Investigating heat conduction in a sphere with heat absorption using generalized Caputo fractional derivative

In this paper, we study the ρ-Laplace transform and the finite sin-Fourier transform as powerful tools in solving fractional differential equations with generalized Caputo derivative. We use these transforms to solve the time-fractional heat equation with a generalized Caputo fractional derivative associated with heat absorption in spherical coordinates. We obtain the solutions in two cases of Dirichlet boundary conditions. The effect of the parameter $\rho$, which characterizes the generalized Caputo derivative is illustrated through some numerical examples.     

Adhesion of a rigid punch to a confined elastic layer revisited

The adhesion of a punch to a linear elastic, confined layer is investigated. Numerical analysis is performed to determine the equivalent elastic modulus in terms of layer confinement. The size of the layer relative to the punch radius and its Poisson’s ratio are found to affect the layer stiffness. The results reveal that the equivalent modulus of a highly confined layer depends on its Poisson’s ratio, whereas, in contrast, an unconfined layer is only sensitive to the extent of the elastic film. The solutions of the equivalent modulus obtained from the simulations are fitted by an analytical function that, subsequently, is utilized to deduce the energy release rate for detachment of the punch via linear elastic fracture mechanics. The energy release rate strongly varies with layer confinement. Regimes for stable and unstable crack growth can be identified that, in turn, are correlated to interfacial stress distributions to distinguish between different detachment mechanisms.     

SBP-SAT方法及其在波动领域的应用

基于分部求和(Summation By Parts)方法和同时逼近项(Simultaneous Approximation Terms)技术建立的有限差分方法,具有更高的精度和稳定性。同时在介质几何不连续、参数突变条件具有较大的优势。国内对SBP-SAT方法的相关研究目前较少,论文对该方法的研究背景,方法发展过程进行了介绍并基于SBP-SAT方法和弹性波动理论,结合初边值条件,推导出曲线网格条件下的弹性波动SBP-SAT离散方程。最后,通过数值模拟实现地震波传播过程,介绍该方法在地震数值模拟领域中的应用价值和前景。     

Model reduction for nonlinear multiscale parabolic problems using dynamic mode decomposition

In this article, a model reduction technique is presented to solve nonlinear multiscale parabolic problems using dynamic mode decomposition. The multiple scales and nonlinearity bring great challenges for simulating the problems. To overcome this difficulty, we develop a model reduction method for the nonlinear multiscale dynamic problems by integrating constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with dynamic mode decomposition (DMD). CEM-GMsFEM has shown great efficiency to solve linear multiscale problems in a coarse space. However, using CEM-GMsFEM to directly solve multiscale nonlinear parabolic models involves dynamically computing the residual and the Jacobian on a fine grid. This may be very computationally expensive because the evaluation of the nonlinear term is implemented in a high-dimensional fine scale space. As a data-driven method, DMD can use observation data and give an explicit expression to accurately describe the underlying nonlinear dynamic system. To efficiently compute the multiscale nonlinear parabolic problems, we propose a CEM-DMD model reduction by combing CEM-GMsFEM and DMD. The CEM-DMD reduced model is a coarsen linear model, which avoids the nonlinear solver in the fine space. It is crucial to judiciously choose observation in DMD. Only proper observation can render an accurate DMD model. In the context of CEM-DMD, we introduce two different observations: fine scale observation and coarse scale observation. In the construction of DMD model, the coarse scale observation requires much less computation than the fine scale observation. The CEM-DMD model using the coarse scale observation gives a complete coarse model for the nonlinear multiscale dynamic systems and significantly improves the computation efficiency. To show the performance of the CEM-DMD using the different observations, we present a few numerical results for the nonlinear multiscale parabolic problems in heterogeneous porous media.     

一种压电半导体纳米线的热电耦合性能研究

采用有限元分析方法,研究了一种n型压电半导体纳米线(氧化锌)的电热耦合性能,分析了外部温度对氧化锌纳米线内部机械场、电场及电流场分布的影响,并讨论了本构方程线性化对电学参数的影响。研究结果表明,温度对氧化锌纳米线的电场、载流子浓度和电流密度影响很大,采用线性本构和非线性本构求得的电场、电子浓度和电流密度最大相差分别为24%,32%和68%,基于非线性本构分析压电半导体的电学性能会引起很大误差。该研究结果可为压电半导体器件利用温度调控电场、电流提供理论依据。     

HVOF喷涂WC-12Co粒子沉积行为分析

目的 研究不同超音速火焰喷涂条件下WC-12Co粒子在45^#碳钢基体上的沉积变形行为。方法 基于Johnson-Cook塑性材料模型与Thermal-Isotropy-Phase-Change热材料模型，采用LS-DYNA进行建模分析。结果 不同喷涂参数下，WC-12Co粒子在45^#碳钢基体上的沉积行为存在明显差异。沉积过程中，粒子等效塑性应变幅度高于基体;粒子边缘位置等效塑性应变幅度高于粒子中心轴线位置;粒子初始速度与初始温度的增加有助于提升结合界面温度与粒子扁平化程度;粒子初始温度与粒子初始速度对接触界面能量变化影响程度基本一致，单位粒子初始速度与温度提升的能量贡献比 分别为0.78以及0.76，二者的能量贡献比近似相同;适度的基体预热( =500 K)可以促进粒子变形，加深沉积坑深度，增大粒子与基体的结合面积，有助于提升粒子与基体之间的结合强度。基体过冷( =300 K)将导致粒子“翘曲”，降低粒子与基体之间的结合面积，基体过热( =600 K)将导致二者结合处于不稳定状态，易引起粒子剥落，二者均不利于粒子与基体的有效结合。结论 一定范围内提升粒子初始速度、温度与基体初始温度，可以提高粒子扁平化程度，增大粒子与基体结合面积，提升粒子与基体的结合性能，进一步提高涂层质量。     

耐冲击型金刚石圆锯片锯切受力的数值模拟(二)——以新型半圆形水槽锯片为例

建立耐冲击型金刚石锯片锯切受力的有限元分析模型，围绕新型半圆形水槽和传统U型水槽的2种齿形结构，以数值模拟对比研究金刚石圆锯片的锯切受力。仿真结果表明:在承受相同载荷的情况下，新型半圆形水槽锯片较传统U型水槽锯片在锯切受力时的变形、应力方面都得到了明显改善，其变形量减少11.56%，第一、第三主应力分别降低24.04%和34.19%，因而其承受大载荷和耐冲击性能良好。      

Effect of microstructure inhomogeneity on mechanical properties of different zones in TA15 electron beam welded joints

The effects of microstructure inhomogeneity on the mechanical properties of different zones in TA15 electron beam welded joints were investigated using a micromechanics-based finite element method. Considering the indentation size effect, the mechanical properties for constituent phases of the base metal (BM) and heat affected zone (HAZ) were determined by the instrumented nano-indentation test. The macroscopic mechanical properties of BM and HAZ obtained from the tensile test agree well with the numerical results. The incompatible deformation between the constituent phases tends to localize along the softer primary phase α where failure usually initiates in form of localized plastic strain. Compared with the BM, the mechanical properties of constituent phases in the HAZ differ substantially, leading to more serious strain localization behavior.