基于Lord-Shulman理论的热弹性波在偶应力三明治固体中的反射和透射

在温度急剧变化、短时间极速加热等极端情况下,基于Fourier定律的热流矢量与温度梯度成正比关系的经典热传导理论不能准确描述其物理过程．经典热弹性理论的热传导方程是抛物型的,而广义热弹性理论包含双曲型方程,热将以具有有限传播速度的波动形式传播．本文基于Lord-Shulman广义热弹性理论和修正偶应力弹性理论,得到在偶应力热弹性固体中四种色散波,研究热弹性波的传播和在偶应力固体三明治结构中的反射透射问题,重点研究横波入射时偶应力参数和热弛豫时间对各种热弹性耦合波反射透射系数的影响．     

偶应力理论的等效量定义

从应力和偶应力、外加面力和体力、外加面力偶矩和体力偶矩满足的平衡方程及其边界条件出发,讨论应力和偶应力场的静力学性质.由此导出代表性体积上等效应力和等效偶应力的定义,给出它们与相应的体积平均值间的差异.用本文给出的等效应力和等效偶应力的定义,单位体积上虚功的表达式与均匀介质具有同一性.如果用体积平均值作为等效应力和等效偶应力的定义,则虚功的表达式与均匀介质不具有同一形式.     

基于偶应力模型的连续体结构拓扑优化设计

经典连续介质理论不包含材料尺度参数,因而基于经典理论的结构拓扑优化无法显现尺度效应.本文在偶应力理论的框架下,构造了四节点四边形离散偶应力单元,将传统的SIMP方法推广至偶应力介质.结果表明,在以结构的最大刚度为目标的设计中,偶应力介质的最优结果取决于宏观结构尺寸与材料微结构尺寸(或者特征长度)的比值,最优结果具有明显的尺度效应,具体为,二者比值较大将产生与传统理论相似的结构,而二者比值相当则产生独特的偶应力主导的结构.     

基于改进三阶剪切梁理论和偶应力理论的梁运动方程

基于改进三阶剪切梁理论和采用偶应力理论考虑梁微元体刚体转动的动能,用哈密顿原理推导了矩形截面梁横向振动的变分一致运动方程.所得运动方程是以梁挠度和横截面的平均转角为基本变量的六阶偏微分方程,并且含有一个材料/结构内禀尺度.通过考虑极限条件下(波长趋于零时)的相速度极值,利用参数匹配法求得梁在横向振动时的内禀尺度.求解了无限长梁的振动波长趋于梁高度时的相速度,所得结果与弹性力学解吻合.计算结果表明,当梁的振动波长趋于梁高度时,偶应力对梁的横向振动频率有较大的影响.同时采用改进三阶剪切梁理论和拟协调元法推导了考虑偶应力效应的两节点梁单元,和求解了不同边界条件下梁的高阶频率.与文献结果对比表明,论文所给梁单元不仅精算效率高,且计算准确.     

基于偶应力理论的格栅材料等效介质模型

考察了结构最小尺寸与材料特征长度量级相当的格栅材料等效性能,建议了基于偶应力理论的格栅材料等效介质模型以及确定等效模量的代表体元模型,给出了相应的位移边界条件. 在此基础上导出了正交各向异性偶应力介质的特征长度表达式和偶应力介质梁的抗弯刚度表达式,定义了偶应力影响因子\delta以表征梁的偶应力效应. 具体计算了几种典型的格栅材料的等效偶应力模量以及格栅梁在一定工况下的挠曲线,并与相应的有限元离散解进行对比,结果表明,等效结果具有较高精度,且当宏观结构的尺寸和微结构尺寸相差不大时,宏观结构表现出强烈的偶应力效应.偶应力介质的特征长度表征了偶应力效应的强弱,进而分析了格栅材料的相对密度,单胞尺寸以及几何构型对等效介质特征长度的影响.      

微薄梁三点弯曲的尺度效应研究

应用高灵敏度的力传感器以及时间序列电子散斑干涉法，同时测出了不同厚度纯镍薄片三点 弯曲试件的抗力与变形，得到薄梁中心点处的载荷与挠度曲线. 应用Fleck和Hutchinson 的偶应力理论，结合平面应变弯曲模型，建立了薄梁处于弹性状态和弹塑性状态的 控制方程, 应用Runge-Kutta法进行数值求解，并将计算得到的载荷-挠度曲线以及无量纲化弯矩-表面 应变曲线和实验结果进行了比较. 在理论计算过程中，没有拟合任何材料参数，所有的材料 参数均来自实验测量的结果，材料特征尺度也是根据Stolken和Evans的工作给出 的. 结果表明: 应用偶应力理论预测的结果和实验结果符合良好，而经典理论的预测结果与 实验不相符合.     

温度梯度介质的偶应力理论——多相固体混合物的热失配

在强烈热沉积、较大温升率和温度梯度条件下材料性能的研究中,应用应变梯度理论,提出一种将温度梯度通过偶应力理论纳入本构方程的特殊的模型介质,并将其称为温度梯度固体.由此解释了具有显著细结构的多相固体混合物在强烈热沉积条件下,因热失配而表现出的特殊的热力耦合行为.     

偶应力的弹性理论

1.引言在经典的连续介质力学中,物体是假设由无穷小的质点所组成,因而不能承受分布的体力偶及面力偶的作用,不然的话就要导致无限大应力的出现.在此假设下,得到的应力张量是对称的.1887年W.Voigt 设想过物体是由非常小但不为零的体积元素所组成,内面力偶的存在是可能的.1909年Cosserat 兄弟提出了一个偶应力(couple-stresses)的理论,但长期内,这个理论没有受到应有的注意.1910年C.Somigliana,1953年S.Bodaszewski 考虑了非对称应力的情况,但他们的结果是错误的.1956年R.Tiffen 和A.C.Stevenson 研究了受有体力偶的弹性体的无     

含弱界面的微纳尺度双层梁的热弹性分析

众多微尺度实验已经证实了一些材料在微纳尺度下的力学行为具有尺寸效应.这种现象采用经典的弹性理论无法得到合理的解释,因而需要新的理论,修正偶应力理论就是其中一种.采用修正偶应力理论研究微纳尺度下两端自由铁木辛柯双层梁受热载荷后的弯曲响应,考虑两层之间存在弱界面.获得了梁的挠度、曲率以及界面剪力等表达式,并与经典弹性力学的结果进行了比较.通过分析计算可知,采用修正偶应力理论可预测微纳尺度下双层梁的尺寸效应,而当梁的特征尺寸远大于其材料的内禀尺度时,则与经典理论的结果一致.     

偶应力理论下拉力型锚固体的受力特性

锚固体的受力特征及其影响因素是锚固体设计的重要依据,直接影响锚固效果。传统的经典弹性理论没有考虑应变梯度的影响。偶应力理论引进弯曲曲率,考虑了弯曲效应对介质变形特性的影响。基于偶应力理论,建立了平面应变问题的有限元计算模型,研究锚固体锚固段界面上的剪应力分布、锚固体轴力分布、偶应力的尺度效应以及弹性模量和围压对锚固力的影响,并将偶应力理论的计算结果和经典弹性理论的计算结果进行了比较。结果表明,在偶应力理论下,锚固体锚固段界面的剪应力有所减小,特别是峰值处的剪应力减小明显;岩土的弹性模量越大,锚固界面局部剪应力越大;锚固力随着围压的增大而增大,偶应力尺度效应明显。     

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress (MCS) theory. Although many models have been incorporated into the literature, there is still room for introducing an improved model in this context. In this work, we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity. The MCS theory is used to investigate the material length scale effects. Using the Laplace transform, the temperature, deflection, displacement, flexure moment, and stress field variables of the micro-beam are derived. The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced. The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.     

Mode I crack tip field with strain gradient effects

A plane strain mode I crack tip field with strain gradient effects is investigated. A new strain gradient theory is used. An elastic-power law hardening strain gradient material is considered and two hardening laws, i. e. a separation law and an integration law are used respectively. As for the material with the separation law hardening, the angular distributions of stresses are consistent with the HRR field, which differs from the stress results^[19]; the angular distributions of couple stresses are the same as the couple stress results^[19]. For the material with the integration law hardening, the stress field and the couple stress field can not exist simultaneously, which is the same as the conclusion^[19], but for the stress dominated field, the angular distributions of stresses are consistent with the HRR field; for the couple stress dominated field, the angular distributions of couple stresses are consistent with those in Ref. [19]. However, the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only, while the crack tip field of mode I is dominated by the tension gradient, which will be shown in another paper. Supported by the National Science Foundation of China (No. 19704100), Science Foundation of Chinese Academy of Sciences (Project KJ951-1-20), CAS K. C. Wong Post-doctoral Research Award Fund and the Post Doctoral Science Fund of China.     

Mode I and mode II crack tip asymptotic fields with strain gradient effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material lengthl, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient. The project supported by the National Natural Science Foundation of China (19704100), National Natural Science Foundation of Chinese Academy of Sciences (KJ951-1-20), CAS K.C. Wong Post-doctoral Research Award Fund and Post-doctoral Science Fund of China     

Symplectic solution for three dimensional couple stress problem and its variational principle

A new state vector is presented for symplectic solution to three dimensional couple stress problem. Without relying on the analogy relationship, the dual PDEs of couple stress problem are derived by a new state vector. The duality solution methodology in a new form is thus extended to three dimensional couple stress. A new symplectic orthonormality relationship is proved. The symplectic solution to couple stress theory based a new state vector is more accordant with the custom of classical elasticity and is more convenient to process boundary conditions. A Hamilton mixed energy variational principle is derived by the integral method.     

Electrorheological Rayleigh-Taylor instability at the interface between a porous layer and thin shell with poorly conducting couple stress fluid

This paper is concerned with the study of the Electrorheological Rayleigh-Taylor instability (ERTI) at the interface between a densely packed saturated poorly conducting couple stress porous layer accelerated by a lighter poorly conducting couple stress fluid in a thin shell in the presence of a transverse electric field and laser radiation. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of ERTI. The cutoff and the maximum wave numbers and the corresponding maximum frequencies are obtained. It is shown that the effects of couple stress parameter and the electric field reduce the growth rate considerably compared to a non-conducting fluid in the absence of an electric field. These are favorable to control the surface instabilities in many practical applications discussed in this paper.     

偶应力问题的杂交／混合元分析

将弹性力学中Hellinger—Reissner交分原理推广到偶应力理论中，并以罚函数的形式引入其约束条件，提出了一种有效的杂交／混合单元。文中分别分析了带中心小孔平板在轴向均匀加载时的应力集中情况，以及含中问裂纹的无限平板单轴拉伸时的位移场和应力场。算例表明，该单元计算效率高，精度好，即使在材料本征长度很小时，仍然能够得到相当理想的结果。     

基于Hellinger-Reissner变分原理的应变梯度杂交元设计

从一般的偶应力理论出发，基于Hellinger-Reissner变分原理，通过对有限元 离散体系的位移试解引入非协调位移函数，得到了偶应力理论下有限元离散系统的能量相容 条件，并由此建立了应变梯度杂交元的应力函数优化条件. 根据该优化条件，构造了一 个C0类的平面4节点梯度杂交元，数值结果表明，该单元对可压缩和不可压缩状态的 梯度材料均可给出合理的数值结果，再现材料的尺度效应.     

An analysis of interface boundary layers based on the couple stress theory

Investigated in this paper are the effects of strain gradients on the stress distribution near an interface. The quasi axis-symmetry interface problem is solved by using the couple stress theory and the perturbation method. The results show that a boundary layer exists near an interface or a fixed boundary, where the shear stress perpendicular to the interface is significantly different from that obtained from the classical elasticity theory. Supported by the National Natural Science Foundation of China (No. 19891180).     

考虑转动梯度的界面问题研究

在考虑转动梯度效应的基础上,对界面附近的应力状态进行了研究,首先应用摄动法求解了基于偶应力理论的准轴对称问题,并在此基础上分析了界面问题和边界约束效应,结果表明,在剪应力作用下,在界面附近和固定边界附近存在一组边界效应解,相对于经典的弹性理论结果,它对剪应力的可观的修正。