软铁磁材料平面裂纹问题的耦合场

由磁弹性问题的线性化理论导出磁场下平面软铁磁体问题的控制方程和复势解。利用复势解和奇异积分方程方法,对面内磁场和远场载荷作用下的含裂纹无限大软铁磁平面问题进行了求解,得到耦合场的解。并对不同磁力模型的结果和磁场与机械载荷共同作用下的裂尖应力强度因子进行了讨论。     

含孔平板弹性波散射问题的复变函数方法

本文采用平板弯曲波动理论及复变函数方法，对平板开孔弹性波的散射及动应力集中问题进行了分析研究，得到了传播急剧记波时此种平板弯曲波动问题的分析解。若同时采用保角射技术，就为主解平板任意形状开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。作为算例，本文给出了平板开圆孔和椭圆孔附近的动应力集中系数的数值结果，并对其进行了讨论。     

含孔曲板弹性波散射与动应力分析

基于敞口浅柱壳弹性波动方程及摄动方法,对无限大含孔曲板弹性波散射及动应力问题进行了分析研究. 将经典薄板弯曲波动问题的分析解作为本问题的主项,给出了在稳态波下孔洞附近散射波的零阶渐近解. 建立了求解含孔曲板弹性波散射与动应力问题的边界积分方程法,利用积分方程法可获得问题的近似分析解. 并给出了无限大曲板圆孔附近动应力集中系数的数值结果,且对计算结果进行了分析与讨论.     

软铁磁薄板磁弹性屈曲的理论模型

铁磁弹性薄板的磁弹性屈曲问题一直作为电磁——弹性力学相互作用的一个基本模型进行研究,而作用在其磁介质上的磁力计算则是定量理论预测准确与否的关键．到目前为止,文献上已有的理论模型对悬臂铁磁梁式悬臂板在横向磁场中磁弹性屈曲的理论预测值始终高于实验值,有的甚至相差１００％左右．本文基于电磁力计算的微观安培电流模型,严格给出了软铁磁薄板等效横向磁力的宏观计算表达式．在此基础上,建立了电磁——力学相互耦合作用的非线性理论模型．该模型能描述铁磁薄板结构在非均匀横向磁场环境中的磁弹性失稳（或屈曲）．其定量分析采用了有限元法和有限差分法相结合．数值结果显示：本模型给出的磁弹性屈曲的临界磁场值与实验值符合良好．与此同时,文中还对文献中认为较成功的Ｍｏｏｎ－Ｐａｏ模型的基本假设进行了分析．定量结果发现：Ｍｏｏｎ－Ｐａｏ理论模型的基本假设仅在梁式板的长厚比Ｌ／ｈ比较大时（约在２００左右）,是可以接受的,而当Ｌ／ｈ较小时,该假设将导致理论值与实验值的较大误差．Ｌ／ｈ比值越小,理论值与实验值的误差越大     

弹性波绕任意形状界面孔的散射

求解了弹性波绕任意形状界面孔的散射问题.通过入射波、反射波或折射波及孔的散射波场的叠加,得到了界面孔在SH波绕射下的总波场.总波场波函数的级数项待定系数可采用边界配点法来确定,该法不受边界正交性的限制,能够适用于任意形状的边界.最后,对界面椭圆孔进行了实例计算,得到了椭圆孔边的动应力集中系数.     

小内力平板弹性波散射问题的摄动方法

基于平板小挠度弯曲波动方程,采用摄动方法具有纵向内力作用下的平板开孔弹性波的散射问题进行了研究,得么了传播稳态波时此种平板弯曲波动问题的分析解,分析了均匀纵向内力对弹性波散射结果的影响,作为算例,本文给出了平板圆形开孔的动应力集中系数的数值结果,并对计算结果进行了讨论。     

周期界面裂纹的弹性波散射问题研究

本文研究了分布于两个关元限空间的周期界面对垂直入射Ｐ波及ＳＨ波的散射问题，文中利用有限Ｆｏｕｒｉｅｒ变换将一个周期带内散射场的边值问题转化为求解一个带周期核的奇异积分方程，并对ＳＨ波入射的情形进行了详细的分析，求解了相应的异积分方程，最后给出裂纹尖端的应力强度因子的计算公式及远离裂纹时散射位移场的渐进形式，并对散场的动态特性进行了数值分析。     

SH波诱发的阵列纳米孔洞周围的弹性波散射和动应力集中

研究了 SH 波诱发的阵列纳米孔洞周围的弹性波散射和动应力集中问题.当孔洞的尺寸缩小到纳米尺度时,其比表面积显著增加,表面效应对材料力学特性的影响变得非常重要.基于表面弹性理论和经典弹性理论,采用位移势函数法、波函数展开法、弹性波的多重散射理论,分别求得了无限大空间中一组以正六边形方式排列和一组以正方形方式排列的纳米圆柱孔洞附近由SH 波诱发的应力场,分析了表面效应对孔洞周围动应力集中的影响.结果表明纳米圆柱孔洞周围的动应力集中不仅与表面效应有关,而且与孔洞之间的距离有关:表面效应减弱了孔周的动应力集中现象;当孔洞之间的距离增大到一定程度时,孔洞间距对动应力集中的影响可以忽略.这些结果可以作为纳米构件和纳米材料动力学问题研究的基础.     

压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题

分析了压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题。利用傅立叶变换,使问题的求解转换为对一对以裂纹表面上的位移差为未知变量的对偶积分方程的求解。为了求解对偶积分方程,把裂纹面上的位移差展开为雅可比多项式形式,进而得到了裂纹长度、入射波波速及入射波频率对裂纹应力强度因子的影响。从数值结果可以看出,压电压磁复合材料中可导通裂纹的反平面问题的动应力奇异性与一般弹性材料中的反平面断裂问题动应力奇异性相同。     

SH波对界面圆柱形弹性夹杂散射及动应力集中

运用Ｇｒｅｅｎ函数法求解ＳＨ波对界面圆柱形弹性夹杂的散射。首先,给出含有半圆柱形弹性夹杂的弹性半空间表面上任意一点、承受时间谐和的出平面线源荷载作用时的位移函数。其次,取该位移函数作为Ｇｒｅｅｎ函数,推导出定解积分方程。最后,给出介质参数对界面圆柱形弹性夹杂的动应力集中系数的影响。     

Scattering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout

Using the complex variable method and conformal mapping, scattering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied. The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique, the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations. As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular, elliptic cutout are graphically presented in sequence. The project supported by the National Natural Science Foundation of China     

DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR FLEXURAL WAVES IN THIN PLATE WITH CUTOUT

The theoretical analysis and numerical calculation of scattering of elastic waves and dynamic stress concentrations in the thin plate with the cutout was studied using dual reciprocity boundary element method (DRM). Based on the work equivalent law, the dual reciprocity boundary integral equations for flexural waves in the thin plate were established using static fundamental solution. As illustration, numerical results for the dynamic stress concentration factors in the thin plate with a circular hole are given. The results obtained demonstrate good agreement with other reported results and show high accuracy.     

Scattering of elastic waves in an elastic matrix containing an inclusion with interfaces

Based on the theory of elastic dynamics, the scattering of elastic waves and dynamic stress concentration in fiber-reinforced composite with interfaces are studied. Analytical expressions of elastic waves in different medium areas are presented and an analytic method of solving this problem is established. The mode coefficients are determined by means of the continuous conditions of displacement and stress on the boundary of the interfaces. The influence of material properties and structural size on the dynamic stress concentration factors near the interfaces is analyzed. It indicates that they have a great influence on the dynamic properties of fiber-reinforced composite. As examples, numerical results of dynamic stress concentration factors near the interfaces are presented and discussed. This paper provides reliable theoretical evidence for the study of dynamic properties in fiber-reinforced composite. Project supported by the National Natural Science Foundation of China (No. 19972018).     

Scattering of elastic waves by a periodic array of cracks in 3-D space

The problem of scattering of normal incident time harmonic plane elastic waves by a co-planar periodic array of cracks in 3-D space is investigated. The scattered waves consist of a superposition of an infinite number of wave modes [M, N]^T and [M, N]^L,M. N=0, 1, 2, , but only a finite number of them are propagating wave modes. The numerical calculation has been made for rectangular cracks and P wave incidence. The reflection coefficient of [O, O] order,R ₀ ³ , has been studied in detail for various wave numbers and parameters of the geometry for the problem. The reliability of the numerical calculation has been checked by an application of the balance of rates of energies. For an elongated rectangular crack,R ₀ ³ in the corresponding 2-D problem in [2] is recovered. The dynamic stress intensity factors around the crack edge have been obtained. The results as the wave number goes to zero have been compared with those in the correspoding static case. Good agreement is observed.     

MULTIPLE SCATTERING AND DYNAMIC STRESS ANALYSIS OF ELASTIC WAVES IN A FIBER—REINFORCED COMPOSITE WITH INTERFACES

Based on the theory of elastic dynamics, multiple scattering of elastic waves and dynamic stress concentrations in fiber-reinforced composite are studied. The analytical expressions of elastic waves in different regions are presented. The mode coefficients of elastic waves are determined in accordance with the continuous conditions of displacement and stress on the boundary of the multi-interfaces. By using the addition theorem of Hankel functions, the formula of scattered wave fields in different local coordinates are transformed into those in one local coordinate to determine the unknown coefficients and dynamic stress concentration factors (DSCFs). The influences of the distance between two inclusions, material properties and structural size on the DSCFs near the interfaces are analyzed. As examples, the numerical results of DSCFs near the interfaces for two kinds of fiber-reinforced composites are presented and discussed. The project supported by the National Natural Science Foundation of China (19972018)     

Multiple scattering of flexural waves by random configurations of inclusions in thin plates

Flexural waves are scattered by inclusions in a thin plate. For a single inclusion of arbitrary shape, reciprocity relations are obtained connecting coefficients in circular multipole expansions. Then, a formula for the effective wavenumber in a random arrangement of identical circular inclusions is derived, using the Lax quasi-crystalline approximation.     

A theoretical model of magnetoelastic bucking for soft ferromagnetic thin plates

As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results. This project was supported in part by the National Natural Science Foundation of China and the Foundation of the SEdC of China for Returned Chinese Scholars from Abroad.     

Dynamics stress concentrations in Ambartsumian's plate with a cutout

Based on the motion equations of flexural wave in Ambartsumian's plates including the effects of transverse shear deformations, by using perturbation method of small parameter, the scattering of flexural waves and dynamic stress concentrations in the plate with a cutout have been studied. The asymptotic solution of the dynamic stress problem is obtained. Numerical results for the dynamic stress concentration factor in Ambartsumian's plates with a circular cutour are graphically presented and discussed. The project supported by the National Natural Science Foundation of China.     

Elastic wave scattering and dynamic stress in composite with fiber

IntroductionTheproblemofscatteringofelasticwavesinsolidstructureshasnotonlytheoreticalsignificancebutalsowideoutlookinengineering .Thisproblemhasabsorbedmanypeople’sattentionsinmanyfieldssuchasaeronautics,compositemechanics,civilengineeringandearthquakeengineering[1～ 3 ] .Thepropagatingvelocityanddirectionofelasticwaveareinvariableasitpropagatesinaninfiniteuniformmedium .Butscatteringofelasticwavescanoccurifthereexistsincontinuitysuchasinclusion ,crackandcavityinelasticmedium .Fiber_reinfor…