四边简支热弹性复合材料层合正交双曲壳的解析解

在正交双曲坐标系下,对于考虑温度梯度的热弹性复合材料,首先基于基本方程,由状态空间法推导出其非齐次状态方程;再根据对偶变量理论,将热传导关系并入到复合材料的本构关系中,得到热弹性复合材料包含温度的增维本构关系,由此增维本构关系,结合状态空间法,消去平面内的应力分量,便可直接推导出可独立求解的热弹性复合材料的齐次状态方程.齐次状态方程的导出,将大大简化层合正交双曲壳的求解过程,提高计算精度,且齐次状态方程可以直接进行有限元离散,为工程实践中复杂边界条件下层合结构的分析求解提供一种新方法.     

层合开口壳脱层损伤分析的半解析法

首先应用柱坐标系下弹性材料修正后的混合H-R(Hellinger-Reissner)变分原理,推导开口圆柱壳的状态向量方程和相应的有限元列式.然后充分利用柱坐标系下状态向量方程半解析法的优越性,建立含脱层损伤层合开口壳的数学模型,为层合开口壳脱层问题的分析提供一种可选的方法.数值实例的分析结果表明方法是成功的.     

含有固支边热弹性复合材料层合板的精确解

基于含有固支边的热弹性复合材料层合板,将固支边变为简支边,由热弹性复合材料的基本方程和其包含温度的增维本构关系,利用状态空间法,推导出机—热耦合并含有固支边的热弹性复合材料层合板的非齐次状态方程;通过增维方法,将非齐次状态方程转化为齐次状态方程,并由精细积分法求解。从而得到含有固支边热弹性复合材料层合板静态问题的精确解。齐次状态方程的导出可避免矩阵求逆,提高计算效率和数值计算的稳定性。数值算例验证了方法的正确性。     

含有固支边热弹性复合材料层合板的精确解

基于含有固支边的热弹性复合材料层合板,将固支边变为简支边,由热弹性复合材料的基本方程和其包含温度的增维本构关系,利用状态空间法,推导出机—热耦合并含有固支边的热弹性复合材料层合板的非齐次状态方程;通过增维方法,将非齐次状态方程转化为齐次状态方程,并由精细积分法求解。从而得到含有固支边热弹性复合材料层合板静态问题的精确解。齐次状态方程的导出可避免矩阵求逆,提高计算效率和数值计算的稳定性。数值算例验证了方法的正确性。     

热磁电弹性材料层合板的半解析法

以三维弹性体的HR混合变分原理为基础,考虑熵变量,重构热磁电弹性体的本构方程,并应用Hamilton正则方程半解析法,求解热磁电弹性层合板问题,主要原因为熵变量的引入,可以将热磁电弹性非齐次的Hamilton正则方程直接齐次化,齐次的Hamilton正则方程半解析法简化热磁电弹性板问题的分析过程.     

含固支边的压电层合开口圆柱壳的精确解法

通过柱坐标系下压电材料的广义Helinger-Reissner变分原理,推导压电开口圆柱壳的非齐次状态方程,然后假设边界应力函数,建立含固支边压电开口圆柱壳的非齐次状态方程,接着应用增维方法将非齐次状态方程转化为齐次状态方程,最后采用状态转移矩阵技术,得出含固支边的压电层合开口圆柱壳的齐次状态方程.齐次状态方程的求解避免了求解非齐次状态方程过程中的矩阵求逆运算,有利于程序的实现和数值运算稳定性的提高,大大地提高了计算效率.数值算例表明文中方法是有效的.     

四边简支电磁热弹性层合正交双曲壳的拉式解

基于电磁热弹性的本构方程,进一步以相关文献为依据建立了其增维形式的本构关系,推导了电磁热弹性材料正交双曲壳的齐次状态方程。然后,通过对齐次状态方程进行了拉氏变换,得到了复杂的高次项多项式形式的系数矩阵。考虑到逆变换的方便性和求解效率问题,对拉氏变换后的系数矩阵中复杂的高次项多项式进行了分式分离处理。最后通过数值实例验证了方法的正确性,其求解效率与精细积分法相当。     

对边固支对边自由边界下复合材料层合板的解析解

在状态空间理论体系下,研究四边简支层合板壳精确解的文献比较多,而关于其它边界条件问题的文献却不是很多见。以边界位移函数方法为基础,推导了对边固支对边自由矩形层合板的非齐次状态方程,并给出了求解该方程时满足边界条件的控制方程。将非齐次状态方程增维齐次化后可避免积分时可能出现的数值病态问题。边界位移沿厚度方向非线性分布的假设可以适当减少数值结果收敛要求的薄层数。数值结果可作为其它数值方法或半解析法的标准解。     

基于四元数向量的机器人运动学逆解研究

以齐次变换矩阵为基础,用四元数向量来表示机器人的位姿,提出了机器人运动学逆解的一种算法.以SCARA机器人为实例求解,通过四元数向量运算,得到8组解,采用C语言编程,验证了该算法的实用性.     

弹性-粘弹性复合结构动力响应的增维精细积分法

引入扩阶状态变量,将弹性-粘弹性复合结构的微分-积分型动力方程转化为一般形式的状态方程。利用复合结构状态方程的增维精细积分解法,将原非齐次状态方程化为齐次状态方程,简化求解过程。通过增维处理,在实施精细积分过程中避免矩阵求逆,并且将与时间有关的非齐次项纳入精细积分的细化过程,对算法的稳定性和程序实现十分有利,可在大型问题中明显提高计算效率,扩展精细积分的应用范围。数值算例说明方法的有效性。     

Effect of functionally graded material on frictionally excited thermoelastic instability

Thermoelastic instability (TEI) is investigated focusing on the effect of functionally graded materials (FGM) where the FGM half plane slides against a homogeneous conducting or rigid non-conducting body at speed V. Results confirm analytically that there is maximum critical speeds occurring at a certain value of non-homogeneous parameter of FGM within a range of thermal conductivity, which was reported previously in the simulation model [Y.H. Jang, S.-H. Ahn, Frictionally-excited thermoelastic instability on functionally graded material, Wear 262 (2007) 1102–1112]. The effect of non-homogeneous parameters for FGM on thermoelastic instability shows that the non-homogeneous parameters of the elastic modulus and thermal expansion coefficient are strong influential factors. It is also found that when the non-homogeneous parameters of FGM range between two positive bounded values, unconditionally stable behavior is shown for a range of thermal conductivity.     

轴向运动耦合热弹梁的稳定性分析

研究了轴向运动梁的耦合热弹稳定性.根据轴向运动梁的运动微分方程和考虑变形影响时的热传导方程,得出了温度场和变形场耦合情况下梁的耦合热弹运动微分方程.对两端简支轴向运动梁耦合热弹振动的复频率进行了数值计算,得出了无量纲复频率与无量纲运动速度之间的关系曲线.分析了无量纲热弹耦合因子、无量纲运动速度和梁的长高比对梁的临界速度和稳定性的影响.     

The effects of thermoelastic and wear on the leakage of compressible gases in shaft seals

Analysis are presented for a compressible gas flow across shaft seals. The leakage flow rate is developed analytically for a sealing gap due to eccentricity, misalignment of a shaft, sinusoidal wavy surfaces for both bodies, thermoelastic deformation on the edge of the body, and wear on the mating surfaces. A pressure distribution is determined as a power series based on the simplified nonlinear Reynolds equation. The restriction to exclude the thermoelastic effects was presented. Analytical results indicate that the thermoelastic distortion may dominate the seal performance when the eccentricity is large and width of the seal small at high speeds.     

Anti-plane analysis of functionally graded materials weakened by several moving cracks

This paper considers several finite moving cracks in a non-homogeneous material. The shear modulus and mass density of the plane are considered for a class of functional forms for which equilibrium equation has analytical solutions. The distributed dislocation technique is used to carry out stress analysis in a non-homogeneous plane containing moving cracks under anti-plane loading. The solution of a moving screw dislocation is obtained in a non-homogeneous plane by means of Fourier transform method. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is employed to derive integral equations for a plane weakened by moving cracks. Finally several examples are solved to show the effects of the material non-homogeneity and speed of cracks on the stress intensity factors.     

Wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross-section immersed in a fluid

The wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross-section immersed in a fluid is discussed in this paper. The solid medium is assumed to be linear, isotropic, temperature rate-dependent thermoelastic and the fluid medium is assumed to be inviscid. By imposing the continuity conditions on the interface between solid and fluid mediums, the frequency equation corresponding to the problem is obtained using the Fourier expansion collocation method. To compare the model with the existing literature, the results of a generalized thermoelastic solid cylinder without fluid are obtained and they show very good agreement. Also graphs and tables for various values of the material parameters are furnished.     

NON-LINEAR DYNAMIC BEHAVIOR OF THERMOELASTIC CIRCULAR PLATE WITH VARYING THICKNESS SUBJECTED TO NON- CONSERVATIVE LOADING

The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.     

Effect of gravity field,initial stress and rotation on the S-waves propagation in a non-homogeneous anisotropic medium with magnetic field

In this paper, we investigated the propagation of shear wave under the influences of the magnetic field, gravitational field, rotation and initially stressed in anisotropic non-homogeneous incompressible elastic medium. It is well known in the literature that the earth medium is not at all initial stress free and homogeneous throughout, but it is initially stressed and non-homogeneous. The frequency equation that determines the velocity of the shear waves has been obtained. Keeping these things in mind, we have discussed the frequency equation in an initially stressed, non-homogeneous medium with gravity field, magnetic field, and rotation. It has been observed that the inhomogeneity parameter, gravity field, magnetic field, and the initial stress play an important role in the propagation of S-waves propagation. The numerical values on the dimensionless phase velocities are calculated and presented graphically to illustrate the dependences upon gravity field, initial stress, magnetic field, anisotropy and rotation comparatively. The results indicate that the effects of gravity field, initial stress, magnetic field, anisotropy, and rotation are very pronounced.     

Analysis of thermoelastic damping in microresonators by considering the stretching effect

In this paper, the previous theory for obtaining the quality factor of thermoelastic damping in microresonators has been modified. Here, the stretching term for the neutral axis of bending is considered, which has been neglected in previous work. The Taylor expansion of electric actuation has described the static position of microbeam, which is more accurate than previous work that extends it about the straight position of a microbeam. Also, the theory of this work may be used for two layered microresonators without this assumption that the length of two layered electrically actuated microresonators may be obtained, for the first time. To obtain this complete theory firstly the equations of motion coupled with thermal effects are obtained in a two layered microbeam where the second layer is deposited on a part of the first layer length. Then, the quality factor of thermoelastic damping of the system, i.e. the half of the ratio of the real part of the free vibration resonance frequency to its imaginary part, has been obtained by solving the free vibration equation using the strained parameter perturbation method. It has been shown that neglecting the stretching of neutral axis of bending and expanding the electrostatic actuation about the straight position of the microbeam considered in previous researches cause an error that is not negligible for the voltage larger than 30% of the pull-in voltage. Also, it is shown that the quality factor of thermoelastic damping in two layered microresonators depends on the value of length, thickness and the kind of material of the deposited layer.