梯度功能材料拟静态热弹性问题的泛函和变分原理

本文从梯度功能材料拟静态热弹性问题的控制方程出发,说明了梯度功能材料在其物性系数为坐标变量的函数时的三维拟静态热弹性问题的泛函是存在的,导出了相应的泛函,并建立了相应的变分原理.     

功能梯度板条Ⅲ型裂纹问题研究

现存文献关于梯度材料断裂问题的研究大都是假设材料性质为坐标的指数函数或幂函数,而对其它函数形式较少采用.作者假设功能梯度材料剪切模量的倒数为坐标的线性函数,而泊松比为常量,研究功能梯度板条的反平面裂纹问题.利用Fourier积分变换技术和传递矩阵法将混合边值问题化为一对奇异积分方程,通过数值求解奇异积分方程获得板条裂纹在反平面载荷作用下的应力强度因子,并讨论了裂纹相对尺寸以及材料非均匀性对应力强度因子的影响.     

细观结构参数对功能梯度压电板的力场和挠度场的影响

假定功能梯度压电材料的物性参数沿着厚度方向,按照幂函数、e指数函数及正弦函数3种不同的梯度模型分布,从三维电弹性耦合的基本方程出发,采用层合模型并利用状态变量法对功能梯度压电板的应力场和挠度进行分析.分别考虑作用机械荷载和电荷载,并且在此基础上分析了不同的材料组份和几何尺寸对功能梯度压电材料的板得力场和挠度场的影响,并对数值结果进行了对比分析研究.为功能梯度压电结构设计及材料优化提供一定参考依据.     

梯度功能材料热传导问题的泛函和变分原理

本文尝试从梯度功能材料热传导问题的控制方程出发，证明了梯度功能材料在其物性系数为坐标变量约函数时的三维热传导问题的泛画是存在的，导出了相应约泛函，建立了相应的变分原理．     

梯度功能材料热传导问题的泛函和变分原理

本文尝试从梯度功能材料热传导问题的控制方程出发，证明了梯度功能材料在其物性系数为坐标变量的函数时的三维热传导问题的泛函是存在的。导出了相应的泛函，建立了相应的变分原理。     

磁电弹性旋转圆环(圆盘)的三维分析

由控制方程直接得到磁电弹性旋转圆环相应于离心力的特解，利用位移、电势和磁势的通解推导出一个关于应力、电位移和磁感应强度的通解，再在特解上叠加一个准调和函数形式的通解且满足边界条件，从而给出磁电弹性旋转圆环的解析解，同样方法可以得到磁电弹性旋转圆盘的解析解，给出了算例，对磁电材料、压电材料和横观各向同性弹性材料的数值结果作了比较，磁电材料与压电材料的径向位移很相近，与弹性材料有较大差别；磁电材料与压电材料的径向、环向应力都很相近，且与纯弹性材料的应力曲线很相似，三种材料的最大应力都出现在圆盘中心处；径向电位移与半径呈线性规律；磁电材料与压电材料的电位移略有差别。     

梯度功能材料拟静态热弹性问题的泛函和变分原理

本文从梯度功能材料拟静态热弹性问题的控制方程出发,说明了梯度功能材料在其物性系数为坐标变量的函数时的三维拟静态弹性问题的泛函是存在的,导出的相应的泛函,并建立了相应的变分原理。     

旋转功能梯度压电空心圆柱的精确

针对内外表面作用均布压力和电势的功能梯度径向极化无限长压电空心圆柱旋转问题,给出了其精确解.分析了旋转功能梯度压电空心圆柱内径向应力、环向应力及电势的分布情况,还研究了材料的非均匀特性、空心圆柱的内外径比率以及外加电势对机械场和电场的影响.通过设计合适的功能梯度形式、选择合适的内外径比率以及在内外表面施加恰当的外加电势能够达到改善旋转功能梯度压电空心圆柱的力学行为.得到的解可应用于沿径向按幂函数规律变化的旋转压电功能梯度空心圆柱构件的精确分析和优化设计中.     

线性分布载荷作用下功能梯度简支梁弯曲解析解

针对线性分布载荷作用下,材料属性在厚度上任意变化的功能梯度简支梁弯曲问题,利用应力函数法,对其解析解进行了研究.首先引入了一个应力函数Φ,根据平面应力状态的基本方程,得出了功能梯度梁的应力函数应满足的偏微分方程,并根据应力边界条件得出了应力函数及各向应力的表达式;进而根据功能梯度材料的本构方程和位移边界条件,得出了结构应变和位移的分布.通过将本文的解析解与有限元仿真结果进行对比,验证了计算结果的正确性;并求解了材料组分呈幂律分布的功能梯度梁的应力和位移分布,得到了上下表层材料的弹性模量比λ与组分材料体积分数指数n对应力和位移分布的影响.     

横观各向同性功能梯度圆板弯曲问题的精确解

对周边为弹性支承边界条件下的横观各向同性功能梯度材料圆板轴对称弯曲问题进行了分析.将位移函数写成傅里叶-贝塞尔级数的形式,根据横观各向同性功能梯度材料基本方程,并针对指数函数形式的梯度分布情况,对功能梯度圆板轴对称弯曲问题的位移和应力进行了精确分析.并通过具体算例,分析了在圆板上、下表面荷载作用下,材料性质的不同梯度变化对圆板结构响应的影响.分析结果表明,材料性质的梯度变化对圆板的力学性能有显著影响.     

Fundamental solutions for transversely isotropic magneto-electro-elastic media and boundary integral formulation

Smart or intelligent materials with piezoelectric and/or piezomagnetic, due to their ability of converting energy from one form to the other(among magnetic, electric, and mechanical energies) have been widely used in such hi-tech areas as electrics, laser, supersonics, microwave, infrared, etc. Furthermore, composites made of piezoelectric/piezomagnetric materials exhibit a magneto- electric effect that is absent in single-phase piezoelectric or piezomagnetic materials[1,2]. In order to study …     

Behavior of two parallel symmetry permeable cracks in functionally graded piezoelectric materials subjected to an anti-plane shear loading

The behavior of two parallel symmetry permeable cracks in functionally graded piezoelectric materials subjected to an anti-plane shear loading was investigated. To make the analysis tractable, it was assumed that the material properties varied exponentially with coordinate vertical to the crack. By using the Fourier transform, the problem could be solved with the help of two pairs of dual integral equations, in which the unknown variables were the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials. The normalized stress and electrical displacement intensity factors were determined for different geometric and property parameters for permeable electric boundary conditions. Numerical examples were provided to show the effect of the geometry of the interacting cracks and the functionally graded material parameter upon the stress intensity factors of cracks.     

The non-local theory solution of a Griffith crack in functionally graded materials subjected to the harmonic anti-plane shear waves

In this paper, the dynamic stress field near crack tips in the functionally graded materials subjected to the harmonic anti-plane shear stress waves was investi- gated by means of the non-local theory. The traditional concepts of the non-local theory were extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it was assumed that the material properties vary exponentially with coordinate parallel to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. The magnitude of the finite dynamic stress field depends on the crack length, the parameter describing the functionally graded materials, the circular frequency of the incident waves and the lattice parameter of materials.     

带矩形槽半平面在自重下的应力场和位移场

根据复势理论，导出半平面内一点集中力产生的应力及位移表达式，并导出求解带矩形槽的弹性半平面在自重作用下这类问题的一组两变元四个未知函数的Cauchy型奇异积分方程及其应力场和位移场的表达式。     

Design and Development of a Vector Control System of Induction Motor Based on Dual CPU for Electric Vehicle

A vector control system for electric vehicle (EV) induction motor drive system is designed and devel-oped. Its hardware system based on dual CPU( microcomputer 80C196KC and DSP TMS320F2407) is imple-mented. The fundamental mathematics equations of induction motor in the general synchronously rotating refer-ence frame (M-T frame) used for vector control are achieved by coordinate transformation. Rotor flux equation and torque equation are deduced. According to these equations, an induction motor mathematical model and rotor flux observer model are built separately. The rotor flux field-oriented vector control method is implemented based on these models in system software, some of the simulation results with Matab/Simulink are given. The simula-tion results show that the vector control system for EV induction motor drive system has better static and dynamic performance, and the rotor flux field-oriented vector control method was practically verified.     

无限长条功能梯度材料自由边界反平面裂纹动力学问题

利用功能梯度材料剪切模量的指数模型,对无限长条自由边界反平面Yoffe裂纹的动力学问题进行了研究.通过积分变换求得了应力场和位移场,将混合边界值问题简化为一组对偶积分方程,并利用Copson方法对动应力强度因子进行了求解.分析了裂纹运动速度、梯度参数及裂纹长度对裂纹尖端动应力强度因子的影响.数值计算表明,动应力强度因子随着裂纹运动速度和裂纹长度的增加而增大,随着梯度参数的增加而降低.     

经典电磁场麦克斯韦方程组的理论推证

放弃麦克斯韦的涡旋电场假说和位移电流假说 ,从物理学的基本定义和实验出发 ,以数学为工具 ,对经典电磁场麦克斯韦方程组进行了理论推证     

全向电动底盘转向角度的检测与控制

全向电动底盘可实现四轮独立驱动(4WD)和四轮独立转向(4WS),是未来非道路车辆发展的重要方向.电动轮转向角度的精密检测和准确控制对于全向电动底盘四轮独立转向(4WS)功能的实现至关重要.介绍了一种检测和控制电动轮旋转角度的新方法.采用绝对编码器检测电动轮的实际位置,由中央控制器PLC接收绝对编码器输入的格雷码并转换为标准二进制数,经计算得到电动轮的实际转角.通过与电动轮的目标转角相比较,由PLC根据比较结果控制电动轮的运动,再通过电磁离合器的配合,实现电动底盘转向角度的检测与控制.实验表明,这种检测和控制电动轮旋转角度的方法测量准确,控制灵敏,安全可靠,为旋转角度的测量和控制提供了一种行之有效的新方法.     

Basic solution of two parallel Mode-I cracks in functionally graded materials

The solution of two parallel cracks in functionally graded materials subjected to a tensile stress loading is derived in this paper. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate parallel to the crack. The problem is formulated through Fourier transform into four pairs of dual integral equations, in which the unknown variables are jumps of displacements across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces are directly expanded as a series of Jacobi polynomials to obtain the shielding effects of the two parallel cracks in functionally graded materials.     

The nonlocal theory solution of a Mode-I crack in functionally graded materials

The behavior of a Mode-I finite crack in functionally graded materials is investigated using the non-local theory. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate vertical to the crack. The problem in this paper can be solved through the Fourier transform with the help of two pairs of dual integral equations, in which the unknown variables are jumps of dis- placements across crack surfaces. To solve dual integral equations, the jumps of displacements...