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.

An Improved Three-Dimensional Model for Emotion Based on Fuzzy Theory

Emotion Model is the basis of facial expression recognition system. The constructed emotional model should not only match facial expressions with emotions, but also reflect the location relationship between different emotions. In this way, it is easy to understand the current emotion of an individual through the analysis of the acquired facial expression information. This paper constructs an improved three-dimensional model for emotion based on fuzzy theory, which corresponds to the facial features to emotions based on the basic emotions proposed by Ekman. What’s more, the three-dimensional model for motion is able to divide every emotion into three different groups which can show the positional relationship visually and quantitatively and at the same time determine the degree of emotion based on fuzzy theory.

Head Pursuit Variable Structure Guidance Law for Three-dimensional Space Interception

This article aims to develop a head pursuit （HP） guidance law for three-dimensional hypervelocity interception, so that the effect of the perturbation induced by seeker detection can be reduced. On the basis of a novel HP three-dimensional guidance model, a nonlinear variable structure guidance law is presented by using Lyapunov stability theory. The guidance law positions the interceptor ahead of the target on its tlight trajectory, and the speed of the interceptor is required to be lower than that of the target, A numerical example of maneuvering ballistic target interception verifies the rightness of the guidance model and the effectiveness of the proposed method.

AN ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL DIFFRACTION OF PLANE P-WAVES BY A HEMISPHERICAL ALLUVIAL VALLEY WITH SATURATED SOIL DEPOSITS

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot＇s dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot＇s dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Three-dimensional nonlinear analysis of creep in concrete filled steel tube columns

This paper proposes a based on 3D-VLE （three-dimensional nonlinear viscoelastic theory） three-parameters viscoelastic model for studying the time-dependent behaviour of concrete filled steel tube （CFT） columns. The method of 3D-VLE was developed to analyze the effects of concrete creep behavior on CFT structures. After the evaluation of the parameters in the proposed creep model, experimental measurements of two prestressed reinforced concrete beams were used to investigate the creep phenomenon of three CFT columns under long-term axial and eccentric load was investigated. The experimentally obtained time-dependent creep behaviour accorded well with the cu~＇es obtained from the proposed method. Many factors （such as ratio of long-term load to strength, slenderness ratio, steel ratio, and eccentricity ratio） were considered to obtain the regularity of influence of concrete creep on CFT structures. The analytical results can be consulted in the engineering practice and design.

Seismic responses of a hemispherical alluvial valley to SV waves: a three-dimensional analytical approximation

Abstract An analytical solution to the three-dimen-sional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expan-sion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot＇s dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn： （1） there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; （2） the nor-malized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; （3） with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

Using"Three-dimensional Space Resources"for Fenlong Technology to Improve Grain Econoloy and Expand Human Living Spaces

Fenlong Technology has been applied to increase yield by 20%-50%,improve quality by 5%,and retain water by 100%in 40 kinds of crop cultivated land and saline-alkali land in 26 provinces of China.This paper clarified for the first time the scientific theory system of Fenlong Technology using three-dimensional space resources"Fenlong Agricultural Nature Theory"and the development of the relative"limits"of agricultural growth,which provides a huge power support and natural force for expanding human living spaces.Through inventing and creating a scientific and technological system of farming tools,farming machinery,farming modes,and magic weapons for cultivation,Fenlong Technology can increase grain,promote ecological development,and greatly expand the living spaces of the Chinese nation and achieve sustainable development.Using Fenlong Technology,China has expanded from the current single"cultivated land agriculture"to the"big pattern agriculture"of Fenlong"cultivated land+saline land+degraded grassland+marginal land+desertified land+river water",flexibly used 147 million ha of"three-dimensional space resources"of land,and the newly increased food,meat,and fish can feed 300 million to 400 million people,increased the water storage by 100 billion m^(3),and reduced the collection of groundwater by 20 million to 60 billion m^(3).

Unsteady three-dimensional MHD flow of the micropolar fluid over an oscillatory disk with Cattaneo-Christov double diffusion

Cattaneo-Christov heat and mass flux models are considered rather than Fourier and Fick laws due to the presence of thermal and concentration transport hyperbolic phenomena. The generalized form of the Navier-Stokes model is considered in hydromagnetic flow. Three-dimensional (3D) unsteady fluid motion is generated by the periodic oscillations of a rotating disk. Similarity transformations are used to obtain the normalized fluid flow model. The successive over relaxation (SOR) method with finite difference schemes are accomplished for the numerical solution of the obtained partial differential non-linear system. The flow features of the velocity, microrotation, temperature, and concentration fields are discussed in pictorial forms for various physical flow parameters. The couple stresses and heat and mass transfer rates for different physical quantities are explained via tabular forms. For better insight of the physical fluid model, 3D fluid phenomena and two-dimensional (2D) contours are also plotted. The results show that the micropolar fluids contain microstructure having non-symmetric stress tensor and are useful in lubrication theory. Moreover, the thermal and concentration waves in Cattaneo-Christov models have a significance role in the laser heating and enhancement in thermal conductivity.

A numerical investigation of bubble dynamics based on the potential-flow theory

In this paper, the flow field is assumed to be inviscid, irrotational and incompressible, triangular elements are adopted to discretize the boundary of flow field, the boundary integral method is used to solve the flow field and the Mixed-Eulerian-Lagrangian method is applied to simulate the evolution of bubble. Three-dimensional smoothing method is used to smooth the bubble surface and the velocity potential to make the computing process more accurate and stable. In the analysis process, three-dimensional model simulates the dynamics of a bubble in the free field, gravitational field and near the rigid wall respectively, and the calculated results coincide well with the exact results and experimental data, which show that the algorithm and 3D model in this paper are of high accuracy. Calculation process indicates that bubble takes on strong non-linear under the combine effect of gravity and rigid wall.

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.

Constructal design of a rectangular parallel phase change microchannel in a three-dimensional electronic device

Based on constructal theory,a rectangular parallel phase change microchannel model in a three-dimensional electronic device(TDED)is established with R134a as the cooling fluid.Based on the minimization of a complex function(CF)composed of linear weighting sum of maximum temperature difference and pumping power consumption,constructal design of the TDED is conducted first;and then,maximum temperature difference and pumping power consumption are minimized by non-dominated sorting genetic algorithm-II methods.The results reveal that there exist an optimal mass flow rate(0.0012 kg/s)and a quadratic optimal aspect ratio(AR)(0.39)of the microchannel which lead to quadratic minimum CF(0.817).Compared with the original value,the CF after optimization is reduced by 18.34%.Reducing the inlet temperature of cooling fluid and microchannel number appropriately can help to enhance the overall performance of TDED.By using the artificial neural network and genetic algorithms in the toolboxes of Matlab software,the optimal AR gained in the Pareto solution set is located between 0.2–0.45.The smallest deviation index among three discussed strategies is 0.346,and the corresponding optimal AR is 0.413,which is selected as the optimal design strategy of the microchannel in the TDED under multiple requirements.The findings in this study can serve as theoretical guides for thermal designs of electronic devices.

“Volume-point” heat conduction constructal optimization based on entransy dissipation rate minimization with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale

Based on constructal theory,the constructs of three "volume-point" heat conduction models with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale are optimized by taking minimum entransy dissipation rate as optimization objective.The optimal constructs of the three "volume-point" heat conduction models with minimum dimensionless equivalent thermal resistance are obtained.The results show that the optimal constructs of the three-dimensional cylindrical assembly based on the minimizations of dimensionless equivalent thermal resistance and dimensionless maximum thermal resistance are different,which is obviously different from the comparison between those of the corresponding two-dimensional rectangular assembly based on the minimizations of these two objectives.The optimal constructs based on rectangular and triangular elements on microscale and nanoscale when the size effect takes effect are obviously different from those when the size effect does not take effect.Because the thermal current density in the high conductivity channel of the rectangular and triangular second order assemblies are not linear with the length,the optimal constructs of these assemblies based on the minimization of entransy dissipation rate are different from those based on the minimization of maximum temperature difference.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the construct.The studies on "volume-point" heat conduction constructal problems at three-dimensional conditions and microscale and nanoscale by taking minimum entransy dissipation rate as optimization objective extend the application range of the entransy dissipation extremum principle.

Statistical Distribution of Surface Slope in A 3-D Ocean Wave Field

A joint probability density function (PDF) for surface slopes in two arbitrary directions is derived on the basis of Longuet Higgins's linear model for three-dimensionol (3-D) random wave field. and the correlation moments of surface slopes. as parameters in the PDF, are expressed in terms of directional spectrum of ocean waves. So long as the directional spectrum model is given, these parameters are determined. Since the directional spectrum models proposed so far are mostly parameterized by the wind speed and fetch, this allows for substituting these parameters with thc wind speed and fetch. As an example, the wind speed and fetch are taken to be 14 m ' s and 200 km, and the Hasselmann and Donclan directional spectra are, respectively, use to compute these parameters. Some novel results a reobtained. One of the increasing interesting results is that the variances of surface slope in downwind and cross-wind directions determined by the Donclan directional spectra are close to those measured by Cox and Munk (1954). Some discussions are made on these results.

A Modified Symmetric and Antisymmetric Decomposition-Based Three-Dimensional Numerical Manifold Method for Finite Elastic-Plastic Deformations

There are relatively few studies on large rotation or deformation by means of the three-dimensional(3D)numerical manifold method(NMM).A new modified symmetric and antisymmetric decomposition(MSAD)theory is developed and implemented into the 3D NMM,eliminating the false-volume expansion and false-rotation strain/stress problems.The Jaumann rate is used to measure the material rotation,and the geometric stiffness built on the Jaumann rate is deduced.The incremental formulas of the MSAD-based 3D NMM and a practical guide on the implementation of the MSAD theory are given in detail and exemplified.The new theory and formulas can be applied to analyze both large rotation and large deformation problems.Based on the hypoelasto-plasticity theory and the unified strength theory,the unified yield criterion with associated flow rule is implemented into the MSAD-based 3D NMM.Several typical examples are studied,showing the advantage and potential of the new MSAD theory and the MSAD-based 3D NMM.

Width effects on hydrodynamics of pendulum wave energy converter

Based on two- and three-dimensional potential flow theories, the width effects on the hydrodynamics of a bottom-hinged trapezoidal pendulum wave energy converter are discussed. The two-dimensional eigenfunction expansion method is used to obtain the diffraction and radiation solutions when the converter width tends to be infinity. The trapezoidal section of the converter is approximated by a rectangular section for simplification. The nonlinear viscous damping effects are accounted for by including a drag term in the two- and three-dimensional methods. It is found that the three- dimensional results are in good agreement with the two-dimensional results when the converter width becomes larger, especially when the converter width is infinity, which shows that both of the methods are reasonable. Meantime, it is also found that the peak value of the conversion efficiency decreases as the converter width increases in short wave periods while increases when the converter width increases in long wave periods.

Dynamic Design of Thick Orthotropic Cantilever Plates with Consideration of Bimoments

The paper is devoted to dynamic design of thick orthotropic cantilever plates by applying the bimoment theory of plates, which takes into account the forces, moments and bimoments;and the theory takes into account nonlinear law of displacements distribution in cross section of the plate. The methods for constructing bimoment theory are based on Hooke’s Law, three-dimensional equations of the theory of dynamic elasticity and the method of displacements expansion into Maclaurin series. The article gives the expressions to determine the forces, moments and bimoments. Bimoment theory of plates is described by two unrelated two-dimensional systems with nine equations in each. On each edge of the plate, depending on the type of fastening, nine boundary conditions are given. As an example, the solution of the problem of dynamic bending of thick isotropic and orthotropic plate under the influence of transverse dynamic loads in the form of the Heaviside function is given. The equations of motion of the plate are solved by numerical method of finite differences. The numerical results are obtained for isotropic and orthotropic plate. The graphs of changes of displacements and stresses of faces surfaces of the plate are presented. Maximum values of these displacements are found and analyzed. It is shown that by Timoshenko theory numerical values of stresses are much smaller compared to the ones obtained by bimoment theory of plates. Maximum numerical values of generalized displacements, forces, moments, and bimoments are obtained and presented in tabular form. The analysis of numerical results is done and the conclusions are drawn.

A Framework for Exploring the Dynamics of Autonomous Work Groups in Manufacturing Organizations

Nowadays, new paradigm of enterprise organization i s constantly changing due to the emergence of the global marketplace, the rise of information technology, and the emphasis of the social developments. This re quires a more flexible form of organization that are more adaptable to rapid cha nges in business environment such as autonomous work groups (AWGs) in order to achieve higher productivity and effectiveness. AWGs are work units responsib le for the production of goods and the provision of services. They involve team members in making decisions that are traditionally the responsibility of the sup ervisors and managers (Cohen & Bailey, 1997). Team members of AWGs are allowed t o self-regulate their behavior on jobs such as task assignments, methods for ca rrying out the work, and scheduling of activities etc. (Cohen & Ledford, 1994). For example, Motorola achieved a high organizational performance due to the succ essful implementation of AWGs in quality management (Piczak & Hauser, 1996). Xer ox also reported their operational successes based on the team-oriented work gr oups (Wageman, 1997). In recent years many organizations have replaced the traditional layers of manag ement with autonomous team-based work arrangements. Surveys indicated that the adoption of AWGs has soared in responding to the competitive business challenges . Many enterprises are making a deliberate effort to use AWGs to carry out work and operational processes as an alternative for hierarchical approaches (Lawler et al., 1995). There is a growing body of evidence that AWGs are more effective than traditionally managed groups and they contributes to organizational perform ance, such as improvement in operational performance, productivity, quality, cos t savings, employee attitude and behavior, and employee satisfaction (e.g. Pears on, 1992; Cohen & Ledford, 1994; Seers et al. 1995). Given the complexity and cognitive nature of team-based organizations, the mech anisms that the enterprises use in the development of the increasingly sophistic ated models, which can contribute to the effective functioning of AWGs, are extr emely important. The process of developing effective AWGs enables enterprises to inherent built-in intelligence of the organizations so that they will be more able to accommodate to external pressures and changes. The context of this paper is the construction of a dynamics framework and a stra tegic path for autonomous work groups in the technology-oriented manufacturing organization re-design. The framework is a conceptual one drawn from the litera ture survey. The importance of studying autonomous work groups for today’s manuf acturing organizations is claimed. Based on the General System Theory (GST), the characterization of AWGs is addressed. Three-dimensional domains such as t echnical content, service content, and relationship content are identified. A st rategic path is proposed to guide the organizations how the development of AWGs progresses at different levels of maturity that are associated with organization al effectiveness and performance. The utility of the model for AWGs is expected to provide technology-oriented organizations with a strategic path to achieve h igher organizational performance.

Soliton solutions,travelling wave solutions and conserved quantities for a three-dimensional soliton equation in plasma physics

Many physical systems can be successfully modelled using equations that admit the soliton solutions.In addition,equations with soliton solutions have a significant mathematical structure.In this paper,we study and analyze a three-dimensional soliton equation,which has applications in plasma physics and other nonlinear sciences such as fluid mechanics,atomic physics,biophysics,nonlinear optics,classical and quantum fields theories.Indeed,solitons and solitary waves have been observed in numerous situations and often dominate long-time behaviour.We perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first time.Direct integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function,elliptic functions,elementary trigonometric and hyperbolic functions solutions of the equation.Besides,various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral technique.These solutions comprise dark soliton,doubly-periodic soliton,trigonometric soliton,explosive/blowup and singular solitons.We further exhibit the dynamics of the solutions with pictorial representations and discuss them.In conclusion,we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral formula.We state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new.

Two and Three Dimensions of Generalized Thermoelastic Medium without Energy Dissipation under the Effect of Rotation

The purpose of this paper is to study the effect of rotation on the general three-dimensional model of the equations of the generalized thermoelasticity for a homogeneous isotropic elastic half-space solid. The problem is studied in the context of the Green-Naghdi theory of type II (without energy dissipation). The normal mode analysis is used to obtain the expressions for the temperature, thermal stress, strain and displacement. The distributions of variables considered are represented graphically.

A THREE-DIMENSIONAL ELASTICITY SOLUTION FOR TWO-DIRECTIONAL FGM ANNULAR PLATES WITH NON-UNIFORM ELASTIC FOUNDATIONS SUBJECTED TO NORMAL AND SHEAR TRACTIONS

In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-shear tractions is investigated using the exact three- dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two- directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material proper- ties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction： linear, parabolic, and sinu- soidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters （e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions） is carried out. The results are reported for the first time and are discussed in detail.