小波数值方法及其在计算力学中的应用

随着力学研究不断向多学科交叉、跨尺度关联及极端环境影响推进,强非线性、强间断、多场强耦合、多尺度与复杂几何构型已成为解决各类力学问题定量分析所面临的共性特征.长期的定量研究表明,实现具有这类特征力学问题有效求解的核心之一,是构建在多尺度情形、非线性因素作用下具有准确识别、定位、捕获以及分离各个尺度特征尤其是小尺度局部特征能力的数值工具,这些能力包括大尺度低阶近似解与小尺度高阶微小截断误差的有效分离解耦.而小波理论固有的多分辨分析和时频局部化特性,以及丰富的基函数可选择性,恰好能满足这一数学特征需求,因此,可为发展各类复杂力学问题的高效定量求解方法提供有效的理论支撑和丰富多样的技术途径.基于这一事实,本文对小波理论进行了全面探讨,着重介绍了双正交多分辨分析的理论框架和常用小波基的构造方法.在此基础上,深入研究了有限区域上小波逼近格式的构建方法,并系统阐述了各类基于小波理论的数值方法的基本原理、发展历程及其优缺点.特别关注了近期出现的具有突出性能的几类新型小波方法,并详细评述了它们在典型力学问题求解中的应用效果.同时,本文也指出了当前小波方法在复杂强非线性力学问题求解中所面临的挑战,旨在为小波数值方法的未来发展及其在复杂力学与工程问题中的应用拓展提供有益的参考,并为最终实现这些问题的高效、高精度普适定量求解提供新的视角和方法.

小波方法及其力学应用研究进展

小波理论在进行信号处理与函数逼近时体现出非常独特的时频局部性与多分辨分析能力,小波基函数则可兼具正交性、紧支性、低通滤波与插值性等优良的数学性质,这均使得小波分析理论在计算数学与计算力学领域具有很大的应用潜力,也进一步为这些领域的突破性发展带来了新的契机.自20世纪90年代以来,大量的研究已经证明,基于小波理论的数值方法在微分方程求解中具有非常明显的优势,但与此同时也暴露出了一些由小波基函数本身与其特有逼近方式所造成的数值计算应用局限.为了促进小波理论在计算数学与力学领域的创新性应用,给研究人员提供新的研究视角,该文简要梳理了小波分析的发展背景以及基于小波理论的数值方法的研究历史,并着重讨论分析了后者所面临的问题,以及近年来针对这些问题中的基础性难题所取得的研究进展.这些总结与评述有望为后续进一步发展并完善基于小波理论的定量数学求解方法,以及拓展其在力学乃至广泛工程问题求解中的应用提供有意义的参考.

高山景行携后学,仰止追忆感师恩

王仁先生是著名力学家、地球动力学家和教育家,他为我国的科学研究和高等教育发展做出了奠基性的贡献。尤其王仁先生无私地鼓励和支持我们年轻人开拓新的研究领域、瞄准国家重大需求和科学前沿开展科学研究的感人事迹,使我与郑晓静终身难忘。1991年,王仁先生在兰州开会期间,让我与郑晓静去见他。当时王先生是中国力学学会理事长,是我们敬仰的大科学家,我们不知何事,就有些忐忑不安。见面后,王先生笑容满面、和蔼亲切地说,听说你们要开展电磁固体力学研究.

不同盐度对冰菜生长和色素积累的影响

为加快新型耐盐蔬菜的利用,以盆栽冰菜为试材,测定其在不同盐度下的形态指标、生物量和色素含量。结果表明:6‰~12‰.盐度下冰菜叶片数、叶片大小、株高和根长分别比对照大25%、52.8%、75.7%、21.7%和23.6%;茎叶干重和鲜重分别是对照的2.35倍和4.03倍;花青素含量是对照的3.56倍。说明一定盐度能够促进冰菜生长,主要表现为植株长高、分枝增多、叶片增多变大,根系伸长,茎叶生物量和花青素积累,但对根系生物量和叶绿素积累具有抑制作用。6‰~12‰是其生长的最适盐度,大于30%。的高盐浓度则引起胁迫效应。

PERTURBATION ANALYSIS FOR MAGNETO-PLASTIC INSTABILITY OF FERROMAGNETIC BEAM-PLATES WITH GEOMETRIC IMPERFECTION

The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is considered when the plate is located in a strong uniformly distributed magnetic ?eld. After the distribution of magnetic ?elds related to the de?ected con?guration of plate is imaginably divided into two parts, i.e., one is related to the ?at plate and the other dependent on the perturbation of magnetic ?elds for which the plate con?guration changes from the ?at into the deformed state, the perturbation technique is employed to analyze the distribution of the perturbation magnetic ?elds in and out-of the magnetic medium of the ferromagnetic structure in a transverse magnetic ?eld, which leads to some analytical formulae/solutions for the magnetic ?elds and the resulting magnetic force exerted on the plate. Based on them, the magneto-plastic buckling and snapping of the plate in a transverse magnetic ?eld is discussed, and the critical magnetic ?eld is analytically formulated in terms of the parameters of geometry and material of the plate employed by solving the governing equation of the magneto-plastic plate in the applied magnetic ?eld. Further, the sensitivity of the initial imperfection on the magneto-plastic instability, expressed by an ampli?cation function, is obtained by solving the dynamic equation of de?ection of the plate after the inertial force in the transverse direction is taken into account. The results obtained show that the critical magnetic ?eld is sensitive to the plastic characteristic, e.g., hardening coe?cient, and the instability mode and de?ection of the plate are dependent on the geometrical imperfection as well.

APPLICATIONS OF WAVELET GALERKIN FEM TO BENDING OF PLATE STRUCTURE

A kind of calculating method for high order differential expandedby the wavelet scal- ing functions and the of their product used inGalerkin FEM is proposed, so that we can use the wavelet Galerkin FEMto solve boundary-value differential equations with orders higherthan two. To combine this method with the Generalized Gaussianintegral method in wavelt theory, we can find That this method hasmany merits in solving mechanical problems, such as the bending ofplates and Those with variable thickness. The numerical results showthat this method is accurate.

STABILITY ANALYSES ON DYNAMIC CONTROL FOR A MOVING BODY LEVITATED MAGNETICALLY OVER ELASTIC GUIDEWAYS

Based on the Floquet theory on ordinary differential equationswith periodically variable coefficients and the bifurcation approachto nonlinear equations, a numerical approach to determining thestability region of control parameters is established for a dynamiccontrol system composed of a moving body levitated magnetically overflexible guideways. The system is nonlinearly coupled among theelastic deformation of guideways, disturbance the levitation positionof the body and electromagnet- ic control forces.

AN ANALYSIS ON CHARACTERISTIC OF MAGNETOELASTICITY OF A MAGNETIC FIELD MICROSENSOR MADE OF CANTILEVERED PLATES WITH FERROMAGNETIC FILMS

The purpose of this paper is to study the magnetomechanicalcharacteristic of a microsensor which is composed of a cantileveredbeam-plate with ferromagnetic films in order to measure the magneticfield from the deformation of plate when the microsensor is locatedin the magnetic field. To this end, a nu- merical approach made up ofthe finite element method for magnetic field and the finitedifference method for deflection of the microsensor is proposed toperform the numerical analysis of deflection under magnetoelasticinteraction. Some quantitative results of a case study for themagnetoelastic characteristic between the mag- netic field anddeflection of the microsensor in the magnetic field are given. Theresults show that this mi- crosensor can be used not only to measurethe magnitude of magnetic intensity, but also to possibly monitor thedirection of the vector of the magnetic field.

Three-dimensional simulation of the coupled electromagnetic-mechanical responses in a no-insulation racetrack coil

This study investigates the coupled behavior of the mechanical and electromagnetic responses of a high-temperature superconducting(HTS)no-insulation(NI)racetrack coil.A three-dimensional(3D)equivalent circuit network model and mechanical model with nonlinear contact are incorporated into the coupled model.The stress and separation of adjacent turns under a high magnetic field are analyzed by considering the electromagnetic force and cooling process.The numerical results demonstrate that the straight and curved parts of the racetrack coil exhibit distinct mechanical behaviors.Under a strong external magnetic field,the separation between adjacent turns reduces the charging delay of the coil.The maximum stress occurs in the transition regions between the curved and straight parts.The straight part exhibits a larger rotation angle,while the separation regions between adjacent turns are relatively fewer in those parts.The curved part shows a higher proportion of separation regions in the steady stage.The different separation areas in the straight and curved parts also result in distinct turn-to-turn losses during the charging process.Subsequently,a comparative study is conducted on the influence of residual currents induced by discharging.Finally,the effects of overband and inner diameter on the separation behavior are investigated.

Discrete element simulation of localized deformation in stochastic distributed granular materials

The deformation in granular material under loading conditions is a problem of great interest currently. In this paper,the micro-mechanism of the localized deformations in stochastically distributed granular materials is investigated based on the modi-fied distinct element method under the plane strain conditions,and the influences of the confining pressure,the initial void ratio and the friction coefficient on the localized deformation and the stability of granular materials are also studied. It is concluded,based on the numerical simulation testing,that two crossed shear sliding planes may occur inside the granular assembly,and deformation patterns vary with the increasing of transverse strain. These conclusions are in good agreement with the present experimental results. By tangential velocity profiles along the direction normal to the two shear sliding planes,it can be found that there are two different shear deformation patterns: one is the fluid-like shear mode and the other is the solid-like shear mode. At last,the influences of various material parameters or factors on localized deformation features and patterns of granular materials are discussed in detail.

Wavelet solutions of Burgers' equation with high Reynolds numbers

A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.

Numerical analysis of magnetization AC losses in high-temperature superconducting slabs subjected to uniform strains

High-temperature superconductors in superconductor apparatuses are subjected to mechanical strains under operating conditions.These strains cause the degradation of the critical current densities and influence AC losses in the superconductors.Based on the dynamic process of thermomagnetic interaction,we report the results of numerical analysis of AC losses in an infinite high-temperature superconducting slab subjected to a uniform in-plane strain in an alternating external magnetic field parallel to the sample surface.The numerical analysis shows the details of electromagnetic phenomena in the slab and the dependences of AC loss on various external parameters including the uniform strain in the slab and the amplitude and frequency of the external magnetic field.In this paper,we find that whether the magnetic field fully penetrates the superconductor is the key factor that influences the features of AC loss.When the magnetic field cannot fully penetrate the superconductor,the loss rises with increasing strain or decreasing frequency.When the magnetic field can fully penetrate the superconductor,the feature is just opposite.We also analyze the effects of periodic strain on AC loss.It is interesting to find that when the periodic strain frequency equals the external magnetic field frequency,the AC loss reaches the maximum,regardless if the magnetic field fully penetrates the superconductor or not.

Monte Carlo simulation of the electromagnetic wave propagation in the duststorm

Monte Carlo simulations of the extinction rate of electromagnetic wave propagation in the duststorm were presented. The numerical procedure was based on the multiple scattering and independent scattering. The calculated multiple scattering attenuation rate is in good agreement with the measured one,but differs significantly from those obtained under the independent scattering assumption. At the same time,the factors of size parameter,frequency of incident wave,the angle of incident,and sands permittivity and water content have been considered in the attenuation of electromagnetic wave propagation in the duststorm. Numerical results obtained showed that the attenuation rate increases as the fractional volume,frequency of incident wave and sands permittivity increase,and as the angle of incident increases,the attenuation rate decreases.

The effect of electric charge on the mechanical properties of graphene

The effect of electric charge on the mechanical properties of graphene under tensile loading is investigated by using molecular dynamics method.A modified atomistic moment method based on the classical electrostatics theory is proposed to obtain the distribution of extra charges induced by an external electric field and net electric charges stored in graphene.The electrostatic interactions between charged atoms are calculated using the coulomb law.The results show that the Young's modulus and the critical fracture stress under uniaxial tension decrease with the increase of electric potential and net charges on graphene.The failure of graphene induced by electric charges is found to be controlled by charge level.The results indicate that the carbon-carbon bonds at the edge of graphene will break first.