A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered fi- nite volume/finite element method for solution of the two di- mensional （2D） incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by join- ing the centroid of cells sharing the common vertex. For the temporal integration of the momentum equations, an im- plicit second-order scheme is utilized to enhance the com- putational stability and eliminate the time step limit due to the diffusion term. The momentum equations are discretized by the vertex-centered finite volume method （FVM） and the pressure Poisson equation is solved by the Galerkin finite el- ement method （FEM）. The momentum interpolation is used to damp out the spurious pressure wiggles. The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both veloc- ity and pressure. The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.

A simplified multisupport response spectrum method

A simplified multisupport response spectrum method is presented.The structural response is a sum of two components of a structure with a first natural period less than 2 s.The first component is the pseudostatic response caused by the inconsistent motions of the structural supports,and the second is the structural dynamic response to ground motion accelerations.This method is formally consistent with the classical response spectrum method,and the effects of multisupport excitation are considered for any modal response spectrum or modal superposition.If the seismic inputs at each support are the same,the support displacements caused by the pseudostatic response become rigid body displacements.The response spectrum in the case of multisupport excitations then reduces to that for uniform excitations.In other words,this multisupport response spectrum method is a modification and extension of the existing response spectrum method under uniform excitation.Moreover,most of the coherency coefficients in this formulation are simplified by approximating the ground motion excitation as white noise.The results indicate that this simplification can reduce the calculation time while maintaining accuracy.Furthermore,the internal forces obtained by the multisupport response spectrum method are compared with those produced by the traditional response spectrum method in two case studies of existing long-span structures.Because the effects of inconsistent support displacements are not considered in the traditional response spectrum method,the values of internal forces near the supports are underestimated.These regions are important potential failure points and deserve special attention in the seismic design of reticulated structures.

Uniform Convergence for Finite Volume Element Method for Non-selfadjoint and Indefinite Elliptic Problems

In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption.

A Numerical Method for Nonlinear Singularly Perturbed Multi-Point Boundary Value Problem

We consider a uniform finite difference method for nonlinear singularly perturbed multi-point boundary value problem on Shishkin mesh. The problem is discretized using integral identities, interpolating quadrature rules, exponential basis functions and remainder terms in integral form. We show that this method is the first order convergent in the discrete maximum norm for original problem (independent of the perturbation parameter ε). To illustrate the theoretical results, we solve test problem and we also give the error distributions in the solution in Table 1 and Figures 1-3.

Finding the buckling load of non-uniform columns using the iteration perturbation method

The aim of this study is to calculate the critical load of variable inertia columns. The example studied in this paper can be used as a paradigm for other non-uniform columns. The wavelength of equivalent vibratory system is used to calculate the critical load of the trigonometrically varied inertia column. In doing so, the equilibrium equation of the column is theoretically studied using the perturbation method. Accuracy of the calculated results is evaluated by comparing the solution with numerical results. Effect of improving the initial guess on the solution accuracy is investigated. Effects of varying parameters of the trigonometrically varied inertia and the uniformly tapered columns on their stability behavior are studied. Finally, using the so-called ＂perfectibility＂ parameter, two design goals, i.e., being lightweight and being strong, are studied for the discussed columns.

Research on the design method for uniform wear of shield cutters in sand-pebble strata

During shield tunneling in highly abrasive formations such as sand–pebble strata,nonuniform wear of shield cutters is inevitable due to the different cutting distances.Frequent downtimes and cutter replacements have become major obstacles to long-distance shield driving in sand–pebble strata.Based on the cutter wear characteristics in sand–pebble strata in Beijing,a design methodology for the cutterhead and cutters was established in this study to achieve uniform wear of all cutters by the principle of frictional wear.The applicability of the design method was verified through three-dimensional simulations using the engineering discrete element method.The results show that uniform wear of all cutters on the cutterhead could be achieved by installing different numbers of cutters on each trajectory radius and designing a curved spoke with a certain arch height according to the shield diameter.Under the uniform wear scheme,the cutter wear coefficient is greatly reduced,and the largest shield driving distance is increased by approximately 47%over the engineering scheme.The research results indicate that the problem of nonuniform cutter wear in shield excavation could be overcome,thereby providing guiding significance for theoretical innovation and construction of long-distance shield excavation in highly abrasive strata.

均匀设计法优选掌叶大黄(Rheum palmatum L.)总蒽醌类物质的薄层层析展开剂体系

以陇东地区子午岭掌叶大黄为实验材料,采用均匀设计法设计试验,以各成分的Rf值为评价指标,分析比较了各展开体系对掌叶大黄总蒽醌类成分的展开情况。结果表明:基于均匀设计法进行的12种展开系统中,以丙酮∶甲醇∶正己烷∶1,2-二氯乙烷=1∶1∶1∶1展开体系效果最佳,展开斑点个数达9个,且各Rf值间差异极显著(P<0.01)。本研究采用均匀设计法优选了大黄总蒽醌类成分的薄层层析展开剂,与药典记录的游离蒽醌展开剂相比,具有样品预处理简单、节约有机溶剂等优越性,可为大孔吸附树脂法进一步分离蒽醌类物质的定性分析提供数据参考。

基于UML进行无状态组件的建模

简要说明了现代软件组件的两种类型———有状态组件和无状态组件,以及无状态组件在企业应用中的应用。分析了面向对象软件工程方法对无状态组件的建模中存在的问题,提出了解决方案,并基于UML对这种建模进行了描述。

离散变量参数UMA限中均匀数取值的研究

本文用Jeffreys的无信息先验分布的Bayes方法与随机化的Fiducial方法,对UMA置信限中的均匀数u的取值问题进行了研究,结果表明,Mann建议u取1/2,对二项分布与有替换定时截尾的指数分布这是合适的,但对预定成功数或失败数的负二项分布,此值略为偏小,其相对误差与样本量n的关系为1/(2n+1)

基于UM、DM和IM的应用软件开发方法

本文提出了一种基于用户模型 (UM )、设计者模型 (DM )和实现模型 (IM )的开发方法 ,该方法模拟了人类认知客观世界中新生事物的渐进过程 ,它认为应用软件的开发过程就是一个用户模型、设计者模型、实现模型的建立和使这三个模型实现一致的过程 ,文中还给出该方法的开发过程和采用的主要技术手段 .该方法为应用软件的开发提供了一种新思路 ,为最终保证应用软件的质量提供了一个有效的途径 .

ELASTIC MODULUS REDUCTION METHOD FOR LIMIT LOAD EVALUATION OF FRAME STRUCTURES

A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio （EBR）,and the elastic modulus reduction method （EMRM） is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion,and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility,accuracy and effciency of the proposed method.

The height-width ratio limited value for rubber bearing isolated structure computed by uniform design method

Rubber isolation is the most mature control technology in practical application, and is widely used by short rigid buildings. However, many high isolation buildings have been built around the world in recent years, which do not follow the existing criterions and codes. Many researchers began to research the special problems caused by larger height-width ratio isolation structures. The overturning effect of high height-width ratio structures with rubber bearing is firstly studied. Considering the main factors, such as the height-width ratio of structures, type of site, the designed basic acceleration of ground motion and the decouple factor in horizon, computing experiment is defined with the Uniform Design Method, which is also known as designing isolation structure. The forces of the bearing under edge of structures based on the position of the rubber bearing are calculated. The result indicates that the rubber bearings will lose its functionality under very high tension and compressing force of earthquake motion in horizon and vertical, when the height-width ratio is over a certain value. Thus, based on the calculation result of isolation structures defined in the uniform design method, regression analysis is conducted, and also the rubber edge force regression formula are gotten, which has higher correlation and smaller standard deviation. This formula can be used to roughly calculate whether the pull force occurs at the edge of the building. By the edge bearings of isolation structure minimum force formula, the height-width ratio limited value of the isolation structure is deducted when rubber bearing has minimum force of zero.

The Complex System Modeling Method Based on Uniform Design and Neural Network

In this paper, the method based on uniform design and neural network is proposed to model the complex system. In order to express the system characteristics all round, uniform design method is used to choose the modeling samples and obtain the overall information of the system;for the purpose of modeling the system or its characteristics, the artificial neural network is used to construct the model. Experiment indicates that this method can model the complex system effectively.

Dynamical Behaviors of Nonlinear Coronavirus (COVID-19) Model with Numerical Studies

The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious diseases.For the new strain of coronavirus(COVID-19),there is no vaccine to protect people and to prevent its spread so far.Instead,control strategies associated with health care,such as social distancing,quarantine,travel restrictions,can be adopted to control the pandemic of COVID-19.This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods:the homotopy perturbation method(HPM)and the modied reduced differential transform method(MRDTM).We invoke a novel signal ow graph that is used to describe the COVID-19 model.Through our mathematical studies,it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus.The numerical simulation results are in reasonable agreement with the study predictions.The free equilibrium and stability point for the COVID-19 model are investigated.Also,the existence of a uniformly stable solution is proved.

Simulation analysis of significance and interaction of influencing factors on mixing uniformity of double-drum recycling mixing plant

To examine the influence of the structural parameters and working parameters of a double-drum regeneration mixing station on its mixing uniformity,the influence of the discrete element method and response surface method on the uniformity of the aggregate mixing when the interaction between two different factors was analyzed.A mathematical model of the influence of various factors and interactions on the coefficient of variation of the aggregates was established.The matching of each parameter was optimized with the goal of minimizing the coefficient of variation.The results show that when the aggregate particle size is different,the significance of each parameter affecting its mixing uniformity is also different.Moreover,increasing the speed and reducing the axial installation angle of the blade can reduce the coefficient of variation of the three aggregates.To obtain a good mixing uniformity,the mixing-arm phase angle when the drum inclination angle is large should be smaller than the phase angle when the drum inclination angle is small,and the mixing of large particles should not be arranged with a large mixing-arm phase angle.With a blade radial installation angle of 38°,a blade axial installation angle of 35°,a drum inclination angle of 6°,a drum rotation speed of 10 r/min,and a mixing-arm phase angle of 32°,the aggregate as a whole can exhibit the best mixing uniformity.

Pseudo Almost Periodic Solutions of Nonlinear Hyperbolic Equations with Piecewise Constant Argument

In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model for the dynamics of gas absorption,

Measurement Method of the Thickness Uniformity for Polymer Films

Several methods for investigating the thickness uniformity of polymer thin films are presented as well as their measurement principles. A comparison of these experimental methods is given.The cylindrical lightwave reflection method is found to can obtain the thickness distribution along a certain direction.It is a simple and suitable method to evaluate the film thickness uniformity.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

Free vibration of non-uniform axially functionally graded beams using the asymptotic development method

The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.

CONTINUOUS FINITE ELEMENT METHODS FOR REISSNER-MINDLIN PLATE PROBLEM

On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming （bi）linear macroelements or （bi）quadratic elements, and the rotation by conforming （bi）linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.