爆炸荷载下岩石破坏的数值流形方法模拟

为了更好地利用数值流形方法对动力学问题进行分析,在对原数值流形方法中的动力学问题求解思想进行分析的基础上,采用动力有限元方法中的Newmark法对该算法进行了改进。改进后的数值流形方法与原来相比具有三个明显的优势:（1）当选择合适的参数后,该方法能够保证解的无条件收敛;（2）可以采用比原算法大得多的时间步长;（3）充分考虑了动力学问题中的阻尼效应。最后通过一个算例说明了改进后的数值流形方法能够很好地模拟岩石在冲击载荷作用下破坏的全过程,克服了有限元法不能模拟岩石破坏后块体运动情况的不足。     

OGY method for a class of discontinuous dynamical systems

In this paper, we prove that the OGY method to control unstable periodic orbits (UPOs) of continuous-time systems can be applied to a class of systems discontinuous with respect the state variable, by using a generalized derivative. Because the discontinuous problem may have not classical solutions, the initial value problem is transformed into a set-valued problem via Filippov regularization. The existence of the ingredients necessary to apply OGY method (UPO, Poincaré map and stable and unstable directions) is proved and the numerically implementation is explained. Another possible way analyzed in this paper is the continuous approximation of the underlying initial value problem, via Cellina??s theorem for differential inclusions. Thus, the problem is approximated by a continuous initial value problem, and the OGY method can be applied as usual.     

Analysis of a discontinuous Galerkin approximation of the Stokes problem based on an artificial compressibility flux

In this work, we propose and analyse a discontinuous Galerkin (DG) method for the Stokes problem based on an artificial compressibility numerical flux. A crucial step in the definition of a DG method is the choice of the numerical fluxes, which affect both the accuracy and the order of convergence of the method. We propose here to treat the viscous and the inviscid terms separately. The former is discretized using the well‐known BRMPS method. For the latter, the problem is locally modified by adding an artificial compressibility term of the form (1/c²)(?p/?t) for the sole purpose of interface flux computation. The flux is obtained as the exact solution of a local Riemann problem. The analysis of the method extends the well‐established strategies for the DG discretization of the Laplacian to the resulting partially coercive problem. Copyright © 2007 John Wiley & Sons, Ltd.     

三维复杂流动的间断有限元方法模拟

本文基于三维可压缩Euler方程,采用基于Runge-Kutta时间离散的间断有限元方法(RKDG方法),对三维前台阶、三维Riemann问题和球Riemann等问题进行了模拟。结果表明,本文的RKDG方法能够在很少的网格内清晰地捕捉到三维复杂流场中的激波和接触间断;同时,将球Riemann问题中z=0.4平面压强沿到对称轴距离的分布与文献中的近似精确解相比,吻合较好,这也验证了本文的RKDG方法不仅能够进行三维复杂流场的定性描述,也能够应用于三维复杂流场的定量计算。     

对流项占优问题的MLPG/SUPG方法数值模拟

在计算对流项占优问题时易产生假扩散,本文把流线型迎风格式应用于MLPG方法中可以减少对流项的影响,通过两个典型例子（旋转流场问题和Brezzi问题）验证该格式的精度与有效性,并与文献中的迎风格式的计算结果进行比较,计算结果表明,该方法能有效地克服假扩散现象,有较好的稳定性和较高的计算精度。     

Influence of shear strains on damping the vibrations of a rectangular plate with piezoelectric actuators

The problem of active damping of the nonstationary vibrations of a hinged rectangular plate with distributed piezoelectric actuators is solved using Timoshenko’s hypotheses. To this end, two methods are employed: (i) a classical method of balancing the principal vibration modes by applying the appropriate potential difference to the actuator and (ii) the dynamical-programming method that reduces the problem to the matrix algebraic Riccati equation. The results obtained by both approaches are compared. The effect of the shear modulus on the amplitude of the damping potential difference and the deflection of the plate is analyzed     

Mathematical programming analysis of bilinear rheological lubrication mechanics

Bilinear rheological lubrication mechanics provides an important basis for the designs of recently developed electrorheological (ER) “smart”journal bearings and those lubricated by mixed fluid-solid lubricants. But there is not yet a reliable and efficient numerical method for such a problem of non-Newtonian fluid mechanics. In the present paper, a finite element method (FEM) together with mat hematical programming solution is successfully used to solve such a problem. A reliable and generalized numerical method for the designs of electrorheological “smart” journal bearings and the bearings lubricated by mixed fluid-solid lubricant is presented.     

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.     

Force reconstruction based on the union of singular spectral analysis and regularization method

Abstract

To overcome the problem of some ill-posed inverse problem of force reconstruction, which is caused by the noise in the measured responses and small singular values of the structure, a technology of force reconstruction based on a hybrid method of singular spectral analysis (SSA) and the Landweber regularization method is proposed in this study for the first time. The SSA is used to filter the structural response before using Landweber regularization. A new choice method of phase space reconstruction dimension is theoretically proposed, and the minimum embedding dimension is determined by the concept of optimizing difference spectrum theory. The feasibility of this method was demonstrated through three kinds of force reconstructions. The numerical simulation results and an acoustic vibration experiment demonstrated that the proposed method is more effective than the traditional method.

Communicated by Wei-Chau Xie.     

Réduction de modèle en convection naturelle par une méthode d'identificationModel Reduction in natural convection using an identification method.

In this numerical study, a natural convection Reduced Model (RM) is built by using results of a Detailed Model (DM, obtained by a pseudo-spectral method), associated with an optimisation problem. RM's structure is defined from a matrix formulation obtained after spatial discretisation of the problem local equations. RM's matrices are identified through the minimisation of a functional build on the discrepancy between DM's and RM's responses, for several values of Rayleigh number. The method is applied to a laminar steady flow in a 2D differentially heated cavity (Window problem). The RM allows one to strongly reduce computing time. To cite this article: M. Girault et al., C. R. Mecanique 332 (2004).     

Dynamical problems of continuous media with random boundary data

A spatial correlation method is formulated for linear dynamical problems in continuum mechanics with random boundary data. The essential feature of the method is the formulation of a nonstochastic mixed initial-boundary value problem for the (matrix) spatial correlation function of the (vector) state variable. Whenever the Green's function of the (stochastic) problem can not be obtained in terms of known functions, a numerical solution of the meansquare response and other second order response statistics by the spatial correlation method is several hundred folds more efficient than any other available method. Further improvements in the computational efficiency of the method for a steady state stationary response process are also noted.     

Un nouveau préconditionneur pour les problèmes elliptiques à coefficients variablesA new preconditonner for general elleptic problems

In this Note we describe a preconditionner for iteratively solving the linear system arising from the discretization of a general nonseparable elliptic problem by spectral element method. This preconditionner is constructed from approximating the original problem with the closest (in some sense) separable elliptic problem. A direct method is then used to invert the preconditionner. To cite this article: M. Azaïez et al., C. R. Mecanique 331 (2003).     

Hypersingular integral equation method for a three-dimensional crack in anisotropic electro-magneto-elastic bimaterials

Using Green’s functions, the extended general displacement solutions of a three-dimensional crack problem in anisotropic electro-magneto-elastic (EME) bimaterials under extended loads are analyzed by the boundary element method. Then, the crack problem is reduced to solving a set of hypersingular integral equations (HIE) coupled with boundary integral equations. The singularity of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main-part analysis method of HIE, and the exact analytical solutions of the extended singular stresses and extended stress intensity factors (SIFs) near the crack front in anisotropic EME bimaterials are given. Also, the numerical method of the HIE for a rectangular crack subjected to extended loads is put forward with the extended crack opening dislocation approximated by the product of basic density functions and polynomials. At last, numerical solutions of the extended SIFs of some examples are obtained.     

The minimal error method for the Cauchy problem in linear elasticity. Numerical implementation for two-dimensional homogeneous isotropic linear elasticity

In this paper, yet another iterative procedure, namely the minimal error method (MEM), for solving stably the Cauchy problem in linear elasticity is introduced and investigated. Furthermore, this method is compared with another two iterative algorithms, i.e. the conjugate gradient (CGM) and Landweber–Fridman methods (LFM), previously proposed by Marin et al. [Marin, L., Háo, D.N., Lesnic, D., 2002b. Conjugate gradient-boundary element method for the Cauchy problem in elasticity. Quarterly Journal of Mechanics and Applied Mathematics 55, 227–247] and Marin and Lesnic [Marin, L., Lesnic, D., 2005. Boundary element-Landweber method for the Cauchy problem in linear elasticity. IMA Journal of Applied Mathematics 18, 817–825], respectively, in the case of two-dimensional homogeneous isotropic linear elasticity. The inverse problem analysed in this paper is regularized by providing an efficient stopping criterion that ceases the iterative process in order to retrieve stable numerical solutions. The numerical implementation of the aforementioned iterative algorithms is realized by employing the boundary element method (BEM) for two-dimensional homogeneous isotropic linear elastic materials.     

Augmented Lagrangian technique applied to a spatially periodic,harmonic Navier-Stokes problem

An application and an extension (to complex variables) of the classical augmented Lagrangian method is performed. Finite element computations are realized in the two-dimensional case of an harmonic Navier-Stokes problem with periodic boundary conditions. A formulation (extended from the traditional Stokes problem) involving a simple Lagrangian, solved by the Uzawa algorithim, was previously used.¹ This treatment proved unsatisfactory for large frequencies. The efficient and well-known augmented Lagrangian technique solved by the Uzawa algorithm is used to overcome these shortcomings. Other, better techniques could be used. Nevertheless the simple method used here is efficient. Moreover the numerical implementation needs little memory storage, which is an important factor in this particular case. The well-known conditioning technique employed is shown to be well-adapted in this case, a fact which emerges from the study of the non-symmetric problem involved. Finally, many tests, computations and experimental data are presented.     

Distributed proportional plus second-order spatial derivative control for distributed parameter systems subject to spatiotemporal uncertainties

In this paper, a robust distributed control design based on proportional plus second-order spatial derivative (P-sD $^2$ ) is proposed for exponential stabilization and minimization of spatial variation of a class of distributed parameter systems (DPSs) with spatiotemporal uncertainties, whose model is represented by parabolic partial differential equations with spatially varying coefficients. Based on the Lyapunov’s direct method, a robust distributed P-sD $^2$ controller is developed to not only exponentially stabilize the DPS for all admissible spatiotemporal uncertainties but also minimize the spatial variation of the process. The outcome of the robust distributed P-sD $^2$ control problem is formulated as a spatial differential bilinear matrix inequality (SDBMI) problem. A local optimization algorithm that the SDBMI is treated as a double spatial differential linear matrix inequality (SDLMI) is presented to solve this SDBMI problem. Furthermore, the SDLMI optimization problem can be approximately solved via the finite difference method and the existing convex optimization techniques. Finally, the proposed design method is successfully applied to feedback control problem of the FitzHugh–Nagumo equation.     

Upwind local differential quandrature method for solving coupled viscous flow and heat transfer equations

The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics. But it is only limited to the flow problems in regular regions. At the same time, here is no upwind mechanism to deal with the convective property of the fluid flow in traditional DQ method. A local differential quadrature method owning upwind mechanism (ULDQM) was given to solve the coupled problem of incompressible viscous flow and heat transfer in an irregular region. For the problem of flow past a contraction channel whose boundary does not parallel to coordinate direction, the satisfactory numerical solutions were obtained by using ULDQM with a few grid points. The numerical results show that the ULDQM possesses advantages including well convergence, less computational workload and storage as compared with the low-order finite difference method. Foundation item: the Municipal Key Subject Programs of Shanghai Biographies: A. S. J. Al-Saif (1964 ~)     

一种改进格林元方法及在渗流问题中的应用

采用格林公式和基本解推导出直接边界积分方程来求解渗流问题.边界积分方程数值离散基于格林元方法(Green element methond),改进了原方法中压力和压力导数的求解方法,命名为混合边界元方法(Mixed boundary element method).相较于格林元类方法,该方法显式考虑了求解节点的外法向流量值和压力值,并使求得的数值解在求解区域上能够连续,符合实际的物理过程,在不增加额外未知数的情况下提高了计算精度.分析了不同网格类型对模拟计算结果的影响,并对稳定渗流问题、非稳定(瞬态)渗流问题和非稳态问题进行了实例计算,结果显示改进方法提高了计算精度,并对各类渗流问题有较好的适应性.     

Manufacturing tolerant topology optimization

In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in （uniformly） too thin （eroded） or too thick （dilated） structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization approach, under- and over-etching is modelled by image processing-based ＂erode＂ and ＂dilate＂ operators and the optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show that the method provides manufacturing tolerant designs with little decrease in performance. As a positive side effect the robust design formulation also eliminates the longstanding problem of one-node connected hinges in compliant mechanism design using topology optimization.