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Graphene oxide (GO) was prepared by modified Hummer’s method, and reduced by solvothermal method using ethanol as the solvent and modified diethylene triamine (amine curing agent 593) as reducing agent and modifier. The effect of reduction time and temperature on the structure and conductive property of reduced graphene oxide (593-rGO) was investigated by SEM, FT-IR and XRD. The results show that the graphene modified by 593 is obviously improved in dispersibility and sedimentation stability in dichloromethane, as well as in conductivity. The optimal reduction processing is that the mass ratio of GO to 593 is 2:1, the reduction time and temperature is 6 h and 160°C, respectively.

The torque balancing equations and the torque equation of the turbine flow meter is deduced in the paper. The driving torque, the viscous drag torque and the bearing friction drag torque on the impeller is calculated by unsteady numerical simulation methods. The change rule of the various torques is gotten considering or not the influence of bearing drag torque. Also, the effect of different viscosity on the torque is calculated, which is used to explain the phenomenon of meter factor change law with the viscosity. It makes clear that the possibilities to improve the accuracy of the meter and to predicate the meter factor by unsteady numerical simulation.

Optimization of fiber orientation angle is studied to minimize the deflection of the laminated composite plates by the genetic algorithm. The objective function of optimization problem is the minimum deflection of laminated composite plates under the external load; optimization parameters are fiber orientation angle of laminated composite plates. The results for the optimal fiber orientation angle and the minimum deflection of the 4-layer plates are presented to demonstrate the validity of present method.

The genetic algorithm is used to minimize the stress of the laminated composite plates by optimizing the fiber orientation angle. The objective function of optimization problem is the minimum stress in center of laminated composite plates under the external load; optimization variables are fiber orientation angle. The results for the optimal fiber orientation angle and the minimum stress of the 2-layer plates and 3-layer plates are presented.

Meshless collocation method based on generalized multiquadrics radial basis function is used to study the free vibration of simply supported laminated composite plates. The generalized multiquadric radial basis function g=[r2+c2]q has the exponent q and shape parameter c that play an important role in the accuracy of the approximation. Genetic algorithm is utilized to optimize the shape parameter and exponent of generalized multiquadrics radial basis function. The natural frequencies of simply supported laminated composite plates are calculated using the generalized multiquadrics with optimal shape parameter, exponent and compared with the analytical solutions.

Free vibration of simply laminated composite plates is studied by the global collocation method based on inverse multiquadrics radial basis function. The choice of shape parameter of radial basis function has the important effect on the accuracy of meshless radial basis function collocation method. Genetic algorithm is used to optimize the shape parameter of inverse multiquadrics radial basis function. The natural frequencies of simply supported laminated composite plates are calculated using the inverse multiquadrics radial basis function with optimal shape parameter and compared with the analytical solutions.

In order to study the seismic behavior of square concrete-filled steel tubular (CFT) columns with binding bars under cyclic lateral load, numerical simulation is carried out based on the finite element software OpenSEES. The influence factors of seismic performance on square CFT columns with binding bars were studied. The results indicate that the analysis results exhibit good agreement with the experiment data. The axial load level is the main factor that influences the envelope curve. The stiffness decreases with the incresing of axial load level, while the ultimate lateral load increases with the axial load level less than 0.2, and decreases with the axial load level more than 0.3. The thickness of steel tube has a significant influence on the ultimate lateral load, while has little impact on the shape of envelope curve.

Porous starch was prepared by replacing ice crystals in frozen starch gel with ethanol using a solvent exchange method. Porous starch was packed in a laboratory scale fixed-bed column to continuous remove Methylene Blue (MB) from aqueous solution through adsorption. The effects of bed height, feed flow rate and initial MB concentration on the breakthrough time were investigated. The breakthrough time decreased with increase in the flow rate and initial MB concentration, and also varied with the change in bed height. Bed Depth Service Time (BDST) model was used to determine the column kinetic parameters, and showed good agreement with the experimental data.

Application of coil diameter calculation is very important in the industrial field. The demanding for the precision of control is increasingly strict. There are three methods to achieve a higher precision. They are the Count-method, Linear /Angular Velocity and Distance Calculation respectively. In the process of coiling and uncoiling, advantages and disadvantages are existed. There are different requests for realization of the functions as well. In the Siemens PLC S7-300 control system, these three methods can be used to achieve a higher precision of coil diameter calculation and control. Different improvements and adjustments, according to methods, are given in the process of the test. Some algorithm has been optimized. Finally, by using the three algorithms, the dynamic change of roll diameter can be calculated and meet the need in the course of steel strip.

Dissolution process of polystyrene in decahydronaphthalene solution was conducted and compared under different conditions. The effects of dissolution time and temperature on the dissolution ratio of polystyrene were performed with the assistance of ultrasonic and mechanical agitation, respectively. The dissolution ratio of polystyrene increased with the increment of dissolution time and dissolution temperature, polystyrene dissolved faster under ultrasonic-assisted process. The polystyrene dissolution kinetic model was developed and used to calculate the dissolution rate constant. The kinetic model showed good agreement with the experimental data, and the dissolution rate constant indicated that ultrasonic can obviously enhance the dissolution process of polystyrene in decahydronaphthalene solution.

The penetration resistance to chloride ions of concrete is one of the important factors affecting the durability of concrete structures. The penetration resistance to chloride ions of concrete is measured with the increasing substitution amount of silica fume in this paper. For the low water-binder ratio of 0.28, 0.30 and 0.32, compared with the reference concrete, with the increase of age, the penetration resistance to chloride ions of concrete can be enhanced with the increasing substitution amount of silica fume, but the increased range is smaller. The penetration resistance of chloride ions of concrete is not necessarily improved by gradually decreasing the water-binder ratio. Considering the substitution amount of silica fume, water-binder ratio and concrete age, the best mix proportions are that the substitution amount of silica fume is 9% or 12% when the water-binder ratio is 0.28 and the substitution amount of silica fume is 12% when the water-binder ratio is 0.30.

A numerical model has been established and solved to describe the dehydration reaction from alcohol to ethylene. The influences of the gas velocity and the temperature of the feeding gas to the process of the reaction were discussed. The results showed that, the influence of the radial diffusion on the reaction characteristics could be ignored while the influence of radial heat conduction to the temperature distribution was significant. The temperature distribution decreased alone the axial direction at first and then increased, that is a lowest point of the temperature could be found. When the velocity of the gas slowed down or the temperature of the feeding gas increased, the conversion of the reactant and the selectivity of the target product could be improved, the distance of the lowest temperature point to the entrance got closer and the outlet temperature became higher.

The paper analyzed the influence of the friction factor theoretically on the brake system to produce noise, through complex modal analysis method, established the finite element model of air disc brake to analyze and forecast the brake noise and get brake noises frequency on a certain test conditions. Through the analysis of multiple sets of brake noise under different friction coefficient, it is concluded that the increase of friction coefficient has a promoting effect on brake noise.

With the development of economy, computer technology has been widely used in modular design, which has improved the efficiency of product design and production in all industries. This paper introduces the development and design of functional module of computer application as well as its regulation management in brief, with the hope to do some guidance to others.

This paper analyzes the development trend of modern intelligent machinery manufacturing. Meanwhile, this paper also makes elaborate statement of computer control technology in machinery manufacturing and its specific application.

A kind of Polyimide films (PI films) containing biphenyl and bis-benzimidazole rings were prepared from the its precursor Polyamic acid (PAA) solution synthesized by aromatic diamine containing biphenyl and bis-benzimidazole rings with different commercial aromatic dianhydrides. The PI films exhibited excellent hydrophobicity with the contact angle of higher than 90o and the hydroscopicity are lower than 1%. The PI films also have great dielectric properties of the dielectric constant ranges from 2.10 to 2.94 under the voltage frequency within 1 to 106HZ.

To enhance the efficiency for the shape optimization of complex nonlinear structure, based on the FE analysis combined with the sensitivity analysis, the gradient-based Kriging (GBK) method is applied. A new criterion to determine the likely best spatial correlation parameter in GBK based on Latin Hypercube Design (LHD) presented by authors is also applied. A more practical example for the shape optimization of automotive tire is presented to show the applicability of the GBK method.

The thermal bending response of laminated composite plates has been studied by the use of various higher order shear deformation theories of Levinson, Touratier, Karama and Aydogdu. The governing differential equations are discretized by a meshless method based on inverse multiquadric radial basis function. The center deflections of laminated composite plates subjected to sinusoidal temperature distribution are solved and compared with available published results to assess the performance of the present method.

In the present paper, the higher order shear deformation theories of Touratier and Karama and meshless global collocation method based on the inverse multiquadric radial basis function are used to analyze the bending response of the exponentially graded plates. The material properties of the plates vary exponentially in the thickness direction. The present results are compared with three-dimensional elasticity solutions.

The research examines the phosphorus removal efficiency of modified fly ash on landscape water and its influencing factors, and also study the actual eutrophication landscape water . Results show that when the solution pH is controlled in the range of 5 ~ 9, agitation speed is 150r. min -1and the additive amount modified fly ash is 1.2 g·L-1, the oscillation adsorption time and adsorption temperature are respectively 60 min and at room temperature, for the raw water whose initial concentration of total phosphorus is 10.0 mg·L-1 , the adsorption rate is 98.4%,which has a good adsorption effect. The test about Real urban landscape water shows total phosphorus is 0.35 mg·L-1 , when the additive quantity of modified fly ash is 200 mg·L-1, the concentration of the water reduce to the level of 0.01 mg·L-1 ,which is up to the first class of landscape water quality standard (GB18921-2002)

In this paper the governing equations of cross-ply symmetric laminated composite plates are derived based on the trigonometric shear deformation theory. Generalized Navier type solutions are obtained to predict the free vibration behavior of cross-ply symmetric laminated composite plates. The analytical solutions of natural frequencies are obtained for thick and moderately thick plates as well as for thin plates, and compared with some available results in other papers. Through numerical examples, the high accuracy of present method for free vibration analysis of cross-ply symmetric laminated composite plates is demonstrated.

Many applications have provided functions of automatic searching and reading barcodes in complex scenes with a camera. However state of the art barcode detection systems are limited to their serious requirement, such as shooting angle, light intensity and revolution. This paper proposes an effective solution for automatic barcode localization by exploiting ELM (extreme learning machine) and multichannel Gabor filtering techniques. We first employ Gabor filter to extract texture feature of the barcode, and then the barcode regions and the background region in texture image are use to train the ELM classifier. Finally, we apply our method to the barcode image database, which consists of several different barcode symbologies. Experiment shows our method is superior to the General morphology method and has desirable properties in accuracy, rotation invariance and robustness to noise.

Through pseudo static test on three pieces of fiber reinforced plastics (FRP) transfer beam supported frame with three different reinforcement form, reinforcement ratio and the number of root reinforcement ,which are subjected to the vertical load and horizontal low cycle reciprocating load, the specimen fracture development law, yield mechanism, failure pattern, and bearing capacity, ductility, hysteresis characteristics and seismic performance are analyzed. The test results show that: yield mechanism and failure pattern of transfer beam supported frame equipped with fiber reinforced plastics reinforced bars are reasonable. The bearing capacity and deformation performance of transfer beam supported frame with top and bottom longitudinal bar replaced by FRP bars and symmetrical reinforced box are better than that of single upper replacement for FRP and lower replacement for FRP. The ductility performance of transfer beam supported frame equipped with fiber reinforced plastics bars is good, hysteresis curve is full, and have good seismic performance.

Experimental studies of the long-term performance such have been done in this paper for sea water and sea-sand concrete and sea water and coral sand concrete, such as the elastic modulus, frost resistance and corrosion of reinforcement behavior. The test results show that the compressive elastic modulus of the sea water and sea sand concrete and the sea water and coral sand concrete are slightly lower than that of ordinary concrete, while the adding of fly ash or ground slag in them lead the late compressive elastic modulus slight increase. Compared with the ordinary concrete after freeze-thaw cycle, the mass loss rate and the compressive strength loss rate of the sea water and sea sand concrete and coral sand concrete are slightly larger, but slightly reduced by mixing with ground slag in the concrete, while a little high by mixing with fly ash. Due to the presence of Cl- in the saltwater and sea sand concrete and coral sand concrete, [Cl-] / [OH-] values will be larger, which leads to corrosion of internal reinforced, so it is necessary to adopt appropriate ways to modification for the concrete and reinforced.

The paper analyzes the changes of factors that influence competitiveness of cloud outsourcing facilitators under the promotion of cloud computing technology from perspective of vendor, and gives a fuzzy comprehensive model of competitiveness of vendor.

In this paper, the mechanical property experiments of concrete based on the seawater and sea sand have been carried in different raw materials preparation and different conservation environments. The results show that the early strength and late strength of concrete based on seawater and sea sand are better than concrete based on freshwater and sand. There is no significant strength decreased for concrete based on seawater and sea sand under accelerated alternating wet and dry conditions. For concrete based on seawater and sea sand mixed with admixture, the downward trend of late strength is significantly delayed, the late strength of concrete based on the seawater and sea sand mixed with slag gets the most obvious growth trend, while the late strength of seawater and sea sand concrete mixed with fly ash gets the largest increment.

Coatings such as Cr, Ni, Ti, and SiO2/SnO2 on solar-control and low-emissivity (low-E) glasses are commonly used in the energy efficient glass windows. However, coloring in the re-manufactured glass panels using recycled window glasses resulting from the coatings reduces the glass transparency significantly. Traditional ways to remove coatings by manual wheels and pneumatic removal machines are labor intense and slow processes. In this study a new way to remove the coatings on recycled coated glasses was investigated. The Ultra Violet/Visible/Infrared (UV/VIS/IR) spectra and Secondary Electron Microscope (SEM) pictures were taken before and after 30s. atmospheric pressure oxygen plasma treatments. It was confirmed that the atmospheric oxygen plasma treatment is a fast, efficient, and low pollution way to remove the coatings before the remanufacture of recycled glasses. Other than the physical sputtering off the coatings from the plasma, there are many excited oxygen species in the plasma which effectively react to the coating and the products are then removed.

An experimental program was carried out by the author to investigate the shear behavior of concrete beams reinforced with continuous FRP rectangular spirals, the main variables considered in the test were the shear reinforcement ratio and the shear span to depth ratio and the longitudinal reinforcement ratio. However, the experimental program is inadequate to gain insight into the shear behavior of the members. First, the quantities of test specimens were too small, only six beams were made and tested, the experimental database was so limited that the resultant analytical results and conclusions may not be sound enough. Second, not all the main factors that have influences on the shear behavior of the members have been treated as variables in the experimental program, such as the effective transverse compression stress and the concrete compression strength, the influences of these two factor on the shear behavior of the members were not clear yet through the experimental study. Considering the insufficient information provided by the experimental investigation, the parametric analysis of the shear behavior of the members was carried out, and a revised rotating-angle softened truss model for the shear analysis of the members was proposed as the analytical tool. Based on the proposed model, the influences of various factors on the shear capacity and shear failure modes of the members were discussed, related nonlinear analysis was carried out using the arithmetic of iteration and step approximation, and several FORTRAN codes were written accordingly. Through the experimental study and the parametric analysis, it is indicated that the shear capacity and the shear failure modes of the members are greatly influenced by three major factors, including the shear reinforcement ratio and the shear span to depth ratio and the effective transverse compression stress. The influences of the concrete compression strength and the longitudinal reinforcement ratio on the shear capacity are not noticeable comparatively. The shear capacity is little affected by the shear span to depth ratio in the case of the shear-tension failure, there is no noticeable correlation between longitudinal reinforcement ratio and the shear failure modes.

In order to increase automotive engine development efficiency and reduce the cost, a simulation model is often used, in this paper, with software AMESim the automotive engine lubrication system model was built to simulate the steady lubricant flow rate and pressure in the system at difference engine speed. Comparison between simulation and measurement on the test bench shows that the simulated results are in good accord with experimental data, the lubricant flow rate deviation is less than 3.5% and the pressure deviation at the measurement points is less than 4.0%, so it can be concluded that the model can be used to simulate the automotive engine lubrication system steady lubricant flow and furthermore optimize the system.

In order to explore the effective damage identification method for structure, the structural vibration signal is directly correlation dimension analyzed according to fractal theory, and structural damage is identified by measuring the singularity in system output, then the method for structural damage identification based on correlation dimension of vibration response is proposed. The damage analysis results of a simply supported beam demonstrate that, the proposed method can accurately detect single and multi different degree damage’s location of beam structure, and alteration of correlation dimension will increase along with the damage degree

This study demonstrates the thermal actions of tert-butyl peroxybenzoate (TBPB) which is widely used in the plastic and rubber industries. The thermodynamic and kinetic analysis were performed on the basis of dynamic and adiabatic calorimetric applications which had been accepted as good assistants for investigating materials’ thermal decomposition. In essence, TBPB is reactive and exothermically unstable. Differential scanning calorimetry (DSC) and accelerating rate calorimeter (ARC) were employed to supply basic data and safety index. Experiments were taken under different scanning rates as well as various sample mass. The temperature and pressure curves of TBPB during decomposition were recorded. Based on the significant parameters calculated, self-accelerating decomposition temperature (SADT) of TBPB worked out was 50°C.

Removal of low concentration of phenol from aqueous solutions through the adsorption process by using crosslinked β-Cyclodextrin polymer (β-CD polymer) was investigated. The effects of contact time, sodium chloride content, contact temperature and initial concentration of phenol in the aqueous on adsorption capacity were evaluated through a series of batch experiments. The results show that β-CD polymer on the adsorption of phenol balanced after 6h. The adsorption process was apparently influenced by sodium chloride content, contact temperature and initial phenol concentration in aqueous solution. The adsorption behavior for phenol of β-CD polymer is fitted into the Freundlich isotherm.

In order to improve the efficiency and quality of design of complex parts, cycloid gear, in the pin-cycloidal transmission, this paper used SolidWorks to built accurately cycloid gear 3d model, and the VBA to program procedure for the secondary development, realized the parametric design of cycloid gear. Designer just enter the design parameters of cycloid gear , then gain the accurately generated cycloid gear 3d model rapidly , greatly improving the speed of cycloid gear design.

This paper firstly expounds the scope and principle of riprapping for sludge extrusion, and then details of quality control standard of the construction technology and process are described according to the engineering practice. The points of subsidence, surrounding upheaval, deep horizontal displacement, and pore water pressure are also monitored respectively set in hydraulic fill mud area. The monitoring data are analyzed for conclusion to explore the feasibility and existing problems of riprapping for sludge extrusion in this experiment.

Photoelectrocatalytic oxidation of methyl orange on TiO2 films were investigated in KNO3 solution. In the potential range up to 1.2 V, electro-degradation rates were fairly low that was less than 1%. Degradation rates on the two films were larger at higher potentials. The film prepared without PEG showed better activities than the film prepared with PEG during the whole range of potential. Methyl orange degradation rate increased with increasing KNO3 concentration from 0 to 0.010 mol/l. After 120 min of irradiation, methyl orange degradation rate on the film with PEG was 89.5%, while degradation rate on the film without PEG was 92.0% after the same period.

Based on standard k-ε turbulent, PISO algorithm and the dynamic mesh model, numerical simulation of the 3D, viscous, unsteady compressible gas synthetic jet model was proposed. Two kinds of diaphragm boundary conditions， Helmholtz frequency characteristics and other factors affecting the performance of the 3D synthetic jet were discussed. Simulation results show that the dynamic mesh diaphragm boundary condition is more consistent with the experimental results and the theoretical results, which demonstrates the rationality of the dynamic mesh 3D compressible gas model.

According to the assumption of local thermal non-equilibrium and the heat transfer controlled regime, a mathematical model describing the coupling between the heat and mass transfer processes in a porous packed bed with endothermic chemical reactions was established and solved by the alternate dimension implicit method. The calculated results showed that, the profiles of the temperature distributions of the two phases and the solid conversion ratio all decay near the radial boundary wall corresponding to the momentum boundary layer. However, the concentration of the product gas increases near the wall owing to the slower speed layer. The temperatures difference between the gas flow and solid pellets can not be ignored during the study of ore decomposition in the porous packed bed. The reaction features of the packed bed with endothermic reactions under different conditions can be analyzed by the established model.

The dynamic time-history response analysis method was employed to analyze the dynamic response of composition foundation with CFG piles. The deformation and stress distribution of composite foundation of CFG piles with different length and amount of piles under seismic wave was investigated. The results reveal that the bearing and asti-deformation capacity could be improved effectively for composite foundation under earthquake loads by increasing the length and number of pile. The vertical stress of foundation soil decreases gradually with the increase of the length and number of pile. The practice shows that CFG piles provide a positive contribution to the aseismic effect of foundation soils mass. The present research can provide some references to similar projects.

Gregory’s decomposed theorem of isotropic plate is extended to investigate torsional circular shaft for two-dimensional dodecagonal quasicrystal (2D dodecagonal QCs)with homogeneous boundary conditions, and the theory of equivalence that Cheng’s refined theory and Gregory’s decomposed theorem is extended to the cylindrical coordinate. The decomposed theorem of torsional circular shaft of 2D dodecagonal QCs with homogeneous boundary conditions is proposed on the basis of the classical elasticity theory and stress-displacement relations of 2D dodecagonal QCs without ad hoc assumptions. At first expressions are obtained for all the displacements and stress components in term of some 1D functions. Using Lur’e method, the exact equations were given. And the exact equations for the torsional circular shaft on 2D dodecagonal QCs without surface loadings consist of four governing differential equations: two harmonic equations and two transcendental equations.

In order to validate the pin-hole-output mechanism of FA cycloid drive force analysis theory, and based on the study on the basis of the contact problem, this article used the international advanced finite element analysis software ANSYS, established the output dowel pin and cycloid gear pin hole's contacting finite element model, and analyzed the static three-dimensional contact analysis. The calculation results coincided with the proposed pin-hole-output mechanism with gap dynamic stress analysis method, proved the correctness of the stress analysis theory.

The fire-resistant properties of FRW fire-retardant particleboard and untreated particleboard had been measured under a heat flux of 75 kW/m2 by cone calorimeter (CONE). Through the compare between FRW fire-retardant particleboard and untreated particleboard, the influence on the particleboard by FRW fire retardant had been indicated. The results showed that the indexes of heat release rate (HRR), total heat release (THR) and efficient heat combustion (EHC) etc of FRW fire-retardant particleboard were obviously reduced contrast to the ordinary particleboard, but the char-forming rate had a high increase.

In order to improve the human engineering characteristics of the table tennis wheelchair and promote sport wheelchair, the design of a Table Tennis wheelchair was improved based on the human engineering. With the PRO/E software the table tennis wheelchair three-dimensional model is built and with the CATIA software the three-dimensional human body model is established. At last, in order to validate the human engineering performance of the improved table tennis wheelchair, we carried on the wheelchair man-machine engineering simulation, the operating space analysis of containing, balance analysis and body posture comfort level analysis and appraisal. The results indicated that the improved table tennis wheelchair can satisfy the human engineering request of the security, the efficiency and the comfort.

PET/PTT conjugate yarn has a three-dimension spiral and permanent crimp, which endow the yarn and loomage with excellent performances of crimp extension and crimp recovery. The residual deformation and internal stress of the self-crimp yarn can be eliminated after the moist heat treatment, in order to develop the favorable crimp extension and crimp recovery of the self-crimp yarn, and to give the loomage soft handle and good dimension stability. Crimp shrinkage, crimp module, etc, of the different types of PET/PTT yarn, were tested, and the axial morphology of the yarn was observed, to investigate the effect of linear density, moist heat temperature on PET/PTT yarn.

Taken the pore structure effects into account, a mathematical model to describe the interaction of mass transfers, the chemical reaction and the pore structure in the gas sensitive porous medium is presented and solved. The properties of the mass transfers and the reaction characteristics of the gas-sensitive porous system are analyzed. The effects of pore size distribution and porosity on the concentration field of detected gas and the effective utilization degree of the porous matrix are provided. The results indicate that the Thiele number, which can reflect the relative magnitude of chemical reaction rate and gas diffusion velocity in nature, is the main basis for judging the effects of various parameters. It usefully reproduces the observed effects of pore structure and reaction temperature on diffusion and chemical reaction response, showing that the gas sensitivity and the effective utilization coefficient of the gas sensitive porous medium can be controlled by adjusting key parameters.

Cheng’s refined theory is extended to investigate torsional circular shaft of two-dimensional dodecagonal quasicrystal (2D dodecagonal QCs), and Lur’e method about harmonic function is extended to harmonic function in the respective cylindrical coordinate. The exact deformation of torsional circular shaft of 2D dodecagonal QCs under reverse direction surface loading is proposed on the basis of the classical elasticity theory and stress-displacement relations of 2D dodecagonal QCs, and the exact deformation theory provides the solutions about torsional deformation of a circular shaft without ad hoc assumptions. Exact solutions are obtained for circular shaft from boundary conditions. Using Taylor series of the Bessel functions and then dropping all the terms associated with the higher-order terms, we obtain the approximate expressions for circular shaft of 2D dodecagonal QCs under reverse direction surface. To illustrate the application of the theory developed, one example is examined.

Cheng’s refined theory is extended to investigate torsional circular shaft of cubic quasicrystal, and Lur’e method about harmonic function is extended to harmonic function in the respective cylindrical coordinate. The refined theory of torsional circular shaft of cubic quasicrystal under reverse direction surface loading is proposed on the basis of the classical elasticity theory and stress-displacement relations of cubic quasicrystal, and the refined theory provides the solutions about torsional deformation of a circular shaft without ad hoc assumptions. Exact solutions are obtained for circular shaft from boundary conditions. Using Taylor series of the Bessel functions and then dropping all the terms associated with the higher-order terms, we obtain the approximate expressions for circular shaft of cubic quasicrystal under reverse direction surface. To illustrate the application of the theory developed, one example is examined.

Gregory’s decomposed theorem of isotropic plate is extended to investigate torsional circular shaft of cubic quasicrystal with homogeneous boundary conditions, and the theory of equivalence that Cheng’s refined theory and Gregory’s decomposed theorem is extended to the cylindrical coordinate. The general solution of torsional circular shaft on cubic quasicrystal with homogeneous boundary conditions is proposed on the basis of the classical elasticity theory and stress-displacement relations of cubic quasicrystal without ad hoc assumptions. At first expressions are obtained for all the displacements and stress components in term of some 1D functions. Using Lur’e method, the exact equations were given. And the exact equations for the torsional circular shaft on cubic quasicrystal without surface loadings consist of four governing differential equations: two harmonic equations and two transcendental equations. Using basic mathematic method and the general solutions, an example is examined.

Through generalizing the method of a decay analysis technique determining the interior solution developed by Gregory and Wan, a set of necessary conditions on the end-data of axisymmetric circular cylinder in cubic quasicrystal for the existence of a rapidly decaying solution is established. By accurate solutions for auxiliary regular state, using the reciprocal theorem, these necessary conditions for the end-data to induce only a decaying elastostatic state (boundary layer solution) will be translated into appropriate boundary conditions for the circular cylinder with axisymmetric deformations in cubic quasicrystal. The results of the present paper enable us to establish a set of correct boundary conditions, and mix boundary conditions of which are obtained for the first time.