AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates

This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.

ARCADE 2 Spatial Roar, What Theory of Relation Reveals

The theory of Relation provides an explanation for the Arcade 2 excess. It assumes that the isotropic radio emission measured by the Arcade 2 Collaboration, which is 5 - 6 times brighter than the expected contributions from known extra-galactic sources, is the residue of an immense primitive energy of ordinary matter released by a relativistic bang almost 100 million years after the big bang, which gave the mass-energy the missing gravity to activate contraction. This relativistic bang, via a Lorentz energy transformation, would have released enormous energy held to be the source of the powerful radio noise detected by the NASA researchers. This transformation would have simultaneously triggered the formation of the first stars from dense gas and the reionization of less dense neutral gas. This departs from the idea that continuous reionization began after the formation of the first stars. We emphasize the importance of primordial magnetic fields, which would have generated significant density fluctuations during recombination and acted as a direct seed for cosmic structures. The first stars and galaxies were bathed in strong magnetic fields that gave rise to the radio microwave din (boom) discovered by Arcade 2. These intense magnetic fields alter the trajectory of charged particles zooming near the speed of light, triggering the space roar and emitting radiation that forms a synchrotron radio background. The theory of Relation offers an alternative to the Lambda-CDM cosmological model, which has become the standard model of the big bang, which leads straight to the vacuum catastrophe.

Static and Dynamic Pull-In Instability of Nano-Beams Resting on Elastic Foundation Based on the Nonlocal Elasticity Theory

This paper provides the static and dynamic pullin behavior of nano-beams resting on the elastic foundation based on the nonlocal theory which is able to capture the size effects for structures in micron and sub-micron scales. For this purpose, the governing equation of motion and the boundary conditions are driven using a variational approach. This formulation includes the influences of fringing field and intermolecular forces such as Casimir and van der Waals forces. The differential quadrature （DQ） method is employed as a high-order approximation to discretize the governing nonlinear differential equation, yielding more accurate results with a Considerably smaller number of grid points. In addition, a powerful analytical method called parameter expansion method （PEM） is utilized to compute the dynamic solution and frequency-amplitude relationship. It is illustrated that the first two terms in series expansions are sufficient to produce an acceptable solution of the mentioned structure. Finally, the effects of basic parameters on static and dynamic pull-in insta- bility and natural frequency are studied.

Three-Dimensional Static Analysis of Nanoplates and Graphene Sheets by Using Eringen’s Nonlocal Elasticity Theory and the Perturbation Method

A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.

Static Analysis of Doubly-Curved Shell Structures of Smart Materials and Arbitrary Shape Subjected to General Loads Employing Higher Order Theories and Generalized Differential Quadrature Method

The article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates.The generalized blendingmethodology accounts for a distortion of the structure so that disparate geometries can be considered.Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum.In addition,re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model.The unknown variables are described employing a generalized displacement field and pre-determined through-the-thickness functions assessed in a unified formulation.Then,a weak assessment of the structural problem accounts for shape functions defined with an isogeometric approach starting fromthe computational grid.Ageneralizedmethodology has been proposed to define two-dimensional distributions of static surface loads.In the same way,boundary conditions with three-dimensional features are implemented along the shell edges employing linear springs.The fundamental relations are obtained from the stationary configuration of the total potential energy,and they are numerically tackled by employing the Generalized Differential Quadrature(GDQ)method,accounting for nonuniform computational grids.In the post-processing stage,an equilibrium-based recovery procedure allows the determination of the three-dimensional dispersion of the kinematic and static quantities.Some case studies have been presented,and a successful benchmark of different structural responses has been performed with respect to various refined theories.

视觉对人体姿势控制影响的脑功能网络连接机制

目的研究视觉对人体姿势控制影响及其脑功能网络连接机制。方法以15名健康青年为研究对象,要求受试者分别进行30 s睁眼、闭眼的双腿站立平衡,采集平衡过程中身体压力中心(center of pressure,COP)和脑电。对COP进行样本熵(SampleEn)计算;对脑电θ、α和β频段,计算相位滞后指数(phase lag index,PLI)构建大脑功能网络,并基于图论计算集聚系数(C)、特征路径长度(L)及小世界网络属性(σ)。结果人体在双腿站立平衡过程中,闭眼COPY样本熵显著高于睁眼(P<0.05)。闭眼α频段PLI平均值显著高于睁眼(P<0.05);闭眼α频段C、σ显著高于睁眼,L显著低于睁眼(P<0.05)。闭眼时α频段额区-中央区-顶区之间的网络连接以及中央区和顶区内连接强度显著高于睁眼(P<0.05)。闭眼时α频段PLI平均值以及C值与COPY样本熵中度呈中度负相关(P<0.05)。睁眼时左前额区、左顶区、左枕区α频段PLI平均值与COPY样本熵呈中度负相关;闭眼时左中央区、右枕区α频段PLI平均值则与COPY样本熵呈中度负相关。结论人体在站立平衡时,当没有视觉信息输入时,身体平衡稳定性下降,同时伴随着脑电α频段的脑网络连接增强以及大脑处理信息的效率需提升。人体在不同的视觉条件下进行姿势控制时,大脑会采用不同的神经策略。

用于夹层梁静动力及屈曲分析的新型组合结构单元

推导出新型组合结构单元,用于考虑界面滑移的3层部分作用夹层组合梁的静动力及屈曲特性分析.基于铁木辛柯梁理论,建立考虑夹层梁部分作用效应的能量原理.针对其受力特性,在节点位移、横截面转角和界面滑移插值时均采用含内部自由度的高阶插值函数,以解决含界面有限元数值分析中常遇到的“滑移锁定”现象.通过变分原理得到夹层梁的刚度矩阵、质量矩阵以及几何刚度矩阵的显示表达式.基于MATLAB编译相应夹层结构的有限元程序并验证其准确性.对不同截面3层夹层组合梁进行不同荷载条件和边界条件下的静动力及屈曲特性分析,并探讨不同夹层组合梁跨高比和不同界面抗剪连接刚度下的计算结果及其误差的变化规律.所推导的显示表达式新型组合结构单元计算效率高,并便于推广应用于其他有限元程序或商业软件子程序中.

基于动静观的古琴断纹衍生品设计研究

文章以传统动静观为理论基础,对古琴断纹的静态表现及动态发展进行衍生品的匹配推衍设计,挖掘事物形态背后的变化发展过程,并将其推衍到设计变体上。这种以静态表现下的动态发展演绎过程或内在形成逻辑作为母体原型推衍的衍生品设计,不仅能够极大地拓展古琴断纹衍生品的设计表现,增强衍生品生命力,还能够为其他文创产品的设计创新提供新方向,使产品充分体现其艺术性、时间性及历史性。

Nonlinear static characteristics of piezoelectric unimorph bending micro actuators

The nonlinear static characteristic of a piezoelectric unimorph cantilever micro actuator driven by a strong applied electric field is studied based on the couple stress theory.The cantilever actuator consists of a piezoelectric layer,a passive（elastic）layer and two electrode layers.First,the nonlinear static characteristic of the actuator caused by the electrostriction of the piezoelectric layer under a strong applied electric field is analyzed using the Rayleigh-Ritz method.Secondly,since the thickness of the cantilever beam is in micro scale and there exists a size effect,the size dependence of the deformation behavior is evaluated using the couple stress theory.The results show that the nonlinearities of the beam deflection increase along with the increase of the applied electric field which means that softening of the micro beam rigidity exists when a strong external electric field is applied.Meanwhile,the optimal value of the thickness ratio for the passive layer and the piezoelectric layer is not around 1.0 which is usually adopted by some previous researchers.Since there exists a size effect of the micro beam deflection,the optimal value of this thickness ratio should be greater than 1.0 in micro scale.

混合边界矩形薄板静力问题解析研究

本文利用Hamilton体系中的“辛-叠加”方法,基于弹性薄板理论,对两对边固支、另两对边中部固支两端简支这一混合边界条件矩形薄板静力问题进行了解析研究.首先基于Hamilton求解体系辛几何方法对对边简支这一经典边界条件矩形薄板问题进行了解析求解,然后以此为基本体系采用叠加法思想对两对边固支、另两对边中部固支两端简支这一复杂混合边界条件矩形板问题进行了求解,最后采用有限元数值模拟对本文方法的正确性和收敛性进行了验证.本文方法同时具备辛几何方法的理性和叠加法的规律性优点,其求解过程中无需预先假定解的形式,直接由弹性力学基本方程出发,通过逐步严格推导来获得解析解.该方法通用性强,可用于一些传统方法难以解析求解的矩形板问题中.

基于分形理论的磨削粗糙表面静摩擦系数模型

为更准确地计算磨削粗糙表面的静摩擦系数,本文综合考虑了微凸体相互作用和区域扩展系数的影响,基于分形几何理论和Hertz接触理论,并利用切向接触载荷的基本理论,推导了磨削粗糙表面的真实接触面积、法向总载荷和切向总载荷,建立磨削粗糙表面的静摩擦系数分形模型,通过数值仿真研究了不同法向总载荷、分形维数、高度尺度参数以及材料参数对粗糙表面静摩擦系数的影响规律。仿真结果表明,磨削粗糙表面的静摩擦系数随着法向总载荷的增加而增加,随着高度尺度参数或材料参数的增大而减小;静摩擦系数和分形维数存在非线性关系,当分形维数小于2.65时,静摩擦系数随着分形维数的增大而增大,当分形维数大于2.65时,静摩擦系数随分形维数的增大而减小。最后通过试验和现有模型验证了本文模型的有效性。

基于活塞压载试验预测高压辊磨机静压功指数的方法

以Bond第三粉碎理论为基础,提出将静压功指数作为评价矿石高压辊磨机料层粉碎比能耗的指标。研究活塞压载试验中不同施载压力对矿石粒度、比能耗和破碎比的影响,确定不同矿石活塞压载试验的适宜条件。通过试验测定3种矿石的高压辊磨机静压功指数,并将其与高压辊磨机生产实践中粉碎同种矿石的净输入功率进行对比。研究结果表明:在活塞压载条件试验中,随着压力的增加,金矿、磁铁矿和钒钛磁铁矿这3种矿石粉碎产品细粒级质量分数增高、粒度分布更加均匀,三者粉碎效果的差异逐渐减小;在加载压力为80 MPa、加载速度为0.2 mm/s的情况下,金矿、磁铁矿和钒钛磁铁矿这3种矿石的高压辊磨机静压功指数分别为1.36、1.44和1.42 kW·h/t,试验所得高压辊磨机静压功指数与工业生产实际中净比能耗的相对误差绝对值在5.26%以内。试验结果可为高压辊磨机静压功指数的预测及设备选型提供理论基础。

山区大跨度窄梁悬索桥静风稳定及抖振性能研究

某山区钢-混组合窄梁悬索桥采用水平导流板对其颤振、驰振性能进行了优化,为了解该桥各类风致静、动力效应,以确保施工安全性和行车安全性,进一步研究优化后加劲梁在平均风作用下的静风稳定性和在脉动风作用下的抖振性能。基于全桥有限元模型结构自振特性分析结果及节段模型风洞试验测得的加劲梁断面静风三分力系数和颤振导数,采用三维非线性数值模拟方法对优化前、后加劲梁的静风临界发散风速进行求解,并与基于小变形假定的二维线性理论分析方法计算结果进行对比;采用抖振响应频域分析方法,结合规范中的桥址区风场特性,计算脉动风作用下的加劲梁抖振位移及内力。结果表明:该桥设置水平导流板前、后,加劲梁静风稳定性均满足规范要求且性能良好;设置水平导流板后,加劲梁扭转方向抖振位移有一定程度增大,同时,加劲梁竖向剪力最大值出现位置发生改变,跨中断面扭矩显著增大,该气动措施对抖振性能的提升较为有限。

骨料的相对比表面积对混凝土弹性模量影响

为快速比选并确定工程的混凝土骨料料源,基于分形理论研究了不同岩性骨料的物理特征,提出骨料相对比表面积(RSSA)参数来快速表征不同骨料的可加工程度,并建立了骨料相对比表面积(RSSA)与混凝土弹性模量的关系。结果表明:骨料的RSSA与母岩中的坚固矿物成分、矿物粒径大小关系密切,且坚固矿物成分的微粒含量与破碎后的骨料的RSSA成正相关,而骨料的RSSA与其细度模数、表观密度呈负相关,与石粉含量、压碎指标呈正相关;相同强度等级下,所制成混凝土水胶比、弹性模量与骨料的RSSA基本呈线性递减关系。

深井开采地压基础理论与防控研究进展

目前地表及浅层矿产资源不断减少,未来采矿必然要向深部进军。随着开采深度的增加,采矿作业面临“三高一扰动”的开采环境,严重影响采矿作业的正常生产,开展地压管理工作成为矿山生产的必要前提。从基础理论、监测手段、地压管理3个方面总结目前的相关研究成果,为矿山实际生产工作提供基础指导。基础理论基于动静力组合加载作用和温度-渗流-应力多场耦合作用2个方面展开,可以明晰地压活动的内在力学机理;监测手段基于应力应变监测系统和微震监测系统2部分展开,静态应力应变监测系统和动态实时微震监测系统相互配合,实现对生产过程中地压活动的有力监测;地压管理措施从地压调控方法和支护系统2个方面展开。明晰了目前深井开采地压基础理论和防控手段存在的问题,进而为后续研究指引方向,促进深井矿山的大力开采。

基于渗透注浆原理的非正规垃圾填埋场防渗技术研究

针对非正规垃圾填埋场性质复杂、垃圾填埋不均一、污染源埋深大、容易造成地下水污染等特点,基于宾汉姆流体的柱—半球形扩散理论,进行了水平静压注浆防渗技术研究。通过改进注浆工艺、优化注浆流程,修复含水层隔水顶板,封堵污染因子向下迁移通道,保护地下水源。将该技术应用于河南省某非正规垃圾填埋场地下水污染治理,注浆后防渗层渗透系数为1.04×10^(-6)~3.81×10^(-5) cm/s,达到或高于粉质黏土的渗透级别,注浆段视电阻率显著降低,取得良好防渗效果,据此探索出一种阻隔高风险污染源与其下伏含水层的工程控制模式。

Static and dynamic responses of a microcantilever with a T-shaped tip mass to an electrostatic actuation

In this study, nonlinear static and dynamic responses of a microcantilever with a T-shaped tip mass excited by electrostatic actuations are investigated. The electrostatic force is generated by applying an electric voltage between the horizontal part of T-shaped tip mass and an opposite electrode plate. The cantilever microbeam is modeled as an Euler-Bernoulli beam. The T-shaped tip mass is assumed to be a rigid body and the nonlinear effect of electrostatic force is considered. An equation of motion and its associated boundary conditions are derived by the aid of combining the Hamilton principle and Newton’s method. An exact solution is obtained for static deflection and mode shape of vibration around the static position. The differential equation of nonlinear vibration around the static position is discretized using the Galerkin method. The system mode shapes are used as its related comparison functions. The discretized equations are solved by the perturbation theory in the neighborhood of primary and subharmonic resonances. In addition, effects of mass inertia, mass moment of inertia as well as rotation of the T-shaped mass, which were ignored in previous works, are considered in the analysis. It is shown that by increasing the length of the horizontal part of the T-shaped mass, the amount of static deflection increases, natural frequency decreases and nonlinear shift of the resonance frequency increases. It is concluded that attaching an electrode plate with a T-shaped configuration to the end of the cantilever microbeam results in a configuration with larger pull-in voltage and smaller nonlinear shift of the resonance frequency compared to the configuration in which the electrode plate is directly attached to it.

Nonlinearity analysis of piezoelectric micromachined ultrasonic transducers based on couple stress theory

This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezo- electric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deforma-tion, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.

Static dipole polarizabilities of Sc_n (n ≤15) clusters

The static dipole polarizabilities of scandium clusters with up to 15 atoms are determined by using the numerically finite field method in the framework of density functional theory. The electronic effects on the polarizabilities are investigated for the scandium clusters. We examine a large highest occupied molecular orbital -- the lowest occupied molecular orbital （HOMO-LUMO） gap of a scandium cluster usually corresponds to a large dipole moment. The static polarizability per atom decreases slowly and exhibits local minimum with increasing cluster size. The polarizability anisotropy and the ratio of mean static polarizability to the HOMO-LUMO gap can also reflect the cluster stability. The polarizability of the scandium cluster is partially related to the HOMO-LUMO gap and is also dependent on geometrical characteristics. A strong correlation between the polarizability and ionization energy is observed.

Lateral Pressure of RC Silos with Static and Dynamic Granular Materials

This paper aims at analyzing material-induced lateral pressure of RC cylinder silo in both static and dynamic condition using the finite element method( FEM). In the finite element software ABAQUS,concrete material is modeled by concrete damaged plasticity model,and stored materials in silo is modeled by the hypoplastic theory.In terms of numerical model,shell elements( S4R) and solid elements( C3D8) are applied for model silo wall and stored materials respectively. The interaction between silo wall and stored materials is simulated by Coulomb friction model and penalty contact constrain provided by ABAQUS.The numerical results are verified with the existing experimental data that are designed to ensure the validation of such numerical model using FEM and it obtains good agreements between numerical results and experimental data. Then the material parameters are analyzed in both static and dynamic condition.According to the analysis,it is clear that critical friction angle,initial void ratio and minimum void ratio have an obvious effect on static lateral pressure while all the material parameters affect dynamic lateral pressure at different levels. In addition,differences of silo wall between elastic and plastic state are analyzed in dynamic condition. The numerical results show that it contributes to increasing dynamic pressure when silo wall enters into the plastic state. Finally,this paper discusses the time-history lateral pressure at different heights along silo wall,and analytical results indicate that larger acceleration values play main roles in producing the maximum lateral pressure at higher part of the silo wall.