基于无网格数值求解技术的二维连续体结构拓扑优化设计

将无网格径向点插值法(RPIM)引入到连续体结构拓扑优化设计中。在优化问题中,选取节点的相对密度作为设计变量,以结构的柔度最小化作为目标函数,基于带惩罚的各向同性固体材料模型(SIMP)建立了结构拓扑优化的数学模型,推导了目标函数和体积约束的灵敏度,利用优化准则法进行求解。算例表明了应用无网格径向点插值法进行结构拓扑优化设计的可行性和有效性,同时表明选取节点的相对密度作为设计变量可以有效地克服拓扑优化中的棋盘格现象。     

Modeling particle sedimentation in viscous fluids with a coupled immersed boundary method and discrete element method

Numerical techniques have increasingly been used to model fluid–particle two-phase flows. Coupling the immersed boundary method (IBM) and discrete element method (DEM) is one promising approach for modeling particulate flows. In this study, IBM was coupled with DEM to improve the reliability and accuracy of IBM for determining the positions of particles during the sedimentation process within viscous fluids. The required ratio of the particle diameter to the grid size (D/dx) was determined by comparing the simulation results with the analytical solution and experimental data. A dynamic mesh refinement model was utilised in the IBM model to refine the computational fluid dynamics grid near the particles. In addition, an optimum coupling interval between the IBM and DEM models was determined based on the experimental results of a single particle sedimentation within silicon oil at a Reynolds number of 1.5. The experimental results and the analytical solution were then utilised to validate the IBM–DEM model at Reynolds numbers of 4.1, 11.6, and 31.9. Finally, the validated model was utilised to investigate the sedimentation process for more than one particle by modeling the drafting-kissing-tumbling process and the Boycott phenomenon. Benchmark tests showed that the IBM–DEM technique preserves the advantages of DEM for tracking a group of particles, while the IBM provides a reliable and accurate approach for modeling the particle–fluid interaction.     

Mathematical modeling of methane flow in a borehole coal mining system

Safety in coal mining is greatly increased by the drainage of the methane content of coal seams through boreholes, simultaneously producing significant energy. The design of suitable drainage technology is based on the mathematical modeling of methane flow in coal seams. In the calculation of the methane pressure, the new mathematical model presented in this paper considers both the sorption phenomenon of methane depending upon the methane pressure and the fact that the variation in methane pressure can create a change in the stress condition of the rock and, as a consequence of this, a change in the permeability of the coal. The new mathematical model can be used for the numerical simulation of the flow processes in coal seams and methane drainage technology can be designed more accurately.     

Transition between regular and Mach reflection of shock waves: new numerical and experimental results

New numerical and experimental results on the transition between regular and Mach reflections of steady shock waves are presented. The influence of flow three-dimensionality on transition between steady regular and Mach reflection has been studied in detail both numerically and experimentally. Characteristic features of 3D shock wave configuration, such as peripheral Mach reflection, non-monotonous Mach stem variation in transverse direction, the existence of combined Mach-regular-peripheral Mach shock wave configuration, have been found in the numerical simulations. The application of laser sheet imaging technique in streamwise direction allowed us to confirm all the details of shock wave configuration in the experiments. Close agreement of the numerical and experimental data on Mach stem heights is shown. Received 23 November 2000 / Accepted 25 April 2001     

Flutter suppression of a plate-like wing via parametric excitation

The present work is motivated by the well known stabilizing effect of parametric excitation of some dynamical systems such as the inverted pendulum. The possibility of suppressing wing flutter via parametric excitation along the plane of highest rigidity in the neighborhood of combination resonance is explored. The nonlinear equations of motion in the presence of incompressible fluid flow are derived using Hamilton's principle and Theodorsen's theory for modeling aerodynamic forces. In the presence of air flow, the bending and torsion modes possess nearly the same frequency. Under parametric excitation and in the absence of air flow, each mode oscillates at its own natural frequency. In the neighborhood of combination resonance, the nonlinear response is determined using the multiple scales method at the critical flutter speed and at slightly higher airflow speed. The domains of attraction and bifurcation diagrams are obtained to reveal the conditions under which the parametric excitation can provide stabilizing effect. The basins of attraction for different values of excitation amplitude reveal the stabilizing effect that takes place above a critical excitation level. Below that level, the response experiences limit cycle oscillations, cascade of period doubling, and chaos. For flow speed slightly higher than the critical flutter speed, the response experiences a train of spikes, known as ‘firing,’ a term that is borrowed from neuroscience, followed by ‘refractory’ or recovery effect, up to an excitation level above which the wing is stabilized. The results of the multiple scales method are verified using numerical simulation of the original nonlinear differential equations.     

Resolution of Gibbs phenomenon using a modified pseudo-spectral operator in harmonic balance CFD solvers*

A new pseudo-spectral operator is developed for time-spectral harmonic balance solutions of periodic unsteady flows. The method utilises a mechanism similar to sigma-approximation technique with Lanczos filtering function that alters the inverse of the discrete Fourier transformation matrix, leading to a modified pseudo-spectral operator. The modified operator is then used instead of the original operator that mimics the time-derivative term of the unsteady governing equations. The modified operator is capable of damping high-frequency nonlinearities in the harmonic balance solution, thus alleviating the effects of high-frequency oscillations that result in Gibbs-type phenomena. The effectiveness and robustness of the technique are demonstrated through various test cases.     

峰值/谷值电流型控制开关DC-DC变换器的对称动力学现象分析

峰值电流和谷值电流控制开关DC-DC变换器在较宽的电路参数范围内具有对称动力学现象.文中建立了峰值电流和谷值电流控制buck,boost,及buck-boost变换器的统一离散迭代映射模型,并导出了统一的分段光滑迭代映射方程及特征值方程,通过数值仿真得到了占空比变化时的正、逆分岔图和Lyapunov指数谱.研究结果表明,峰值/谷值电流型控制开关变换器的分岔图和Lyapunov指数具有关于点或轴对称的现象.时域仿真结果验证了数值仿真结果,并进一步表明,随着占空比的变化,峰值/谷值电流型控制开关变换器具有对称动力学现象、对称动力学现象和非对称动力学现象共存、非对称动力学现象.     

(α, β)- 空间中的Killing 向量场

本文证明了非Riemannian (α, β)- 空间中的Killing 向量场最大维数是n(n - 1)/2 + 1. 并且给出了具有最大维数Killing 向量场的非Riemannian (α, β)- 空间的度量形式. 最后, 若进一步假定α 是一个齐性Riemannian 度量, 则可确定(α, β)- 空间的第二空隙. 最后给出几个低维流形上Killing 场空间维数的例子, 这表明在(α, β) 情形下Killing 场空间维数的空隙被压缩.     

More power to X‐rays: New developments in X‐ray spectroscopy

Recent developments in X‐ray spectroscopy in the last decade are reviewed. A specific emphasis is placed on displaying the strong natural connection between X‐ray spectroscopy and materials science. Brief explanations of several X‐ray spectroscopic methods are given. X‐ray spectroscopic instruments such as table‐top X‐ray sources are discussed in detail, whereas those employing synchrotron and other sources are briefly addressed. The spectroscopic methods and results from materials investigations are reviewed according to their positions in a 3D parameter space of time, length, and energy. New experimental measurements on atoms, molecules, nanomaterials, and bulk materials that include insulators, semiconductors, metals and magnetic materials using both static and time‐resolved methods are reviewed.     

Nonintegrability of the Painlevé IV equation in the Liouville–Arnold sense and Stokes phenomena

In this paper we study the integrability of the Hamiltonian system associated with the fourth Painlevé equation. We prove that one two-parametric family of this Hamiltonian system is not integrable in the sense of the Liouville–Arnold theorem. Computing explicitly the Stokes matrices and the formal invariants of the second variational equations, we deduce that the connected component of the unit element of the corresponding differential Galois group is not Abelian. Thus the Morales–Ramis–Simó theory leads to a nonintegrable result. Moreover, combining the new result with our previous one we establish that for all values of the parameters for which the $P_{IV}$ equation has a particular rational solution the corresponding Hamiltonian system is not integrable by meromorphic first integrals which are rational in t.