A quantitative evaluation of time-independent and time-dependent deformations of lead-free and lead-containing solder alloys

A method to separate plasticity and creep is discussed for a quantitative evaluation of the plastic, transient creep, and steady-state creep deformations of solder alloys. The method of separation employs an elasto-plastic-creep constitutive model comprised of the sum of the plastic, transient creep, and steady-state creep deformations. The plastic deformation is expressed by the Ramberg-Osgood law, the steady-state creep deformation by Garofalo’s creep law, and the transient creep deformation by a model proposed here. A method to estimate the material constants in the elasto-plastic-creep constitutive model is also proposed. The method of separation of the various deformations is applied to the deformation of the lead-free solder alloy Sn/3Ag/0.5Cu and the lead-containing solder alloy Sn/37Pb to compare the differences in the plastic, transient creep, and steady-state creep deformations. The method of separation provides a powerful tool to select the optimum lead-free solder alloys for solder joints of electronic devices.     

低碳时变城配送车辆路径-发车调度集成优化

针对交通拥挤环境下日益增长的城市配送需求，通过分析时序依赖对成本和碳排放的影响，引入车辆在节点等待和离散调度策略，研究基于时序依赖的低碳城市配送车辆路径与离散调度问题。为求解该问题，设计基于遗传算法与局部搜索相结合的混合进化搜索算法对模型求解，用积极的局部搜索机制替代随机的变异操作，并通过可行解构造算法、变概率交叉和多种局部搜索策略来提高算法求解质量和求解效率。通过对比仿真实验对算法和模型的有效性进行了验证。     

Approximate Solutions of the Nonlinear Schr?dinger Equation for Ground and Excited States of Bose-Einstein Condensates

I present simple analytical methods for computing the properties of ground and excited states of Bose-Einstein condensates, and compare their results to extensive numerical simulations. I consider the effect of vortices in the condensate for both positive and negative scattering lengths, a, and find an analytical expression for the large-N₀ limit of the vortex critical frequency for a > 0, by approximate solution of the time-independent nonlinear Schrödinger equation.     

耗散平衡概念及时间无关本构关系的构造方法

以不可逆热力学为基础，通过讨论双耗散系统形式下的Ｃｌａｕｓｉｕｓ－Ｄｕｈｅｍ不等式，发现了系统在外变量变化率满足一定条件时具有双向调节功能，即系统的状态无论在屈服面的哪一侧，它的变化总是趋向于屈服面的。此外，还提出了等效性假设和耗散平衡概念，进而得到了时间无关本构关系的构造方法，本构关系的时间无关特性是外变量变化率在一定范围内取值时系统表现出的特性，当外变量变化率超出这一范围上限时本构关系是时间相     

Deformation dynamics at low and ambient temperatures

The variation of tensile yield stress at a constant strain rate as a function of temperature for well-annealed pure metals show, with increasing temperatures, a rather sharp drop in yield stress (low temperature regime), followed by the intermediate temperature regime where yield stress decreases more slowly (and the ratio of yield stress to shear modulus remains more or less constant), which in turn is followed by the high temperature regime where the yield stress drops again rather sharply. The paper discusses the phenomenological framework for studying deformation dynamics in the low and intermediate temperature regimes. The approach adopted is the well-known state variable approach, where the evolutionary nature of deformation structure is described by one or more structure variables such that the current values of mechanical variables and structure variables together completely define the current state of deformation. A critical analysis of experimental results available suggest that at least for deformation at low strain rates, stress-rate is probably not a state variable of deformation. Thus deformation is most conveniently studied in terms of TASRA (thermally activated strain rate analysis) where the stress, plastic strain rate, temperature and structure are interrelated through a Gibb’s free energy for thermal activation by an Arrhenius equation. The stress-dependence of Gibb’s free energy and its maximum value then form the basis of identifying the rate-controlling obstacles. The need for careful experimentation and systematic analysis is illustrated by the example of low temperature deformation of hard hep metals. Modelling for the evolution of deformation structure is also touched upon.     

基于拓展单位分解有限元法分析声波在多域场内的响应

基于拓展单位分解有限元方法，将平面波函数和贝塞尔函数作为基函数进行拓展。将亥姆霍兹方程离散，求解时不变情况下多域场内声波的响应，并分析基函数对求解精度的影响。将波动方程的时间导数利用二阶中心差分方法离散，得到方程的隐式表达式，划分时间步迭代求解时变情况下声波在多域场内的响应，分析迭代时间间隔对计算精度的影响，与典型算例的精确解进行比较，验证精确性。结果表明，平面波函数作为拓展基函数，利用二阶中心差分法离散时间导数，分析时不变以及时变情况下多域场内高波数声波的响应问题，具有较高的计算精度和计算效率。