Integrated multi-scale approach combining global homogenization and local refinement for multi-field analysis of high-temperature superconducting composite magnets

Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.

Topology Optimal Design of Material Microstructures Using Strain Energy-based Method

Sensitivity analysis and topology optimization of microstructures using strain energy-based method is presented. Compared with homogenization method, the strain energy-based method has advantages of higher computing efficiency and simplified programming. Both the dual convex programming method and perimeter constraint scheme are used to optimize the 2D and 3D microstructures. Numerical results indicate that the strain energy-based method has the same effectiveness as that of homogenization method for orthotropic materials.

THE SATELLITE STRUCTURE TOPOLOGY OPTIMIZATION BASED ON HOMOGENIZATION METHOD AND ITS SIZE SENSITIVITY ANALYSIS

With the development of satellite structure technology, more and more design parameters will affect its structural performance. It is desirable to obtain an optimal structure design with a minimum weight, including optimal configuration and sizes. The present paper aims to describe an optimization analysis for a satellite structure, including topology optimization and size optimization. Based on the homogenization method, the topology optimization is carried out for the main supporting frame of service module under given constraints and load conditions, and then the sensitivity analysis is made of 15 structural size parameters of the whole satellite and the optimal sizes are obtained. The numerical result shows that the present optimization design method is very effective.

An eigenelement method and two homogenization conditions

Under inspiration from the structure-preserving property of symplectic difference schemes for Hamiltonian systems, two homogenization conditions for a representative unit cell of the periodical composites are proposed, one condition is the equivalence of strain energy, and the other is the deformation similarity. Based on these two homogenization conditions, an eigenelement method is presented, which is characteristic of structure-preserving property. It follows from the frequency comparisons that the eigenelement method is more accurate than the stiffness average method and the compliance average method.

The Numerical Accuracy Analysis of Asymptotic Homogenization Method and Multiscale Finite Element Method for Periodic Composite Materials

In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems for four kinds of typical periodic composite materials,the main factors to determine the accuracy of first-order AHM and second-order AHM are found,and the physical interpretation of these factors is given.Furthermore,the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed,and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions.Finally,numerical experiments verify that MsFEM is essentially a first-order multiscale method for periodic composite materials.

Determination of the Micro Stress Field in Composite by Homogenization Method

The objective of this study is to investigate the local stress fluctuation in two-phase composite by homogenization method. The composite was described by homogeneous macro structure and periodical micro structure sinudtaneously and the mechanical response of the composite can be described based on both macro and micro dimensional scales. Micro and mocro homogenization problems can be formulated. The effective material properties of the composite and the local stress field in the microstructure of the composite can be determined by solving these equntions.

Prediction of the Overall Elastic Behavior of Composites by Homogenization Method

The objective of this study was to determine the overall thermal elastic behavior of composites by homogenization method. The results obtained were compared with those by other well-known methods such as mean field method , self-consistent method and etc. A good agreement is achieved and thus a reliable nwthod for predicting the effective behavior of composite is presented. It is very easy to extend this method to multi-phase composite. The materiol properties determined here include elastic modulus, Poisson ratio and thermal expansion coefficient （CTE）.

HOMOGENIZATION-BASED METHOD FOR BENDING ANALYSIS OF PERFORATED PLATE

Owing to the existence of distributed holes, it is difficult tosolve the bending problem of perforated plates by the conventionalfinite element method. A homogenization-based method for this problemis presented in this paper. As an example, the bending analysis of acircular perforated plate with distributed step-wise cylindricalholes is made. The deflection and the fundamental frequen- cyobtained by present method are in good agreement with experimentaldata, this implies that the method is effective.

Simulation and analysis of soil homogenization drills based on discrete element method and response surface methodology

Currently,rotary drilling is one of the main pieces of equipment used for in-situ remediation of contaminated soil.However,this equipment has problems such as uneven mixing and low utilization efficiency,which affect the efficiency of in-situ soil remediation.To improve the efficiency of in-situ soil remediation,this paper takes contaminated black soil as the research object,and the structural design of the new three-stage soil remediation auger is carried out based on SolidWorks.The mixing process of soil and heavy metal passivator under different motion and structural parameters was investigated by the discrete element method(DEM)and response surface methodology.The experimental design was based on rotational speed,homogenizing mixing time,crushing section pitch,and homogenizing section pitch as factors,and soil fragmentation ratio,the coefficient of dispersion,and torque as optimization indices.The kinematic and structural parameters of the three-stage auger drill bit were then optimized using the one-factor method,the orthogonal test,and the response surface methodology,respectively.The test method uses a one-way test to determine the central level value of the orthogonal test and a comprehensive balance method to determine the best combination of parameters for the orthogonal test,which is then used as the central value of the response surface test for parameter optimization.The optimal combinations of kinematic and structural parameters of the three-stage auger drill bit are determined and validated using response surface methodology.The optimum combination of parameters was found to be a speed of 129 rpm,a homogenizing mixing time of 24 s,a pitch of 165 mm in the crushing section,and a pitch of 132 mm in the homogenizing section.The error between the optimal value of the predicted model using the response surface method and the actual simulated value under the optimal parameters is 4.2%,4.9%,and 5.3%,respectively.The optimized factor parameters provide a reference for the design of the structural and kinematic parameters of the in-situ homogenization equipment.

Using strain energy-based prediction of effective elastic properties in topology optimization of material microstructures

An alternative strain energy method is proposed for the prediction of effective elastic properties of orthotropic materials in this paper. The method is implemented in the topology optimization procedure to design cellular solids. A comparative study is made between the strain energy method and the well-known homogenization method. Numerical results show that both methods agree well in the numerical prediction and sensitivity analysis of effective elastic tensor when homogeneous boundary conditions are properly specified. Two dimensional and three dimensional microstructures are optimized for maximum stiffness designs by combining the proposed method with the dual optimization algorithm of convex programming. Satisfactory results are obtained for a variety of design cases.

A novel implementation algorithm of asymptotic homogenization for predicting the effective coefficient of thermal expansion of periodic composite materials

Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.

Upconversion luminescence of Y_2O_3:Er^(3+), Yb^(3+) nanoparticles prepared by a homogeneous precipitation method

Y2O3： Er^3＋, Yb^3＋ nanoparticles were synthesized by a homogeneous precipitation method without and with different concentrations of EDTA 2Na. Upconversion luminescence spectra of the samples were studied under 980 nm laser excitation. The results of XRD showed that the obtained Y2O3：Er^3＋,Yb^3＋ nanoparticles were of a cubic structure. The average crystallite sizes calculated were in the range of 28-40 nm. Green and red upconversion emission were observed, and attributed to ^2H11/2,^4S3/2→^4I15/2 and ^4F9/2→^4I15/2 transitions of the ion, respectively. The ratio of the intensity of green emission to that of red emission drastically changed with a change in the EDTA 2Na concentration. In the sample synthesized without EDTA, the relative intensity of the green emission was weaker than that of the red emission. The relative intensities of green emission increased with the increased amount of EDTA 2Na used. The possible upconversion luminescence mechanisms were discussed.

Simplified Homogeneous Balance Method and Its Applications to the Whitham-Broer-Kaup Model Equations

A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation.

The Construction Method for Solving Radial Flow Problem through the Homogeneous Reservoir

On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.

The homogenization temperature in the fluid inclusions of Ordovician halite and paleoclimatic implication

1 Introduction The homogenization temperature of fluid inclusions reflects the temperatures of the brines from which halite crystals grew.Therefore,it is a powerful mean to reveal the paleoclimate.Northern Shaanxi Salt Basin is located in the central and eastern of Ordos Basin.We have detail petrographical research and the homogenization

A new equivalent method to obtain the stoichiometric fuel-air cloud from the inhomogeneous cloud based on FLACS-dispersion

The fuel-air cloud resulting from an accidental discharge event is normally irregular in shape and varying in concentration. Performance of dispersion simulations using the computational fluid dynamics （CFD）-based tool FLACS can get an uneven and irregular cloud. For the performance of gas explosion study with FLACS, the equivalent stoichiometric fuel-air cloud concept is widely applied to get a representative distribution of explosion loads. The Q9 cloud model that is employed in FLACS is an equivalent fuel-air cloud representation, in which the laminar burning velocity with first order SL and volume expansion ratio are taken into consideration. However, during an explosion in congested areas, the main part of the combustion involves turbulent flame propagation. Hence, to give a more reasonable equivalent fuel-air size, the turbulent burning velocity must be taken into consideration. The paper presents a new equivalent cloud method using the turbulent burning velocity, which is described as a function of SL, deduced from the TNO multi- energy method.

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.

Preparation and Characteristics of Hydroxyapatite Whiskers by Homogeneous Precipitation Method

Hydroxyapatite whilkers were prepared by the homogeneousprecipitation method. Soluble calci- um ion and phosphate ion wereused as initial materials, they were refluxed respectively at 85 deg.C, 90 deg. C and 95 deg. C for various lengths of time. A properprecipitation agent was selected to control the releasing speed ofions in the system; it induced the hydroxyapatite crystal to grow indesired way. The pH each solutions were mea- sured continuouslyduring the reaction.

Reiterated homogenization of a laminate with imperfect contact:gain-enhancement of effective properties

A family of one-dimensional(1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method(RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.