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.     

考虑压头曲率半径和应变梯度的微压痕分析

在压头尖端曲率半径取100nm的前提下，采用Chen和Wang的应变梯度理论，对微压痕实验进行了系统的数值分析. 首先通过拟合载荷-位移实验曲线的后半段来确定材料的屈服应力和幂硬化指数值,然后用有限元方法数值模拟压痕实验，并将计算得到的整段载荷-位移曲线及硬度-位移曲线和实验结果进行了比较. 结果表明应变梯度理论所预测的计算结果和实验结果很好地符合,包括压痕深度在亚微米和微米范围内的整段曲线.     

轴向扩散下简支饱和多孔弹性梁的大挠度分析

基于多孔介质理论和弹性梁的大挠度理论,并考虑轴向变形,在孔隙流体仅沿轴向扩散的假设下,建立了微观不可压饱和多孔弹性梁大挠度弯曲变形的一维非线性数学模型.在此基础上,忽略饱和多孔弹性梁的轴向应变,并利用Galerkin截断法,研究了两端可渗透的简支饱和多孔弹性梁在突加横向均布载荷作用下的拟静态弯曲,给出了饱和多孔梁弯曲时挠度、弯矩和轴力以及孔隙流体压力等效力偶等沿轴线的分布曲线.揭示了大挠度非线性和小挠度线性模型的结果差异,指出大挠度非线性模型的结果小于相应小挠度线性模型的结果,并且这种差异随着载荷的增大而增大.计算表明:当无量纲载荷参数q>5时,应该采用大挠度非线性数学模型进行研究.     

基于BP神经网络与小冲杆试验确定在役管道钢弹塑性性能方法研究

为了能够在不停输油气工况下获得在役管道材料的弹塑性力学性能,提出了一种人工智能BP (backpropagation)神经网络、小冲杆试验与有限元模拟相结合,通过确定材料真应力-应变曲线从而获得材料弹塑性力学性能的方法.首先,通过系统改变Hollomon公式中的参数K, n值,获得457组具有不同弹塑性力学性能的假想材料本构关系,其次,将得到的本构关系代入经试验验证的含有Gurson-Tvergaard-Needleman(GTN)损伤参数的小冲杆试验二维轴对称有限元模型,通过有限元计算得到了与真应力-应变曲线一一对应的457条不同假想材料的载荷-位移曲线,最终将两组数据作为数据库输入BP神经网络进行训练,建立了同种材料小冲杆试验载荷-位移曲线与真应力-应变曲线之间的关联关系.通过此关联关系,可利用试验得到的小冲杆载荷-位移曲线获取在役管道钢的真应力-应变曲线,从而确定其弹塑性力学性能.通过对比BP神经网络得到的X80管道钢真应力-应变曲线与单轴拉伸试验的结果以及引用现有文献中不同材料的试验数据对此关系进行验证,证明了该方法的准确性与广泛适用性.     

基于BP神经网络与小冲杆试验确定在役管道钢弹塑性性能方法研究

为了能够在不停输油气工况下获得在役管道材料的弹塑性力学性能, 提出了一种人工智能BP (back-propagation)神经网络、小冲杆试验与有限元模拟相结合,通过确定材料真应力-应变曲线从而获得材料弹塑性力学性能的方法. 首先,通过系统改变Hollomon公式中的参数$K$, $n$值,获得457组具有不同弹塑性力学性能的假想材料本构关系, 其次,将得到的本构关系代入经试验验证的含有Gurson-Tvergaard-Needleman(GTN)损伤参数的小冲杆试验二维轴对称有限元模型,通过有限元计算得到了与真应力-应变曲线一一对应的457条不同假想材料的载荷-位移曲线,最终将两组数据作为数据库输入BP神经网络进行训练,建立了同种材料小冲杆试验载荷-位移曲线与真应力-应变曲线之间的关联关系.通过此关联关系,可利用试验得到的小冲杆载荷-位移曲线获取在役管道钢的真应力-应变曲线,从而确定其弹塑性力学性能.通过对比BP神经网络得到的X80管道钢真应力-应变曲线与单轴拉伸试验的结果以及引用现有文献中不同材料的试验数据对此关系进行验证,证明了该方法的准确性与广泛适用性.      

求解I型裂纹构元J积分的半解析方法

表征裂纹尖端应力应变场程度的J积分是一个定义明确、理论严密的弹塑性断裂力学基础参量. 目前J积分的计算主要是依靠塑性因子法和有限元法,但对各类裂纹构元获得J积分以及载荷-位移关系的解析公式以实现材料断裂韧性理论预测和材料测试是断裂力学的重要和困难的任务. 以J积分为参量的材料断裂测试中应用最广的是I型裂纹试样的断裂韧性测试. 本文在平面应变条件下,针对断裂韧性测试中使用的6种I型裂纹构元,基于能量等效假设,提出了J积分-载荷和载荷-位移的工程半解析统一表征方法,进而结合有限元分析的少量计算获得J积分-载荷和载荷-位移关系的半解析公式待定参数. 分析表明,6种I型裂纹构元的J积分-载荷和载荷-位移统一公式的预测结果与有限元结果吻合良好. 新提出的J积分-载荷工程半解析公式包含了材料的弹性模量、应力强度系数和应变硬化指数,能够广泛适应不同的材料,且运用该公式能够方便获取任意载荷点对应的J积分值. 应用新方法可便于获得各类I型裂纹构元的J积分-载荷和载荷-位移工程半解析公式.      

用能量法计算双模量深梁的弯曲挠度

为了得到双模量深梁弯曲变形挠度的实用计算方法,在考虑剪切变形的基础上,采用能量法研究了双模量深梁在外载荷作用下的弯曲变形挠度计算问题,并推导出了双模量深梁弯曲挠度的计算公式.把能量法的挠度计算结果与弹性理论方法的挠度计算结果进行比较,可知用能量法研究双模量深梁的弯曲变形不但计算过程简便,而且计算精度也很高.研究结果表明,双模量深梁的剪切形状因子与双模量材料的拉压弹性模量有关,而各向同性材料深梁的剪切形状因子却与它的弹性模量无关,所以双模量深梁的剪切形状因子与各向同性材料深梁的剪切形状因子有着本质上的区别.     

求解Ⅰ型裂纹构元J积分的半解析方法

表征裂纹尖端应力应变场程度的J积分是一个定义明确、理论严密的弹塑性断裂力学基础参量.目前J积分的计算主要是依靠塑性因子法和有限元法,但对各类裂纹构元获得J积分以及载荷-位移关系的解析公式以实现材料断裂韧性理论预测和材料测试是断裂力学的重要和困难的任务.以J积分为参量的材料断裂测试中应用最广的是Ⅰ型裂纹试样的断裂韧性测试.本文在平面应变条件下,针对断裂韧性测试中使用的6种Ⅰ型裂纹构元,基于能量等效假设,提出了J积分-载荷和载荷-位移的工程半解析统一表征方法,进而结合有限元分析的少量计算获得J积分-载荷和载荷-位移关系的半解析公式待定参数.分析表明,6种Ⅰ型裂纹构元的J积分-载荷和载荷-位移统一公式的预测结果与有限元结果吻合良好.新提出的J积分-载荷工程半解析公式包含了材料的弹性模量、应力强度系数和应变硬化指数,能够广泛适应不同的材料,且运用该公式能够方便获取任意载荷点对应的J积分值.应用新方法可便于获得各类Ⅰ型裂纹构元的J积分-载荷和载荷-位移工程半解析公式.     

考虑损伤拉压不同模量梁的纯弯曲

根据考虑损伤的变模量弹性理论,建立了考虑损伤的拉压不同模量梁的弯曲基本方程,推导了梁的拉（压)应力、受拉区高度和挠度的计算公式．应用数值计算方法,分别得到了有损与无损时梁极限拉（压）应力、受拉区高度与模量比的关系曲线以及有损梁的最大挠度和模量比的关系曲线,同时得到了梁拉（压）应力比值、损伤引起的中性轴偏移量和梁跨中挠度比值与载荷的关系曲线．这些结论可为工程上具拉压不同模量梁的截面设计提供一定的参考价值．     

废气涡轮增压器涡轮盘的弹塑性有限元分析

本文用弹塑性有限元分析的增置刚度法对废气涡轮增压器涡轮盘作了强度及变形分析。在分析过程中,材料是否进入塑性状态是根据试验所得应力-应变曲线来判定的;在每一步计算时,作者用已算得的等效应力,在实验应力-应变曲线上插值计算相应的等效应变,以校正变刚度法的偏离误差。变形的计算结果与试验测量值接近。     

Axisymmetric magnetohydrodynamic flow of micropolar fluid between unsteady stretching surfaces

This investigation examines the time dependent magnetohydrodynamic (MHD) flow problem of a micropolar fluid between two radially stretching sheets. Both strong and weak concentrations of microelements are taken into account. Suitable transformations are employed for the conversion of partial differential equations into ordinary differential equations. Solutions to the resulting problems are developed with a homotopy analysis method (HAM). The angular velocity, skin friction coefficient, and wall couple stress coefficient are illustrated for various parameters.     

Nonlinear bending of size-dependent circular microplates based on the modified couple stress theory

The present study proposes a nonclassical Kirchhoff plate model for the axisymmetrically nonlinear bending analysis of circular microplates under uniformly distributed transverse loads. The governing differential equations are derived from the principle of minimum total potential energy based on the modified couple stress theory and von Kármán geometrically nonlinear theory in terms of the deflection and radial membrane force, with only one material length scale parameter to capture the size-dependent behavior. The governing equations are firstly discretized to a set of nonlinear algebraic equations by the orthogonal collocation point method, and then solved numerically by the Newton–Raphson iteration method to obtain the size-dependent solutions for deflections and radial membrane forces. The influences of length scale parameter on the bending behaviors of microplates are discussed in detail for immovable clamped and simply supported edge conditions. The numerical results indicate that the microplates modeled by the modified couple stress theory causes more stiffness than modeled by the classical continuum plate theory, such that for plates with small thickness to material length scale ratio, the difference between the results of these two theories is significantly large, but it becomes decreasing or even diminishing with increasing thickness to length scale ratio.     

High-precision stress determination in photoelasticity

Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics. The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization. To improve the accuracy of stress calculation,a novel meshless barycentric rational interpolation collocation method(BRICM) is proposed. The derivatives of the shear stress on the calculation path are determine...     

Natural convection flow of a couple stress fluid between two vertical parallel plates with Hall and ion-slip effects

The Hall and ion-slip effects on fully developed electrically conducting couple stress fluid flow between vertical parallel plates in the presence of a temperature dependent heat source are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, ion-slip parameter and couple stress fluid parameter on velocity and temperature are discussed and shown graphically.     

Dynamic modeling of preloaded size-dependent nano-crystalline nano-structures

The vibration behavior of size-dependent nano-crystalline nano-beams is investigated based on nonlocal, couple stress and surface elasticity theories. A nanocrystalline nano-beam is composed of three phases which are nano-grains, nano-voids,and interface. Nano-voids or porosities inside the material have a stiffness-softening impact on the nano-beam. A Eringen's nonlocal elasticity theory is applied in the analysis of nano-crystalline nano-beams for the first time. Residual surface stresses which are usually neglected in modeling nano-crystalline nano-beams are incorporated into nonlocal elasticity to better understand the physics of the problem. Also, a modified couple stress theory is used to capture rigid rotations of grains. Applying a differential transform method(DTM) satisfying various boundary conditions, the governing equations obtained from the Hamilton's principle are solved. Reliability of the proposed approach is verified by comparing the obtained results with those provided in the literature. The effects of the nonlocal parameter, surface effect, couple stress, grain size, porosities, and interface thickness on the vibration characteristics of nano-crystalline nano-beams are explored.     

铁磁薄板在磁场中变形和应力的理论分析与实验研究

在二维板壳磁弹性理论基本方程基础上,以二维铁磁薄板磁弹性问题为例,建立了含有10个基本未知量的偏微分方程组,再利用Newmark有限等差式,得到了可以应用DOM方法求解的标准型方程组.求解得到了载流铁磁薄板的位移及应力与各电磁量之间的关系,计算了载流铁板在磁场中的变形和应力.同时进行了载流铁磁性薄板在电磁场中变形和应力的实验研究,介绍了电磁场中铁磁性薄板的实验装置和实验方法,给出了实验数据,并将实验结果与理论计算结果进行了分析对比.     

Linear and nonlinear stability of double diffusive convection in a couple stress fluid–saturated porous layer

The linear and nonlinear stability of double diffusive convection in a layer of couple stress fluid–saturated porous medium is theoretically investigated in this work. Applying the linear stability theory, the criterion for the onset of steady and oscillatory convection is obtained. Emphasizing the presence of couple stresses, it is shown that their effect is to delay the onset of convection and oscillatory convection always occurs at a lower value of the Rayleigh number at which steady convection sets in. The nonlinear stability analysis is carried out by constructing a system of nonlinear autonomous ordinary differential equations using a truncated representation of Fourier series method and also employing modified perturbation theory with the help of self-adjoint operator technique. The results obtained from these two methods are found to complement each other. Besides, heat and mass transport are calculated in terms of Nusselt numbers. In addition, the transient behavior of Nusselt numbers is analyzed by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta–Gill method. Streamlines, isotherms, and isohalines are also displayed.     

聚氨酯泡沫塑料压缩杨氏模量的理论预测

通过微分法导出了泡沫塑料剪切模量和体积模量所满足的微分方程组，再利用联系泡沫塑料泊松比和孔隙比的Ｋｅｒｎｅｒ－Ｒｕｓｃｈ经验关系及泡沫塑料弹性常数间满足足的关系，在基体材料不可压缩的假设下，确定了泡沫塑料的杨氏模量。本文针对几种密度的泡沫塑料，分别对它们的杨氏模量进行了理论预测和实验测定，结果表明：理论预测的模量在较高密度下与实验符合的很好，在低密度下也给出相当好的近似值。此外，本文的结果同其他理     

偶应力理论的无网格法

根据偶应力理论的基本方程,在能量泛函中引入罚函数来满足偶应力理论的几何约束条件,从而得到偶应力理论的无网格法的控制方程.通过算例,分析了偶应力对带中心圆孔的无限平板在单轴拉伸及纯剪状态下的应力集中的影响,验证了该无网格方法的有效性和可行性.