Unified Solution Method of Rectangular Plate Elastic Bending

The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...

Synthesis of nanostructured Li_2FeSiO_4/C cathode for lithium-ion battery by solution method

Nanosphere-like Li2FeSiO4/C was synthesized via a solution method using sucrose as carbon sources under a mild condition of time-saving and energy-saving, followed by sintering at high temperatures for crystallization. The amount of carbon in the composite is less than 10% （mass fraction）, and the X-ray diffraction result confirms that the sample is of pure single phase indexed with the orthorhombic Pmn21 space group. The particle size of the Li2FeSiO4/C synthesized at 700 °C for 9 h is very fine and spherical-like with a size of 200 nm. The electrochemical performance of this material, including reversible capacity, cycle number, and charge-discharge characteristics, were tested. The cell of this sample can deliver a discharge capacity of 166 mA-h/g at C/20 rate in the first three cycles. After 30 cycles, the capacity decreases to 158 mA-h/g, and the capacity retention is up to 95%. The results show that this method can prepare nanosphere-like Li2FeSiO4/C composite with good electrochemical performance.

Influence of different solution methods on microstructure, precipitation behavior and mechanical properties of Al-Mg-Si alloy

The effects of different solution methods on microstructure, mechanical properties and precipitation behavior of Al-Mg-Si alloy were investigated by scanning electron microscope, transmission electron microscope, tensile test, and differential scanning calorimetry. The results revealed that the recrystallized grains of the alloy after the solution treatment with hot air became smaller and more uniform, compared with solution treatment with electrical resistance. The texture of the alloy after two solution treatment methods was different. More rotated cube components were formed through solution treatment with electrical resistance, which was better for improving the drawability of the alloy. The strength of the alloy under the solution treatment with hot air was higher before stamping, because of the small uniform grains and many clusters in the matrix. The alloy solution treated with hot air also possessed good bake hardenability, because the transformation occurred on more clusters in the matrix.

The Discrete-Analytical Solution Method for Investigation Dynamics of the Sphere with Inhomogeneous Initial Stresses

The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure.The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics.It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies.For the solution of these equations,which have variable coefficients,the discrete analytical solution method is developed and applied.In particular,it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems.Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.

COMPARISON OF TDOA LOCATION ALGORITHMS WITH DIRECT SOLUTION METHOD

For Time Difference Of Arrival(TDOA) location based on multi-ground stations scene,two direct solution methods are proposed to solve the target position in TDOA location.Therein,the solving methods are realized in the rectangular and polar coordinates.On the condition of rectangular coordinates,first of all,it solves the radial range between the target and reference station,then cal-culates the location of the target.In the case of polar coordinates,the azimuth between the target and reference station is solved first,then the radial range between the target and reference station is figured out,finally the location of the target is obtained.Simultaneously,the simulation and comparison analysis are given in detail,and show that the polar solving method has the better fuzzy performance than that of rectangular coordinate.

Facile synthesis of single-crystalline rutile TiO_2 nano-rods by solution method

A convenient and scalable technique for the synthesis of rutile titanium dioxide(TiO2) nano-rods was presented by using bulk TiO2 powder, sodium hydroxide(NaOH) and distilled water as raw materials. X-ray diffraction(XRD) and field emission scanning electron microscopy(FESEM) studies indicate that the prepared sample is crystalline and free from any impurities, however, it has no distinct shape and possesses a huge degree of agglomeration, and the average crystal size is around 40 nm. After annealing the sample at 600 °C for 2 h, it is observed through FESEM that nano-rods are formed. And XRD analysis shows that the nano-rods are single crystalline with distinct and smooth surfaces in different sizes with average length of about 1 μm and diameter of about 80 nm. Further UV-visible spectroscopy and Raman studies were conducted for the prepared sample and the band gap of the final product is found to be 3.40 eV.

Fundamental solution method for inverse source problem of plate equation

The elastic plate vibration model is studied under the external force. The size of the source term by the given mode of the source and some observations from the body of the plate is determined over a time interval, which is referred to be an inverse source problem of a plate equation. The uniqueness theorem for this problem is stated, and the fundamental solution to the plate equation is derived. In the case that the plate is driven by the harmonic load, the fundamental solution method （FSM） and the Tikhonov regularization technique axe used to calculate the source term. Numerical experiments of the Euler-Bernoulli beam and the Kirchhoff-Love plate show that the FSM can work well for practical use, no matter the source term is smooth or piecewise.

Preparation of Superhydrophobic ZnO Films on Zinc Substrate by Chemical Solution Method

Superhydrophobic surface was prepared on the zinc substrate by chemical solution method via immersing clean pure zinc substrate into a water solution of zinc nitrate hexahydrate[Zn（NO3）2.6H2O] and hexamethylenete- traamine（C6H12N4） at 95 ℃ in water bath for 1.5 h, then modified with 18 alkanethiol. The best resulting surface shows superhydrophobic properties with a water contact angle of about 158° and a low water roll-off angle of around 3°. The prepared samples were characterized by powder X-ray diffraction（XRD）, X-ray photoelectron spectroscopy （XPS）, energy-dispersive X-ray spectroscopy（EDX）, transmission electron microscopy（TEM）, and scanning electron microscopy（SEM）. SEM images of the films show that the resulting surface exhibits flower-shaped micro- and nano-structure. The surfaces of the prepared films were composed of ZnO nanorods which were wurtzite structure. The special flower-like micro- and nano-structure along with the low surface energy leads to the surface superhydro- phobicity.

THE FUNDAMENTAL SOLUTION METHOD FOR INCOMPRESSIBLE NAVIER STOKES EQUATIONS

A complete boundary integral formulation for incompressible Navier Stokes equations with time discretization by operator splitting is developed by using the fundamental solutions of the Helmhotz operator equation with different orders. The numerical results for the lift and the drag hysteresis associated with a NACA0012 aerofoil oscillating in pitch are good in comparison with available experimental data.

Sustainable Dyeing Solution Methods to making cotton more eco-friendly

Throughout the supply chain,there is interest in conserving resources and reducing the textile industry's environmental footprint.Every stage of a textile product's life cycle has environmental impacts-from fiber production through manufacturing and retailing to laundering and disposal by consumers.Of particular concern is the use of water,energy,and chemicals(WEC) in textile processing-an area where technological advances offer significant savings in resources and environmental benefits.In cotton textile processing, dyeing and finishing have the largest WEC requirements and therefore offer the greatest scope for reductions.

A review of optimization modeling and solution methods in renewable energy systems

The advancement of renewable energy(RE)represents a pivotal strategy in mitigating climate change and advancing energy transition efforts.A current of research pertains to strategies for fostering RE growth.Among the frequently proposed approaches,employing optimization models to facilitate decision-making stands out prominently.Drawing from an extensive dataset comprising 32806 literature entries encompassing the optimization of renewable energy systems(RES)from 1990 to 2023 within the Web of Science database,this study reviews the decision-making optimization problems,models,and solution methods thereof throughout the renewable energy development and utilization chain(REDUC)process.This review also endeavors to structure and assess the contextual landscape of RES optimization modeling research.As evidenced by the literature review,optimization modeling effectively resolves decisionmaking predicaments spanning RE investment,construction,operation and maintenance,and scheduling.Predominantly,a hybrid model that combines prediction,optimization,simulation,and assessment methodologies emerges as the favored approach for optimizing RES-related decisions.The primary framework prevalent in extant research solutions entails the dissection and linearization of established models,in combination with hybrid analytical strategies and artificial intelligence algorithms.Noteworthy advancements within modeling encompass domains such as uncertainty,multienergy carrier considerations,and the refinement of spatiotemporal resolution.In the realm of algorithmic solutions for RES optimization models,a pronounced focus is anticipated on the convergence of analytical techniques with artificial intelligence-driven optimization.Furthermore,this study serves to facilitate a comprehensive understanding of research trajectories and existing gaps,expediting the identification of pertinent optimization models conducive to enhancing the efficiency of REDUC development endeavors.

Preparation of Cu nanoparticles with ascorbic acid by aqueous solution reduction method

Cu nanoparticles were prepared by reducing Cu2＋ ions with ascorbic acid through aqueous solution reduction method. The effects of solution pH and average size of Cu2O particles on the preparation of Cu nanoparticles were investigated. Cu particles were prepared at pH 3, 5 or 7, with the smallest Cu particles obtained at pH 7. However, Cu particles could not be prepared at pH 9 or 11. The average size of Cu2O particles can affect that of Cu particles. Larger Cu2O particles result in larger Cu particles. In addition, experiments were conducted to explore the reaction process by measuring the X-ray diffraction （XRD） patterns of specimens collected at different time points during the reaction. It was found that Cu（OH）2 was initially formed as a precursor, followed by the formation of Cu2O, which was finally reduced to Cu particles.

Effects of reaction parameters on preparation of Cu nanoparticles via aqueous solution reduction method with NaBH_4

The preparation of Cu nanoparticles by the aqueous solution reduction method was investigated. The effects of different reaction parameters on the preparation of Cu nanoparticles were studied. The optimum conditions for preparing well-dispersed nanoparticles were found as follows: 0.4 mol/L NaBH4 was added into solution containing 0.2 mol/L Cu2+, 1.0% gelatin dispersant in mass fraction, and 1.2 mol/L NH3?H2O at pH 12 and 313 K. In addition, a series of experiments were performed to discover the reaction process. NH3?H2O was found to be able to modulate the reaction process. At pH=10, Cu2+ was transformed to Cu(NH3)42+ as precursor after the addition of NH3?H2O, and then Cu(NH3)42+ was reduced by NaBH4 solution. At pH=12, Cu2+ was transformed to Cu(OH)2 as precursor after the addition of NH3?H2O, and Cu(OH)2 was then reduced by NaBH4 solution.

Sea Cucumber-like Polyaniline Nanofibers Synthesized by Aqueous Solution Method

The preparation of polyaniline nanofibers in aqueous solution was studied as functions of the concentrations and ratios of reactants. The morphology and microstructure of polyaniline nanofibers are affected by the concentrations and proportions of the reactants. A special kind of sea cucumber-like polyaniline nanofibers can be prepared under control of reaction conditions. Secondary growth is the formation mechanism. In addition, the bulk electrical conductivity of these sea cucumber-like polyaniline nanofibers was higher than that of other common polyaniline nanofibers.

Resin Matrix/Fiber Reinforced Composite Material, Ⅱ: Method of Solution and Computer Code

According to a mathematical model which describes the curing process of composites constructed from continuous fiber-reinforced, thermosetting resin matrix prepreg materials, and the consolidation of the composites, the solution method to the model is made and a computer code is developed, which for flat-plate composites cured by a specified cure cycle, provides the variation of temperature distribution, the cure reaction process in the resin, the resin flow and fibers stress inside the composite, the void variation and the residual stress distribution.

A unified solution method for free vibration analysis of functionally graded rotating type plates with elastic boundary condition

In this paper,a unified solution method for analyzing the free vibration characteristics of functionally graded rotating type plate(FGRTP)of which the distribution of material is defined by four parameters is presented.It is assumed that the considered functionally graded materials(FGM)are distributed in the thickness direction according to four parameters.The displacement fields of any point on the FGRTP are determined by the first order shear deformation theory(FSDT),and all displacement functions are extended by ultraspherical polynomial.By applying the Ritz method to the energy function of the whole system,the constitutive equation of FGRTP is obtained and the natural frequencies are obtained by solving the eigenvalue problem.The boundary conditions are generalized to arbitrary boundary conditions by artificial elastic technique.The accuracy of the proposed method is verified by comparing with the previous literatures.The effects of different parameters on the free vibration characteristics of FGRTP are studied through some numerical examples.

ASYMPTOTIC METHOD OF TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR REACTION DIFFUSION EQUATION

In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.

Effect of Preparation Conditions on Visible Photocatalytic Activity of Titania Synthesized by Solution Combustion Method

Titania catalysts were synthesized by a solution combustion method （SCM）. Photodegradation of 4-chlorophenol （4-CP） using the synthesized catalysts was studied under both visible light （λ≥420nm） and sunlight irradiation. The effect of preparation conditions on photocatalytic activities of the synthesized catalysts was investigated. The optimal photocatalytic activity of the catalyst （denoted as A1 ） was obtained under the following synthesis conditions： ignition temperature of 350~C, fuel ratio （ φ） of 1 and calcination time of lh. The degradation and mineralization ratio of 4-CP were 78.2% and 53.7% respectively under visible light irradiation for 3h using catalyst A1. And the catalyst A1 also showed high photocatalytic activity under sunlight irradiation.

SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS

The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.

THEORETIC SOLUTION OF RECTANGULAR THIN PLATE ON FOUNDATION WITH FOUR EDGES FREE BY SYMPLECTIC GEOMETRY METHOD

The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution.