Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

Development of an improved divergence‐free‐condition compensated coupled framework to solve flow problems with time‐varying geometries

In this article a coupled version of the improved divergence‐free‐condition compensated method will be proposed to simulate time‐varying geometries by direct forcing immersed boundary method. The proposed method can be seen as a quasi‐multi‐moment framework due to the fact that the momentum equations are discretized by both cell‐centered and cell‐face velocity. For simulating time‐varying geometries, a semi‐implicit iterative method is proposed for calculating the direct forcing terms. Treatments for suppressing spurious force oscillations, calculating drag/lift forces, and evaluating velocity and pressure for freshly cells will also be addressed. In order to show the applicability and accuracy, analytical as well as benchmark problems will be investigated by the present framework and compared with other numerical and experimental results.     

Imposing accurate wall boundary conditions in corrective‐matrix‐based moving particle semi‐implicit method for free surface flow

Corrective matrix that is derived to restore consistency of discretization schemes can significantly enhance accuracy for the inside particles in the Moving Particle Semi‐implicit method. In this situation, the error due to free surface and wall boundaries becomes dominant. Based on the recent study on Neumann boundary condition (Matsunaga et al, CMAME, 2020), the corrective matrix schemes in MPS are generalized to straightforwardly and accurately impose Neumann boundary condition. However, the new schemes can still easily trigger instability at free surface because of the biased error caused by the incomplete/biased neighbor support. Therefore, the existing stable schemes based on virtual particles and conservative gradient models are applied to free surface and nearby particles to produce a stable transitional layer at free surface. The new corrective matrix schemes are only applied to the particles under the stable transitional layer for improving the wall boundary conditions. Three numerical examples of free surface flows demonstrate that the proposed method can help to reduce the pressure/velocity fluctuations and hence enhance accuracy further.     

Direct visualization of structural defects in 2D semiconductors

Direct visualization of the structural defects in two-dimensional (2D) semiconductors at a large scale plays a significant role in understanding their electrical/optical/magnetic properties, but is challenging. Although traditional atomic resolution imaging techniques, such as transmission electron microscopy and scanning tunneling microscopy, can directly image the structural defects, they provide only local-scale information and require complex setups. Here, we develop a simple, non-invasive wet etching method to directly visualize the structural defects in 2D semiconductors at a large scale, including both point defects and grain boundaries. Utilizing this method, we extract successfully the defects density in several different types of monolayer molybdenum disulfide samples, providing key insights into the device functions. Furthermore, the etching method we developed is anisotropic and tunable, opening up opportunities to obtain exotic edge states on demand.     

输电铁塔四地脚螺栓塔脚板抗拉承载力试验与计算方法研究

针对架空输电线路铁塔中常用的四地脚螺栓塔脚板进行了抗拉承载力试验和理论计算方法研究。首先,选取8个试件进行塔脚板抗拉承载力试验研究,分析塔脚底板板厚及有无加劲板对塔脚板抗拉承载力的影响;其次,通过有限元模拟塔脚板的应力分布情况,并结合“塑性分析,弹性设计”的思想,提出了一种基于屈服线理论的四地脚螺栓塔脚板抗拉承载力计算公式;最后,与试验结果、有限元仿真结果、已有技术规定中的计算结果进行了对比。结果表明:建议公式与试验结果和仿真结果较为吻合,相关技术规定中的计算结果偏于保守,验证了本文建议公式的精确性;底板厚度和加劲板的作用对塔脚板承载力影响较大。研究结果可为输电铁塔四地脚螺栓塔脚板结构设计提供参考。     

Dynamic and buckling analysis of polymer hybrid composite beam with variable thickness

This work deals with a study of the dynamic and buckling analysis of polymer hybrid composite(PHC) beam. The beam has variable thickness and is reinforced by carbon nanotubes(CNTs) and nanoclay(NC) simultaneously. The governing equations are derived based on the first shear deformation theory(FSDT). A three-phase HalpinTsai approach is used to predict the mechanical properties of the PHC. We focus our attention on the effect of the simultaneous addition of NC and CNT on the vibration and buckling analysis of the PHC beam with variable thickness. Also a comparison study is done on the sensation of three impressive parameters including CNT, NC weight fractions, and the shape factor of fillers on the mechanical properties of PHC beams,as well as fundamental frequencies of free vibrations and critical buckling load. The results show that the increase of shape factor value, NC, and CNT weight fractions leads to considerable reinforcement in mechanical properties as well as increase of the dimensionless fundamental frequency and buckling load. The variation of CNT weight fraction on elastic modulus is more sensitive rather than shear modulus but the effect of NC weight fraction on elastic and shear moduli is fairly the same. The shape factor values more than the medium level do not affect the mechanical properties.     

单颗金刚石切削无氧铜的声发射关联维特征*

声发射技术可以实现无氧铜切削加工特征的监测与评价。采用声发射技术监测单颗金刚石磨粒旋转切削无氧铜，利用G-P算法重构出声发射时域信号相空间，采用自相关函数法计算出相空间时间延迟参数，通过相空间双对数曲线的计算，得到不同切削工况下的关联维数。研究结果表明，进给速度和切削速度对声发射信号影响较不显著，切深与声发射信号振幅呈正效应关系；声发射信号双对数曲线呈现阶段性增加趋势，并逐渐收敛于饱和状态，关联维数随着嵌入维数的增加先快速下降后趋于平稳；金刚石切削无氧铜的声发射信号具有混沌运动变化特性，在较小嵌入维数时，关联维数与切深和切削速度呈现线性负效应关系，与进给速度呈现线性正效应关系。该研究为无氧铜的切削加工提供理论参考。     

平面波输入下海水-海床-结构动力相互作用分析

海洋工程结构的地震反应分析是保证海洋工程结构地震安全的重要环节.由于其所处的复杂环境, 该问题涉及到流固耦合和土-结相互作用.本文基于海水、饱和海床、基岩流固耦合统一计算框架,采用Davidenkov模型和修正的Masing准则考虑饱和海床的非线性,在脉冲SV波垂直入射下, 进行了海域场地和海洋工程结构的动力响应分析. 首先,对比分析了线性自由场和非线性自由场输入情形的海域场地非线性反应,结果表明线性自由场输入时反应不合理,自由场分析和场地分析应该采用相一致的本构模型. 然后,对比分析了海床分别为线性和非线性情形时,海域场地以及海水-海床-结构体系的反应特征. 与线性海床情形相比,非线性对海床反应的影响主要由如下两方面因素控制: 一方面,非线性导致饱和海床模量减小, 饱和海床与基岩间的波阻抗比减小,由基岩到饱和海床间的反射系数和透射系数增加, 导致反应增大; 另一方面,非线性导致阻尼加大, 使海床反应减小. 对于本文算例而言,阻尼对非线性海床结果的影响占主导作用.