基于大变形分析的动不定体系的求解

动不定体系由于内部存在机构位移,其求解过程不同于动定体系。为了全面了解动不定体系的受力性能,本文对其相容及非相容平衡方程的求解进行了详细的分析和推导;同时,由于动不定体系求解过程涉及大位移,本文对通常建立在小变形假定下的变形协调方程进行了重新推导,采用建立在大变形基础上的变形协调方程对有限机构进行求解,并由此编制了相应的计算程序。算例分析表明本文计算方法是精确和有效的,可用于确定动不定体系的平衡状态和内力。     

基于Newmark格式的多柔体系统子循环算法研究

提出一种基于Newmark积分格式的FMD(Flexible Multi-body Dynamics)子循环算法,可用于求解缩并型的FMD方程.推导了FMD方程中快变分量和慢变分量的同步更新及子步更新公式;在积分过程中,采用能量平衡计算校验算法的稳定性;结果表明该算法可以在保持合适的精度要求下,有效地提高计算效率.     

结构层热扩散系数对超薄涂层热力性能的影响

将非傅立叶热传导模型(用于超薄热涂层)与傅立叶热传导模型(用于结构层)相结合求解温度场,运用有限元法求解热涂层热应力和裂纹驱动力,并分析结构层材料热扩散系数的变化对热涂层的热力学性能(温度场、应力场和断裂性能)的影响. 研究表明,结构层材料性能变化对温度场的影响主要表现在热冲击后期,对热应力和裂纹尖端驱动力后期的变化也有一定的影响.     

Falkner-Skan方程的近似解析解

研究了粘性流体绕流楔型物体的Falkner-Skan边界层方程求解问题.利用Adomian拆分方法,通过引入Crocco变量变换将无穷区间的边界值问题转为初值问题并利用Padé逼近技巧确定初值,给出了一种有效的解析分解方法.进一步,本文设计了一种数值解法,将本文得到的近似解析解及数值结果与早期研究者Hartree等人的结果进行了比较,证明了本文提出的解法的有效性和可靠性.     

喷水推进器推力的CFD计算方法研究

简要介绍获取喷水推进器推力的理论、试验及数值计算(CFD)方法,重点研究采用动量流量法和壁面积分法计算喷水推进器推力的CFD方法。采用多块网格技术,用六面体结构化网格和四面体非结构化网格相结合的混合网格离散计算区域,采用稳态多参考系方法求解RANS方程,对喷水推进器进水流道、叶轮、导叶体和喷口所组成的整个流场进行数值计算。计算中采用了k-ε湍流模型和标准壁面函数,对用动量流量法计算推力方法中所需的假想流管分界面和进口面的求取做了分析,将两种方法计算的推力与厂商提供的推力特性曲线进行了对比。结果表明,采用CFD计算和分析方法来研究喷水推进系统推力性能是可行、可信的。     

Geometric shapes of the interface surface of bicomponent flows between two concentric rotating cylinders

In this paper, the shape problem of interface of bicomponent flows between two concentric rotating cylinders is investigated. With tensor analysis, the problem is reduced to an energy functional isoperimetric problem when neglecting the effects of the dissipative energy caused by viscosity. We derive the associated Euler-Lagrangian equation, which is a nonlinear elliptic boundary value problem of the second order. Moreover, by considering the effects of the dissipative energy, we propose another total energy functional to characterize the geometric shape of the interface, and obtain the corresponding Euler-Lagrangian equation, which is also a nonlinear elliptic boundary value problem of the second order. Thus, the problem of the geometric shape is converted into a nonlinear boundary value problem of the second order in both cases.     

Symmetries of boundary layer equations of power-law fluids of second grade

A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.     

三维非稳态热传导逆问题反演算法研究

利用表面温度测量来反演热传导方程中的热源项是一类典型的热传导逆问题,在采用有限体积法对三维非稳态热传导问题进行数值求解的基础上,将该热传导逆问题转化为优化问题,建立了伴随方程法和共轭梯度法这两类反演算法. 采用这两类算法对一个典型算例的计算结果表明:建立的两类反演算法是有效的,具有较好的抗噪性能. 此外,对反演算法中计算收敛准则的选取进行了较深入的分析,结果表明,由于热传导逆问题的不适定性,优化过程中目标函数值越小并不意味着反演结果与真值更为接近,可以通过设定合适的收敛准则来模拟正则化项的作用,克服不适定性的影响.      

CMP流场的数值模拟及离心力影响分析

化学机械抛光(chemical mechanical polishing,CMP)是一项融合化学分解和机械力学的工艺, 其中包含了流体动力润滑的作用.在已有润滑方程的基础上, 提出并分析了带有离心力项的润滑方程.利用Chebyshev加速超松弛技术对有离心力项的润滑方程进行求解,得到离心力对抛光液压力分布的影响. 数值模拟结果表明,压力分布与不带离心力项的润滑方程得出的明显不同;无量纲载荷和转矩随中心膜厚、转角、倾角、抛光垫旋转角速度等参数的变化趋势相同,但数值相差较大, 抛光垫旋转角速度越大差别越大.      

Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method

Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezo-magnetic "comparison body" is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green's function, which is ob-tained using the Radon transform. The expression is further simplified under condi-tions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelec-tric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.