Solid damping in micro electro mechanical systems

This paper focuses on the problem of the numerical evaluation of dissipation induced by thermoelastic coupling in microelectromechanical systems. An ad hoc conceived, FE based, numerical procedure for the evaluation of the thermoelastic dissipation is proposed and the numerical results are compared with analytical solutions. In order to introduce in the numerical response a dependence on the size of the resonating devices, which is experimentally observed at very small dimensions, a new enhanced non-local coupled thermoelastic model is proposed and the first results are discussed. An erratum to this article can be found at     

Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.     

Numerical simulation of the unsteady behaviour of cavitating flows

A 2D numerical model is proposed to simulate unsteady cavitating flows. The Reynolds‐averaged Navier–Stokes equations are solved for the mixture of liquid and vapour, which is considered as a single fluid with variable density. The vapourization and condensation processes are controlled by a barotropic state law that relates the fluid density to the pressure variations. The numerical resolution is a pressure‐correction method derived from the SIMPLE algorithm, with a finite volume discretization. The standard scheme is slightly modified to take into account the cavitation phenomenon. That numerical model is used to calculate unsteady cavitating flows in two Venturi type sections. The choice of the turbulence model is discussed, and the standard RNG k–εmodel is found to lead to non‐physical stable cavities. A modified k–εmodel is proposed to improve the simulation. The influence of numerical and physical parameters is presented, and the numerical results are compared to previous experimental observations and measurements. The proposed model seems to describe the unsteady cavitation behaviour in 2D geometries well. Copyright © 2003 John Wiley & Sons, Ltd.     

部分输入未知时求解动力复合反演问题的补偿算法

将作者提出的全量补偿算法[8] 推广为一类适用于一般多自由度系统的时域补偿识别算法。该方法是基于最小二乘原则的一类迭代计算方法 ,对于结构上的部分作用力已知的情况 ,可用来同时识别结构的参数并反演输入。文中应用不同类型的结构分析实例说明了此方法适用于实际工程动力检测的可能性。     

A mixed‐interpolation finite element method for incompressible thermal flows of electrically conducting fluids

A new mixed‐interpolation finite element method is presented for the two‐dimensional numerical simulation of incompressible magnetohydrodynamic (MHD) flows which involve convective heat transfer. The proposed method applies the nodal shape functions, which are locally defined in nine‐node elements, for the discretization of the Navier–Stokes and energy equations, and the vector shape functions, which are locally defined in four‐node elements, for the discretization of the electromagnetic field equations. The use of the vector shape functions allows the solenoidal condition on the magnetic field to be automatically satisfied in each four‐node element. In addition, efficient approximation procedures for the calculation of the integrals in the discretized equations are adopted to achieve high‐speed computation. With the use of the proposed numerical scheme, MHD channel flow and MHD natural convection under a constant applied magnetic field are simulated at different Hartmann numbers. The accuracy and robustness of the method are verified through these numerical tests in which both undistorted and distorted meshes are employed for comparison of numerical solutions. Furthermore, it is shown that the calculation speed for the proposed scheme is much higher compared with that for a conventional numerical integration scheme under the condition of almost the same memory consumption. Copyright © 2016 John Wiley & Sons, Ltd.     

IMPROVEMENTS OF GEOMETRICALLY NONLINEAR ANALYSIS ALGORITHMS FOR SPATIAL FRAME STRUCTURES

以几何精确梁理论为基础,分别采用高阶拉格朗日插值和埃米特插值构造高精度空间梁单元。提出基于单元层次平衡迭代的自由度凝聚方法,以保证单元的通用性。实现了基于载荷控制或柱面弧长控制的结构几何非线性分析算法。算例研究结果表明,提出的改进方法不但提高了计算效率,而且还具有较高的数值稳定性;特别是基于三次埃米特插值构造的单元表现出较好的性态,适用于结构屈曲后分析。     

A coupling method of difference with high order accuracy and boundary integral equation for evolutionary equation and its error estimates

In the present paper,a new numerical method for solving initial-boundary valueproblems of evolutionary equations is proposed and studied,combining difference methodwith high accuracy with boundary integral equation method.The numerical approximateschemes for both problems on a bounded or unbounded domain in R~3 are proposed and theirprior error estimates are obtained.     

Numerical simulation of the interaction between flow and flexible nets

A numerical approach is proposed to simulate the interaction between flow and flexible nets in steady current. The numerical approach is based on the joint use of the porous-media model and the lumped-mass model. The configuration of flexible nets can be simulated using the lumped-mass model and the flow field around fishing nets can be simulated using the porous-media model. Using an appropriate iterative scheme, the fluid–structure interaction problem can be solved and the steady flow field around flexible nets can be obtained. In order to validate the numerical models, the numerical results were compared with the data obtained from corresponding physical model tests. The comparisons show that the numerical results are in good agreement with the experimental data. Using the proposed numerical approach, this paper presents the flow field around a single flexible net and two flexible nets with a spacing distance. Both the configuration of the flexible nets and the flow velocity results are in accordance with those of the corresponding physical model tests.     

用差分法与超松弛迭代法求高维平稳FPK方程的解

用不同精度的差分格式将高维平稳FPK方程离散化为线性代数方程组,然后用超松弛迭代法求解该线性代数方程组得到平稳FPK方程的近似解。讨论了不同的差分格式、网格密度及超松弛因子对解精度及收敛速度的影响,并与其他方法的计算精度进行比较,提出用多重网格算法提高计算效率。研究了典型的二维及四维随机系统的稳态响应,算例表明,该算法具有简洁、节省存储量且精度高的特点,是求解高维平稳FPK方程解的有效算法。     

累积线性法在细长柔性悬臂梁结构分析中的应用

为了研究几何大位移悬臂梁的结构响应,在充分利用线性有限元原理与流程的基础上,本文提出"累积线性法" 来对这一问题进行结构建模与求解策略的探讨,数值计算过程表明：该方法在常规有限元软件平台上十分容易实现,并与常规的"一次线性法" 和"非线性求解" 进行了数值对比. 针对本文问题,不仅从理论上指出"累积线性法" 的合理与可行和"一次线性法" 存在的结果不可信等问题;同时,数值仿真也表明前两种方法得到的结果也是不同的, 前者更接近非线性求解的结果. 最后,给出4 点结论.     

非平稳随机激励下结构体系动力可靠度时域解法

将结构动力方程写成状态方程形式,采用精细积分法对其进行数值求解,导出了非平稳激励下结构随机响应的时域显式表达式,该过程的计算量仅相当于两次确定性时程分析的计算量. 基于该显式表达式,结合首次超越失效准则,提出了非平稳随机激励下结构体系动力可靠度的数值模拟算法. 与功率谱方法相比,该方法无需同时在时频域内进行大量数值积分,也无需引入关于响应过程跨越界限次数概率分布, 以及各失效模式相关性等方面的假定. 通过数值算例, 对比了该方法与泊松过程法、马尔可夫过程法、传统蒙特卡罗法的计算精度和计算效率,结果显示该方法具有理想的精度和相当高的效率.      

一种基于Hamel形式的无条件稳定动力学积分算法

Time integration algorithm is a key issue in solving dynamical system. An unconditionally stable Hamel generalized α method is proposed to solve the instability issue arising in the time integration of dynamic equations and to eliminate the pseudo high order harmonics incurred by the spatial discretization of finite element simultaneously. Therefore, the development of numerical integration algorithm to solve the above-mentioned problems has important theoretical and application value. The algorithm proposed in this paper is developed based on the moving frame method and Hamel’s field variational integrators along with the strategy to construct an unconditionally stable Hamel generalized α method. It is shown that a new numerical formalism with higher accuracy can be derived under the same framework of the unconditional stable algorithm established through a special variational formalism and variational integrators. The above-mentioned formalism can be extended from general linear space to Lie group by utilizing the moving frame method and the Lie group formalism of the Hamel generalized α method has been obtained. Both the convergence and stability of the algorithm are discussed, and some numerical examples are presented to verify the conclusion. It is demonstrated by the theoretical analysis that the Hamel generalized α method proposed in the paper is unconditionally stable, second-order accurate and can quickly filter out pseudo high-frequency harmonics. Both conventional and proposed methods have been applied to numerical examples respectively. Comparisons between results of numerical examples show that the aforementioned advantages of the proposed method in terms of accuracy, dissipation and stability are tested and verified. At the same time, it can be developed that new numerical integration algorithms with even higher order accuracy. The scheme can also be proposed, which is suitable for both general linear space and Lie group space. A new way for constructing variational integrators is also obtained in this paper.      

材料弹塑性性能数值模拟的多尺度方法

将均匀化方法和渐近分析(Asymptotic Analysis)与参变量变分原理相结合提出了一种模拟复合材料非线性性能的多尺度数值方法.该方法用渐近分析建立宏-细观变量之间的联系,利用参变量变分原理计算非线性响应,求解过程采用迭代算法.为提高计算精度,针对Von-Mises准则和Tsai-Hill准则,提出了一个基于参变量变分原理的改进算法,算例表明该方法可以显著消除传统方法采用线性展开式构造线性互补条件所带来的误差.     

GENERALIZED FINITE SPECTRAL METHOD FOR 1D BURGERS AND KDV EQUATIONS

A generalized finite spectral method is proposed. The method is of high-order accuracy. To attain high accuracy in time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Her-mite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection- diffusion problem) and KdV equation (single solitary and 2-solitary wave problems), where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.     

An efficient three-dimensional semi-implicit finite element scheme for simulation of free surface flows

An efficient semi-implicit finite element model is proposed for the simulation of three-dimensional flows in stratified seas. The body of water is divided into a number of layers and the two horizontal momentum equations for each layer of water are first integrated vertically. Nine-node Lagrangian quadratic isoparametric elements are employed for spatial discretization in the horizontal domain. The time derivatives are approximated using a second-order-accurate semi-implicit time-stepping scheme. The distinguishing feature of the proposed numerical scheme is that only nodal values on the same vertical line are coupled. Two test cases for which analytic solutions are available are employed to test the proposed scheme. The test results show that the scheme is efficient and stable. A numerical experiment is also included to compare the proposed scheme with a finite difference scheme.     

Boundary element method to solve torsion problem of cracked cylinder

Separating the discontinuous solution by use of the single crack solution, together with the regular solution of harmonic function, the torsion problem of a cracked cylinder is reduced to solving a set of mixed-type integral equations and its numerical technique is then proposed by combining the numerical method of singular integral equation with the boundary element method. Several numerical examples are calculated which will be useful to engineering practice. The method proposed is characterized by its fine accuracy and convenience for using, which can be extended to the cases of multiple crack.The project supported by National Natural Science Foundation of China.     

接触力优化设计的熵正则化方法

包含单侧接触的机械和结构系统中,接触面间的局部接触力很大时,容易导致结构局部磨损和破坏。利用结构优化的手段极小化接触面上的最大接触力是调整接触面上接触力分布的一个有效途径。然而在数学上,目标函数的不可微和约束中的接触条件导致该结构优化问题属于非光滑和非凸优化问题,因而常用优化算法的优化结果是不可靠的。为此,本文提出接触力优化的一个熵正则化模型,并利用基于正则化过程的序列二次结构优化算法求解。所提的方法在数值上避免了处理不可微问题,而且正则化参数的调整还有助于获得更小的局部最优解。以离散结构为例的数值算例验证了本文的模型和算法。     

An efficient Legendre-Galerkin spectral method for the natural convection in two-dimensional cavities

An efficient numerical method is developed for solving the natural convection in two-dimensional cavities. The numerical scheme is proposed by using second-order projection scheme in time direction and Legendre-spectral in spatial variable of the incompressible flow. Finally, a series of numerical examples are presented to demonstrate the efficiency of our algorithm. The numerical strategies developed in this article could be readily applied to study other incompressible fluid problems.     

An interface damage model accounting for in-plane effects

The present work deals with the formulation of a kinematic enriched model for cohesive interface. In fact, the interface kinematics is defined by the relative displacement occurring between the two surfaces of the interface and, even, by the strain arising in the plane of the interface. A damage model which accounts for the mode I and mode II and for the axial deformation of the interface is proposed starting from the Drucker–Prager failure criterion. A numerical procedure is developed implementing the proposed interface model into a new finite element. The nonlinear evolutive problem is solved adopting a predictor–corrector technique within the backward time integration scheme. Simple numerical simulations are presented in order to assess the features of the model. Moreover, numerical applications are carried out in order to demonstrate the ability of the proposed model in reproducing the mechanical behavior of the cohesive elements strengthened with external FRP reinforcements. Comparisons between available experimental data and numerical results obtained using the proposed model show the effectiveness of the presented formulation.     

Numerical studies of the cubic non-linear Schrodinger equation

In this paper, we are concerned with the problem of applying cubic non-polynomial spline functions to develop a numerical method for obtaining approximation for the solution for cubic non-linear Schrodinger equation. The truncation error of the method is theoretically analyzed. Using the Von Neumann method, the proposed method is shown to be unconditionally stable. The linearization technique is carried out to solve the system and to prove that the method is unconditionally stable. Two numerical examples are included to illustrate the practical implementation of the proposed method.