The Solution of Elastostatic Problems and the Principles of Minimum Potential Energy,Minimum Complementary Work,under Fuzzy Boundary Conditions

A Solution of elastostatic problem is defined on the basis of set theory andextended to the cases with fuzzy boundary conditions.Extension is alsogiven for the principles of minimum potential energy and minimum comple-mentary work with fuzzy boundary conditions.A quasisolution of an elasto-static problem is defined as an approximate solution with boundary conditionsmost close to the original.And the existance of quasisolution of an elasto-static problem can be proved on the basis of certain assumptions and thetheorem of minimum elementary potential energy.     

COMPOSITION OF INDOOR AEROSOLS AT EMPEROR QIN''''S TERRA-COTTA MUSEUM, XI''''AN, CHINA, DURING SUMMER, 2004

Particle samples were collected in August 2004 both inside and outside Emperor Qin's Terra-Cotta Museum in Xi'an, China. Mass and chemical composition of total suspended particles (JSP, particles with aerodynamic diameter less than-30μm), PM2.5(particles with aerodynamic diameter <2.5μm) were determined. The average levels of indoor PM2.5 and TSP were 108.4 and 172.4 μg·m-3, respectively, with PM2.5 constituting 62.9% of the TSP mass. Sulfate ((32.4±6.2)%), organics ((27.7±8.0)%), and geological material ((12.5±3.4)%) dominated indoor PM2.5, followed by ammonium ((8.9±2.8)%), nitrate ((7.0±2.9)%), and elemental carbon (EC, (3.9±1.5)%). Particle size distribution varied with the number of tourists in the museum. The size of sulfate, organics, EC, nitrate, and ammonium was found to vary in the range of 0.43 to 3.3 μm in fraction. Ion balance indicated that the aerosol was acidic, with insufficient ammonium ions to neutralize the sulfuric and nitric acids. High concentrations of acidic aerosols will erode the Terra-cotta warriors and horses especially in the summer season with high temperature (30℃) and relative humidity (70%) and undesirable solar radiation inside the museum. More attention should be paid to protecting these precious antiques made 2000 years ago.     

The “Inverse Hall-Petch” effect on the impact response of single crystal copper

Based on the available experimental and computational capabilities, a phenomenological approach has been proposed to formulate a hypersurface in both spatial and temporal domains to predict combined specimen size and loading rate effects on the material properties [1-2]. A systematic investigation is being performed to understand the combined size, rate and thermal effects on the properties and deformation patterns of representative materials with different nanostructures and under various types of loading conditions [3- 16]. The recent study on the single crystal copper response to impact loading has revealed the size-dependence of the Hugoniot curve. In this paper, the "inverse Hall-Petch" behavior as observed in the impact response of single crystal copper, which has not been reported in the open literature, is investigated by performing molecular dynamics simulations of the response of copper nanobeam targets subjected to impacts by copper nanobeam flyers with different impact velocities. It appears from the preliminary results that the "inverse Hall-Petch" behavior in single crystal copper is mainly due to the formation and evolution of disordered atoms and the interaction between ordered and disordered atoms, as compared with the physics behind the "inverse Hall-Petch"behavior as observed in nanocrystalline materials.     

PM2.5 in China： Measurements,sources, visibility and health effects,and mitigation

Concern over the health effects of fine particles in the ambient environment led the U.S. Environmental Protection Agency to develop the first standard for PM2.5 （particulate matter less than 2.5 μm） in 1997. The Particle Technology Laboratory at the University of Minnesota has helped to establish the PM2.5 standard by developing many instruments and samplers to perform atmospheric measurements. In this paper, we review various aspects of PM2.5, including its measurement, source apportionment, visibility and health effects, and mitigation. We focus on PM2.s studies in China and where appropriate, compare them with those obtained in the U.S. Based on accurate PM2.5 sampling, chemical analysis, and source apportionment models, the major PM2.5 sources in China have been identified to be coal combustion, motor vehicle emissions, and industrial sources. Atmospheric visibility has been found to correlate well with PM2.s concentration. Sulfate, ammonium, and nitrate carried by PM2.s, commonly found in coal burning and vehicle emissions, are the dominant contributors to regional haze in China. Short-term exposure to PM2.s is strongly associated with the increased risk of morbidity and mortality from cardiovascular and respiratory diseases in China. The strategy for PMzs mitigation must be based on reducing the pollutants from the two primary sources of coal-fired power plants and vehicle emissions. Although conventional Particulate Emission Control Devices （PECD） such as electrostatic precipitators in Chinese coal-fired power plants are generally effective for large particles, most of them may not have high collection efficiency of PM2.5. Baghouse filtration is gradually incorporated into the PECD to increase the PM2.5 collection efficiency. By adopting stringent vehicle emissions standard such as Euro 5 and 6, the emissions from vehicles can be gradually reduced over the years. An integrative approach, from collaboration among academia, government, and industries, can effectively manage and mitigate the PM2.s p     

Sensitivity analysis for a type of statically stable sailcrafts

Two types of sensitivities are proposed for statically stable sailcrafts.One type is the sensitivities of solar-radiation-pressure force with respect to position of the center of mass,and the other type is the sensitivities of solar-radiation-pressure force with respect to attitude.The two types of sensitivities represent how the solar-radiationpressure force changes with the position of mass center and the attitude.Sailcrafts with larger sensitivities undergo larger error of the solar-radiation-pressure force,leading to larger orbit error,as demonstrated by simulation.Then as a case study,detailed formulas are derived to calculate the sensitivities for sailcrafts with four triangular sails.According to these formulas,in order to reduce both types of sensitivities,the angle between opposed sails should not be too large,and the center of mass should be as close to the axis of symmetry of the four sails as possible and as far away from the center of pressure of the sailcraft as possible.     

Transport of airborne particulate matters originating from Mentougou, Beijing, China

In this study, a coupled regional air quality modeling system is applied to investigate the time spatial variations in airborne particulate matters （PM10）, originating from Mentougou to Beijing municipal area in the period of April 1-7, 2004, and the influences of complex terrain and meteorological conditions upon boundary layer structure and PM10 concentration distributions. An intercomparison of the performance with CALPUFF against the observed data is presented and an examination of scatter plots is provided. The statistics show that the correlation coefficient and STD between the modeled and observed data are 0.86 and 0.03, respectively. Analysis of model results illustrates that the pollutants emitted from Mentougou can be transported to Beijing municipal area along certain transport pathways, and PM10 concentration distributions show heterogeneity characteristics. Contributions of the Mentougou sources to the PM10 concentrations in Beijing municipal area are up to 0.1-15 μg/m^3.     

Optimal selection for the weighted coefficients of the constrained variational problems

The aim is to put forward the optimal selecting of weights in variational problemin which the linear advection equation is used as constraint. The selection of the functionalweight coefficients ( FWC) is one of the key problems for the relevant research. It wasarbitrary and subjective to some extent presently. To overcome this difficulty, thereasonable assumptions were given for the observation field and analyzed field, variationalproblems with " weak constraints" and " strong constraints" were considered separately. Bysolving Euler' s equation with the matrix theory and the finite difference method of partialdifferential equation, the objective weight coefficients were obtained in the minimumvariance of the difference between the analyzed field and ideal field. Deduction results showthat theoretically the optimal selection indeed exists in the weighting factors of the costfunction in the means of the minimal variance between the analysis and ideal field in terms ofthe matrix theory and partial differen     

A NOTE ON DIVERGENCE,ROTATION,GRADIENT AND THEIR ASSOCIATED THEOREMS

In this note,the essence and some supplements for the unified definition of divergence,rotation and gradient advanced by Tai have been presented based on the method of exteriordifferential form with an expression of vectors of tensors.The main purpose of this note is tointroduce the useful expressions and their applications,and to simplify the proofs of manytheorems in various field theories,and they are also important because of their utlity forestablishing a wide class of principles.     

DEALING WITH MOVINGS AND COLLISIONS OF ARBITRARY MANY DISCONTINUITIES IN CONSERVATIVE FRONT-TRACKING METHOD

An approach to deal with movings and collisions of arbitrary many discontinuities in the conservative front tracking method is developed. Using this approach one may develop an "all-purposed and robust" front-tracking algorithm. The algorithm with this approach may have some inconsistency and thus will have O(1) magnitude errors in some grid cells at sometimes. Nevertheless, these errors will be eliminated by the conservation-preserving property of the front-tracking method in the following computation. Numerical examples are presented to illustrate the efficiency of the approach.     

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.     

Differential-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads

A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differential quadrature element method （DQEM） is then applied to discretize the nonlinear mathematical model in the spatial domain, An effective method is presented to deal with discontinuity conditions of multivariables in the application of DQEM. A set of DQEM discretization equations are obtained, which are a set of nonlinear differential-algebraic equations with singularity in the time domain. This paper also presents a method to solve nonlinear differential-algebra equations. As application, static and dynamical analyses of large deformation of frames and combined frame structures, subjected to concentrated and distributed forces, are presented. The obtained results are compared with those in the literatures. Numerical results show that the proposed method is general, and effective in dealing with disconti- nuity conditions of multi-variables and solving differential-algebraic equations. It requires only a small number of nodes and has low computation complexity with high precision and a good convergence property.     

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.     

Numerical simulation on the adaptation of forms in trabecular bone to mechanical disuse and basic multi-cellular unit activation threshold at menopause

The objective of this paper is to identify the effects of mechanical disuse and basic multi-cellular unit （BMU） activation threshold on the form of trabecular bone during menopause. A bone adaptation model with mechanical- biological factors at BMU level was integrated with finite element analysis to simulate the changes of trabecular bone structure during menopause. Mechanical disuse and changes in the BMU activation threshold were applied to the model for the period from 4 years before to 4 years after menopause. The changes in bone volume fraction, trabecular thickness and fractal dimension of the trabecular structures were used to quantify the changes of trabecular bone in three different cases associated with mechanical disuse and BMU activation threshold. It was found that the changes in the simulated bone volume fraction were highly correlated and consistent with clinical data, and that the trabecular thickness reduced signi-ficantly during menopause and was highly linearly correlated with the bone volume fraction, and that the change trend of fractal dimension of the simulated trabecular structure was in correspondence with clinical observations. The numerical simulation in this paper may help to better understand the relationship between the bone morphology and the mecha-nical, as well as biological environment; and can provide a quantitative computational model and methodology for the numerical simulation of the bone structural morphological changes caused by the mechanical environment, and/or the biological environment.     

Solution of generalized coordinate for warping for naturally curved and twisted beams

A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross-section, it can also be extended to those with arbitrary cross-sectional shape.     

Elastodynamic analysis at an interface of viscous fluid/thermoelastic micropolar honeycomb medium due to inclined load

In this paper, the effect of angle inclination at the interface of a viscous fluid and thermoelastic micropolar honeycomb solid due to inclined load is investigated. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. Expressions of stresses, temperature distribution, and pressures in the transformed domain are obtained by introducing potential functions. The numerical inversion technique is used to obtain the solution in the physical domain. The frequency domain expressions for steady state are also obtained with appropriate change of variables. Graphic representations due to the response of different sources and changes of angle inclination are shown. Some particular cases are also discussed.     

ANTI-PLANE FRACTURE ANALYSIS OF FUNCTIONALLY GRADIENT MATERIAL INFINITE STRIP WITH FINITE WIDTH

The special case of a crack under mode III conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor (SIF) results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.     

Pendulum with linear damping and variable length

The methods of multiple scales and approximate potential are used to study pendulums with linear damping and variable length. According to the order of the coefficient of friction compared with that of the slowly varying parameter of length, three different cases are discussed in details. Asymptotic analytical expressions of amplitude, frequency and solution are obtained. The method of approximate potential makes the results effective for large oscillations. A modified multiple scales method is used to get more accurate leading order approximations when the coefficient friction is not small. Comparisons are also made with numerical results to show the efficiency of the present method.     

Thermal properties,structure,and morphology of discontinuous solid solutions between phenanthrene and carbazole

Two methods,namely solid-state grinding and solution crystallization,were used to prepare discontinuous solid solutions of phenanthrene(PHE)-carbazole(CAR)with different PHE and CAR molar fractions.The thermal properties and structure of the solid solutions were analyzed using differential scanning calorimetry,hot stage microscopy,and powder X-ray diffraction,and the experimental results revealed that the two compounds could form discontinuous solid solutions where PHE and CAR alternately acted as the host and guest with limited range.This was demonstrated using molecular simulations based on lattice energy calculations using the Materials Studio 8.0 software.The crystal morphology and solubility of the solid solution changed significantly as the molar fraction of the guest molecules changed.     

Generalized variational principles of the viscoelastic body with voids and their applications

From the Boltzmann‘ s constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and theinitial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.     

Bifurcation and chaos of airfoil with multiple strong nonlinearities

The bifurcation and chaos phenomena of two-dimensional airfoils with multiple strong nonlinearities are investigated.First,the strongly nonlinear square and cubic plunging and pitching stiffness terms are considered in the airfoil motion equations,and the fourth-order Runge-Kutta simulation method is used to obtain the numerical solutions to the equations.Then,a post-processing program is developed to calculate the physical parameters such as the amplitude and the frequency based on the discrete numerical solutions.With these parameters,the transition of the airfoil motion from balance,period,and period-doubling bifurcations to chaos is emphatically analyzed.Finally,the critical points of the period-doubling bifurcations and chaos are predicted using the Feigenbaum constant and the first two bifurcation critical values.It is shown that the numerical simulation method with post-processing and the prediction procedure are capable of simulating and predicting the bifurcation and chaos of airfoils with multiple strong nonlinearities.