Multiscale Finite Element Method for Coupling Analysis of Heterogeneous Magneto-Electro-Elastic Structures in Thermal Environment

Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.

A rigid-flexible coupling finite element model of coupler for analyzing train instability behavior during collision

Rail vehicles generate huge longitudinal impact loads in collisions.If unreasonable matching exists between the compressive strength of the intermediate coupler and the structural strength of the car body,the risk of car body structure damage and train derailment will increase.Herein,a four-stage rigid-flexible coupling finite element model of the coupler is established considering the coupler buckling load.The influence of the coupler buckling load on the train longitudinal-vertical-hori-zontal buckling behavior was studied,and the mechanism of the train horizontal buckling instability in train collisions was revealed.Analysis results show that an intermediate coupler should be designed to ensure that the actual buckling load is less than the compressive load when the car body structure begins to deform plastically.The actual buckling load of the coupler and the asymmetry of the structural strength of the car body in the lateral direction are two important influencing factors for the lateral buckling of a train collision.If the strength of the two sides of the car body structure in the lateral direction is asymmetrical,the deformation on the weaker side will be larger,and the end of the car body will begin to deflect under the action of the coupler force,which in turn causes the train to undergo sawtooth buckling.

Application of 1D/3D finite elements coupling for structural nonlinear analysis

An element coupling model (ECM) method was proposed to simulate the global behavior and local damage of a structure.In order to reflect the local damage and improve the computational efficiency,three-dimensional (3D) solid elements and one-dimensional (1D) beam element were coupled by the multi-point constraint equations.A reduced scale 1?8 model test was simulated by the ECM and a full three dimensional model (3DM) contrastively.The results show that the global behavior and local damages of ECM agree well with the test and 3DM.It is indicated that the proposed method can be used in the structural nonlinear analysis accurately and efficiently.

Structural Finite Element Software Coupling Using Adapter Elements

This paper describes a versatile and computationally efficient method for coupling several finite element analysis(FEA)programs together so that the unique modeling and analysis capabilities of each code can be utilized simultaneously to simulate the static or dynamic response of a complete numerical system.An arbitrary number of finite element analysis software packages can be coupled by adding two special types of elements,namely generic and adapter elements,to each of the finite element applications using their programming interface.These elements are inserted at the interfaces between the different sub-domains of the complete system modeled by each finite element analysis software package.Exchange of data between the coupled FEA codes is accomplished in a modular and synchronized manner using OpenFresco(Opensource Framework for Experimental Setup and Control).OpenFresco is an objectoriented,environment independent software framework initially developed for hybrid simulation in which certain aspects of a complete structure are simulated numerically and other aspects are simultaneously tested physically.An important practical advantage of this coupled analysis approach is that all of the connected FEA codes run concurrently and continuously,decreasing analysis time consumption by an order of magnitude or more compared to more traditional approaches that shut down and restart the coupled analysis codes at each integration time step.The implementation and accuracy of this approach to FE software coupling are demonstrated using dynamic analyses of three simple structural models from the field of earthquake engineering.

Study on Approach of Static Security Assessment Accounting for Electro-thermal Coupling

A static security assessment approach considering electro-thermal coupling of transmission lines is proposed in this paper. Combined with the dynamic thermal rating technology and energy forecasting, the approach can track both the electrical variables and transmission lines’ temperature varying trajectory under anticipated contingencies. Accordingly, it identifies the serious contingencies by transmission lines’ temperature violation rather than its power flow, in this case the time margin of temperature rising under each serious contingency can be provided to operators as warning information and some unnecessary security control can also be avoided. Finally, numerical simulations are carried out to testify the validity of the proposed approach.

A New Configuration for Planar Magnetic Elements to Reduce Capacitive Couplings

This paper presents an analysis of planar magnetic element configurations in order to reduce capacitive couplings between the windings. The capacitive couplings between layers of planar magnetic elements introduce a stray capacitor which can conduct high frequency currents when high dv/dt voltage is applied. High frequency current may cause electromagnetic interference （EMI） and harmonic problems. The investigation and simulation results, both 2D and 3D Finite Element （FE） show the effect of shifting the planar layers in reduction of the capacitive couplings. The simulation results are compared with test results to validate the proposition.

Importance of Three-Dimensional Piezoelectric Coupling Modeling in Quantitative Analysis of Piezoelectric Actuators

This paper demonstrates the importance of three-dimensional(3-D)piezoelectric coupling in the electromechanical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator.It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects(i.e.,piezoelectric coupling effect).In addition,there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end(i.e.,3-D effect).Hence,modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices,which contributes to the accurate prediction of their behavior.

A Biological Coupling Extension Model and Coupling Element Identification

Extenics is a newly developed interdisciplinary subject combining mathematics, philosophy and engineering. It provides useful formalized qualitative tools and quantitative tools for solving contradictory problems. In this paper, extension theory is introduced briefly and the primary applications of this theory and methods in bionic engineering research are discussed. The extension model of biological coupling functional system is established. In order to identify the primary and secondary sequencing of coupling elements, the Extension Analytic Hierarchy Process (EAHP) was adopted to analyze the contribution of each coupling element to the coupling functional system. Thus, the influence weight factor of each coupling element can be determined, so as to provide a new approach for solving primary and secondary sequencing problem of coupling elements in a quantitative way, and facilitate the subsequent bionic coupling study.

The determination of 52 elements in marine geological samples by an inductively coupled plasma optical emission spectrometry and an inductively coupled plasma mass spectrometry with a high-pressure closed digestion method

An improved analytical method to determine the content of 52 major, minor and trace elements in marine geological samples, using a HF-HCl-HNO_3 acid system with a high-pressure closed digestion method（HPCD）, is studied by an inductively coupled plasma optical emission spectrometry（ICP-OES） and an inductively coupled plasma mass spectrometry（ICP-MS）. The operating parameters of the instruments are optimized, and the optimal analytical parameters are determined. The influences of optical spectrum and mass spectrum interferences, digestion methods and acid systems on the analytical results are investigated. The optimal spectral lines and isotopes are chosen, and internal standard element of rhodium is selected to compensate for matrix effects and analytical signals drifting. Compared with the methods of an electric heating plate digestion and a microwave digestion, a high-pressure closed digestion method is optimized with less acid, complete digestion,less damage for digestion process. The marine geological samples are dissolved completely by a HF-HCl-HNO_3 system, the relative error（RE） for the analytical results are all less than 6.0%. The method detection limits are 2–40μg/g by the ICP-OES, and 6–80 ng/g by ICP-MS. The methods are used to determine the marine sediment reference materials（GBW07309, GBW07311, GBW07313）, rock reference materials（GBW07103, GBW07104,GBW07105）, and cobalt-rich crust reference materials（GBW07337, GBW07338, GBW07339）, the obtained analytical results are in agreement with the certified values, and both of the relative standard deviation（RSD） and the relative error（RE） are less than 6.0%. The analytical method meets the requirements for determining 52 elements contents of bulk marine geological samples.

Determination of trace elements in high purity nickel by high resolution inductively coupled plasma mass spectrometry

The contents ofMg, Al, Si, Ti, Cr, Mn, Fe, Co, Cu, Ga, As, Se, Cd, Sb, Pb and Bi in high purity nickel were determined by high resolution inductively coupled plasma mass spectrometry （HR-ICP-MS）. The sample was dissolved in HNO3 and HCI by microwave digestion. Most of the spectral interferences could be avoided by measuring in the high resolution mode. The matrix effects because of the presence of excess HC1 and nickel were evaluated. Correction for matrix effects was made using Sc, Rh and T1 as internal standards. The optimum conditions for the determination were tested and discussed. The detection limits range from 0.012 to 1.76 ~tg/g depending on the type of elements. The applicability of the proposed method is also validated by the analysis of high purity nickel reference material （NIST SRM 671）. The relative standard deviation （RSD） is less than 3.3%. Results for determination of trace elements in high purity nickel were presented.

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL—II:FINITE ELEMENT MODELING AND APPLICATION

Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.

ELECTRO-MECHANICAL COUPLING ANALYSIS OF MEMS STRUCTURES BY BOUNDARY ELEMENT METHOD

In this paper,we present the applications of Boundary Element Method(BEM) to simulate the electro-mechanical coupling responses of Micro-Electro-Mechanical systems(MEMS). The algorithm is programmed in our research group based on BEM modeling for electrostatics and elastostatics.Good agreement is shown while the simulation results of the pull-in voltages are compared with the theoretical/experimental ones for some examples.

Determination of Trace Elements in High Purity Gold by High Resolution Inductively Coupled Plasma Mass Spectrometry

Trace elements were determined in high purity gold by high resolution inductively coupled plasma mass spectrometry （HR-ICP-MS）. Sample were decomposed by aqua regia. To overcome some potentially problematic spectra/ interference, measurements were acquired in both medium and high resolution modes. The matrix effects due to the presence of excessive HCl and Au were evaluated. The optimum conditions for the determination was tested and discussed. The standard addition method was employed for quantitative analysis. The detection limits range from 0.01ug/g to 0.28ug/g depending on the elements. The method is accurate, quick and convenient. It has been applied to the determination of trace elements in high purity gold with satisfactory results.

THE COUPLING OF BOUNDARY ELEMENT AND FINITE ELEMENT METHODS FOR THE EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS

In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variational formulation and well posedness of the coupling method are obtained. The convergence and optimal estimates for the approximation solution are provided.

Determination of impurity elements in MnZn ferrites by inductively coupled plasma mass spectrometry

An inductively coupled plasma mass spectrometry(ICP-MS) method was developed for the determination of Na, Mg, Al,K, Ca, Ti, Cr, Co, Ni, Cu, Ga, As, Mo, Ag, Cd and Pb in MnZn ferrites. The sample was digested by HNO3+HCl with microwave digestion followed by dilution with ultrapure water, then the above 16 impurity elements in the solution were analyzed directly by ICP-MS. The impurity elements were introduced by the helium gas or hydrogen gas into the octopole reaction system(ORS) to eliminate the polyatomic interferences caused by the high salty matrixes. The matrix effect was minimized through matrix matching,and Be, Y and Rh were used as internal standard elements. The working parameters of the instrument were optimized. The results show that the method has good precision and high accuracy. The detection limits for the investigated elements are in the range of0.9-37.5 ng/L, the relative standard deviation of each element is within 1.1%-4.8%, and the recovery of each element is 90%-108%.

Stress-corrosion coupled damage localization induced by secondary phases in bio-degradable Mg alloys:phase-field modeling

In this study,a phase-field scheme that rigorously obeys conservation laws and irreversible thermodynamics is developed for modeling stress-corrosion coupled damage(SCCD).The coupling constitutive relationships of the deformation,phase-field damage,mass transfer,and electrostatic field are derived from the entropy inequality.The SCCD localization induced by secondary phases in Mg is numerically simulated using the implicit iterative algorithm of the self-defined finite elements.The quantitative evaluation of the SCCD of a C-ring is in good agreement with the experimental results.To capture the damage localization,a micro-galvanic corrosion domain is defined,and the buffering effect on charge migration is explored.Three cases are investigated to reveal the effect of localization on corrosion acceleration and provide guidance for the design for resistance to SCCD at the crystal scale.

Calculation of the Coupling Coefficient of Twin-Core Fiber Based on the Supermode Theory with Finite Element Method

Currently, coupled mode theory (CMT) is widely used for calculating the coupling coefficient of twin-core fibers (TCFs) that are used in a broad range of important applications. This approach is highly accurate for scenarios with weak coupling between the cores but shows significant errors in the strong coupling scenarios, necessitating the use of a more accurate method for coupling coefficient calculations. Therefore, in this work, we calculate the coupling coefficients of TCFs using the supermode theory with finite element method (FEM) that has higher accuracy than CMT, particularly for the strong coupling TCF. To investigate the origin of the differences between the results obtained by these two methods, the modal field distributions of the supermodes of TCF are simulated and analyzed in detail.

A DOMAIN DECOMPOSITION ALGORITHM WITH FINITE ELEMENT-BOUNDARY ELEMENT COUPLING

A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method （FEM） and the boundary element method （BEM）. The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element （FE-BE） coupling method.

ANALYSIS OF COMPOSITE LAMINATE BEAMS USING COUPLING CROSS-SECTION FINITE ELEMENT METHOD

Beams and plates manufactured from laminates of composite materials have distinct advantages in a significant number of applications. However, the anisotropy arising from these materials adds a significant degree of complexity, and thus time, to the stress and deformation analyses of such components, even using numerical approaches such as finite elements. The analysis of composite laminate beams subjected to uniform extension, bending, and/or twisting loads was performed by a novel implementation of the usual finite element method. Due to the symmetric features of the deformations, only a thin slice of the beam to be analysed needs to be modelled. Conventional threedimensional solid finite elements were used for the structural discretization. The accurate deformation relationships were formulated and implemented through the coupling of nodal translational degrees of freedom in the numerical analysis. A sample solution for a rectangular composite laminate beam is presented to show the validity and accuracy of the proposed method.

NEW ALGORITHM OF COUPLING ELEMENT-FREE GALERKIN WITH FINITE ELEMENT METHOD

Through the construction of a new ramp function, the element-flee Galerkin method and finite element coupling method were applied to the whole field, and was made fit for the structure of element nodes within the interface regions, both satisfying the essential boundary conditions and deploying meshless nodes and finite elements in a convenient and flexible way, which can meet the requirements of computation for complicated field. The comparison between the results of the present study and the corresponding analytical solutions shows this method is feasible and effective.