is firstly studied by an improved uniform random sampling method; secondly, a hybrid global optimization method, which combines the genetic algorithm, the Levenberg–Marquardt algorithm, the augmented Gauss–Newton algorithm and the flexible tolerance method, is constructed and an inverse analysis numerical procedure, which combines the proposed optimization method with the finite element analysis, is proposed; at last, a set of satisfactory material parameters for 26Cr2Ni4MoV is obtained by the proposed inverse analysis numerical procedure.     

Generalized-order perturbation with explicit coefficient for damage detection of modular beam

A general method is formulated to estimate damage location and extent from the explicit perturbation terms in specific set of eigenvectors and eigenvalues. At first, perturbed orthonormal equation is generated from the perturbation of eigenvectors and eigenvalues to obtain the k-th explicit perturbation coefficients. At second, perturbed eigenvalue equation is generated from the perturbation of eigenvector and eigenvalue, and first-order expansion of the stiffness matrix to obtain other explicit perturbation coefficients. Stiffness parameters are computed from these equations using an optimization method. The algorithm is iterative and terminates under certain criteria. A fixed–fixed modular beam with various numbers of elements is used as test structure to investigate the applicability of the developed approach. By comparison with the Euler–Bernoulli beam, discretization errors are analyzed. In six elements beam, first-order algorithm converges faster for small percentage damage. Second-order algorithm is more efficient for medium percentage damage. For large percentage damage, the second-order algorithm converges more effectively. Meanwhile, for eight elements large percentage damage and ten elements small percentage damage, second-order algorithm converges faster to the termination criterion.     

Proximity point algorithm for low-rank matrix recovery from sparse noise corrupted data

The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.     

Online system identification using fractional-order Hammerstein model with noise cancellation

Slow convergence and low accuracy are two main drawbacks in nonlinear system identification methods. It becomes more complicated when time delay and noises are considered. In this paper, considering a fractional-order Hammerstein model, an online identification method is proposed. A combination of an evolutionary optimization method and recursive least square algorithm is used to estimate the system parameters and orders in the presence of unknown noises. Finally, simulation results are taken to prove the effectiveness of the proposed algorithm.

     

用逐点插入法生成Delaunay四面体自适应网格

介绍一种基于Delaunay算法的四面体自适应网格的自动划分方法。该方法用单元尺度场控制生成网格的疏密分布,在不满足尺度场要求的单元面形心处插入新节点,同时计算新节点单元尺寸参数,实现三维实体的Delaunay四面体自动划分。此方法具有几个特点:一是表面网格与体内网格同步划分,无需区分两者;二是结点与单元同时生成;三是生成网格自适应性好,疏密分布任意。另外,还介绍了三维网格划分中两个相关算法:一个是约束面恢复算法,该算法基于约束面不允许有单元边与之相交的性质而提出的;另一个是将二维射线法推广至三维空间,判断一个点是否在一多面体内,实现了凹多面体的划分。最后通过算例对单元质量进行了评价。本文所述方法是一种有效的四面体自适应单元生成算法。     

Optimal control of material concentration using Fourier series

This paper presents an optimal control of the material concentration using Fourier series and finite element method. It is assumed that the optimal control value can be expanded into a Fourier series. The Fourier coefficient is identified to minimize the performance function and the optimal control value is determined. The Sakawa–Shindo algorithm is used for the minimization algorithm. The advection–diffusion equation and shallow water equation are used for the analysis of material concentration and water flow. The Crank–Nicolson scheme and finite element method using bubble function element with stabilized control parameter are employed as temporal and special discretization. Copyright © 2004 John Wiley & Sons, Ltd.     

Symplectic multi-level method for solving nonlinear optimal control problem

By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper.     

基于SPH-FEM耦合方法的柔性导爆索分离装置爆炸分离过程数值模拟

为深入研究柔性导爆索在爆炸分离装置中的作用过程和机理,提出一种改进的光滑粒子流体动力学方法（smoothed particle hydrodynamics, SPH）与有限单元法（ finite element method, FEM）耦合算法。新方法中不仅包含导爆索模拟的SPH方法与分离装置模拟的FEM方法之间的接触算法,同时将完全损伤失效后的单元采用转化算法动态转化成SPH粒子继续参与计算,转化后的粒子与未转化的有限单元之间采用接触算法计算。采用该方法对环型和平板型两种爆炸分离结构的分离过程进行了数值模拟,验证了新方法的准确性与问题适用性;分析了分离板的变形断裂及损伤碎片的飞溅过程,得到了分离装置表面不同时刻的应力分布、损伤因子的变化趋势、von Mises应力的变化趋势;探讨了炸药在不同比内能情况下单元的屈服损伤速度、碎片的飞溅位移速度。     

An operator splitting algorithm for the three-dimensional advection–diffusion equation

Operator splitting algorithms are frequently used for solving the advection–diffusion equation, especially to deal with advection dominated transport problems. In this paper an operator splitting algorithm for the three-dimensional advection–diffusion equation is presented. The algorithm represents a second-order-accurate adaptation of the Holly and Preissmann scheme for three-dimensional problems. The governing equation is split into an advection equation and a diffusion equation, and they are solved by a backward method of characteristics and a finite element method, respectively. The Hermite interpolation function is used for interpolation of concentration in the advection step. The spatial gradients of concentration in the Hermite interpolation are obtained by solving equations for concentration gradients in the advection step. To make the composite algorithm efficient, only three equations for first-order concentration derivatives are solved in the diffusion step of computation. The higher-order spatial concentration gradients, necessary to advance the solution in a computational cycle, are obtained by numerical differentiations based on the available information. The simulation characteristics and accuracy of the proposed algorithm are demonstrated by several advection dominated transport problems. © 1998 John Wiley & Sons, Ltd.     

Numerical solution of the problem of an ice sheet under a moving load

A method for analyzing the bending of an ice sheet subjected to a moving load is proposed. The problem is solved in a dynamic formulation. The algorithm of solution is based on the finiteelement method and the finite-difference method. The method proposed allows one to determine the stress-strain state of an ice sheet for any law of motion of a load over ice. Two versions of initial conditions are considered. Examples of calculations are given. Komsomol’sk-on-Amur State Technical University, Komsomol’sk-on-Amur 681013. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 243–248, July–August, 1999.     

Viscoelastic flow between eccentric rotating cylinders: unstructured control volume method

This paper reports a convergent numerical algorithm for the Upper-Convected Maxwell (UCM) fluid between two eccentric cylinders at various eccentricity ratios (?); the outer cylinder is stationary, and the inner one rotating. The problem is solved by an unstructured control volume method (UCV), which is designed for a general viscoelastic flow problem with an arbitrary computational domain. A self-consistent false diffusion technique and an iteration scheme are used in combination to solve the problem. The computations of the UCM fluid using the numerical algorithm are carried out to a higher value of the Deborah number (De) at each eccentricity tested than hitherto possible with previous numerical simulations. The solutions are compared with previous numerical results, confirming the effectiveness of the UCV method as a general technique for solving viscoelastic flow problems.     

Solution of the shallow‐water equations using an adaptive moving mesh method

This paper extends an adaptive moving mesh method to multi‐dimensional shallow water equations (SWE) with source terms. The algorithm is composed of two independent parts: the SWEs evolution and the mesh redistribution. The first part is a high‐resolution kinetic flux‐vector splitting (KFVS) method combined with the surface gradient method for initial data reconstruction, and the second part is based on an iteration procedure. In each iteration, meshes are first redistributed by a variational principle and then the underlying numerical solutions are updated by a conservative‐interpolation formula on the resulting new mesh. Several test problems in one‐ and two‐dimensions with a general geometry are computed using the proposed moving mesh algorithm. The computations demonstrate that the algorithm is efficient for solving problems with bore waves and their interactions. The solutions with higher resolution can be obtained by using a KFVS scheme for the SWEs with a much smaller number of grid points than the uniform mesh approach, although we do not treat technically the bed slope source terms in order to balance the source terms and flux gradients. Copyright © 2004 John Wiley & Sons, Ltd.     

多目标结构优化设计的中心法

提出一个求解多目标结构优化设计的中心法，该方法可以看作是求解单目标优化问题中 心法的直接推广. 它针对每个目标函数引进一个``移动靶'以形成各目标函数的水平截集， 然后通过计算并跟踪这些目标函数的水平集与原约束集合形成的交集中心，来达到求解多目 标优化问题的目的. 这个方法在不增加额外计算量的情况下，实现了多目标优化与单目标优 化的算法统一，因此非常容易在现有的结构优化设计的程序中实现. 给出了几个结构优化 设计问题的算例，验证了算法的有效性和可靠性.     

广义概率密度演化方程的再生核质点加密算法

采用一般质点近似和再生核质点近似表示系统响应量,给出了动力系统响应量的一般表达式。在此基础上,发展了一类求解广义概率密度演化方程的再生核质点加密算法,给出了详细求解步骤。以单自由度系统为例,从响应概率密度的角度考察了再生核质点加密算法的精度。以多自由度框架结构为例,验证了再生核质点加密算法求取非线性随机动力系统响应概率密度的正确性。     

An application of Roe's flux-difference splitting for k-ϵ turbulence model

In this paper Roe's flux-difference splitting is applied for the solution of Reynolds-averaged Navier-Stokes equations. Turbulence is modelled using a low-Reynolds number form of the k-? tubulence model. The coupling between the turbulence kinetic energy equation and the inviscid part of the flow equations is taken into account. The equations are solved with a diagonally dominant alternating direction implicit (DDADI) factorized implicit time integration method. A multigrid algorithm is used to accelerate the convergence. To improve the stability some modifications are needed in comparison with the application of an algebraic turbulence model. The developed method is applied to three different test cases. These cases show the efficiency of the algorithm, but the results are only marginally better than those obtained with algebraic models.     

求解一类可分离凸规划的对偶显式模型DP-EM方法

推导对偶目标函数的精确显式表达式,可选用更多成熟高效的求解方法,从而进一步提高了非线性规划对偶理论求解结构拓扑优化问题的效率.研究工作来源于非线性凸规划同其对偶规划的间隙为零,可以等价转化为对偶问题求解,通常可以大大地缩小问题的规模,可是二者不具有显式关系却影响了对偶解法的应用.所幸的是,结构优化当中一大类问题包括连续体结构拓扑优化问题,不仅具有凸性,而且具有变量可分离性,于是原变量和对偶变量之间有了显式关系,因此,对偶解法成了38年来被应用的有效方法之一.然而长期以来,对偶问题的目标函数并不是显式,这缘于含参数的极小化问题导致目标函数为隐式表达,常见的显式化方法是进行二阶近似.本文突破了对偶问题难以显式化只能采用近似显式的定势,将我们提出的"对偶规划-显式模型"(DP-EM)方法应用于连续体结构拓扑优化,并与对偶序列二次规划(DSQP)算法及移动渐近线(MMA)算法为求解器的方法进行计算效率对比,结果显示:(1)MMA算法比DP-EM算法和DSQP算法的外部迭代次数均多;(2)DP-EM算法与DSQP算法外循环次数相同,而内循环数显著减少.说明了DP-EM算法具有显式对偶函数的优势.