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.

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.

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.

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.

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.

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.

A Finite Element Procedure for Analysis of Chemo-Mechanical Coupling Behavior of Hydrogels

Chemo-mechanical coupling behavior of materials is a transformation process between mechanical and chemical energy.In this paper,based on the coupled chemo-mechanical constitutive equations and governing equations during isothermal process,the equivalent integral forms of chemo-mechanical coupling governing equations and corresponding finite element procedure are obtained by using Hamilton’s principle.An isoparametric plane element for chemo-mechanical coupling is associated into ABAQUS finite element package through user element subroutine UEL.The numerical examples exhibit that the ionic concentration variation can cause mechanical deformation and mechanical action can produce redistribution of ionic concentration for hydrogels.It is proved that the present developed chemo-mechanical coupling finite element procedure can be utilized to model the coupling behavior of hydrogels effectively.

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.

An explicit finite element method for dynamic analysis in three-medium coupling system and its application

In this paper, an explicit finite element method to analyze the dynamic responses of three-medium coupled systems with any terrain is developed on the basis of the numerical simulation of the continuous conditions on the bounda-ries among fluid saturated porous medium, elastic single-phase medium and ideal fluid medium. This method is a very effective one with the characteristic of high calculating speed and small memory needed because the formulae for this explicit finite element method have the characteristic of decoupling, and which does not need to solve sys-tem of linear equations. The method is applied to analyze the dynamic response of a reservoir with considering the dynamic interactions among water, dam, sediment and basement rock. The vertical displacement at the top point of the dam is calculated and some conclusions are given.

Static Analysis of Buried Pipes Using Coupling between Layerwise Finite Element and Boundary Element Method

This work deals with the analysis of soil-structure interaction modeling of pipeline problems in static behavior using the coupling between FEM （finite element method） and BEM （boundary element method）. The representation of the pipe is made by MEF using one fmite element in the cylindrical panel formulated from the theory of equivalent discrete layers （Layerwise theory）, proposed by J. N. Reddy. The soil is represented by elastic continum infimite or semi-infinite and modeled using boundary elements with special curved surface, associated with cylindrical panel used to represent the soil-structure interaction within the soil, especially at the contact surface with the pipe.

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.

Numerical analysis of coupled finite element with element-free Galerkin in sheet flexible-die forming

A numerical method for coupled deformation between sheet metal and flexible-die was proposed. Based on the updated Lagrangian （UL） formulation, the elastoplastic deformation of sheet metal was analyzed with finite element method （FEM） and the bulk deformation of flexible-die was analyzed with element-free Galerkin method （EFGM）. The frictional contact between sheet metal and flexible-die was treated by the penalty function method. The sheet elastic flexible-die bulging process was analyzed with the FEM-EFGM program for coupled deformation between sheet metal and bulk flexible-die, called CDSB-FEM-EFGM for short. Compared with finite element code DEFORM-2D and experiment results, the CDSB-FEM-EFGM program is feasible. This method provides a suitable numerical method to analyze sheet flexible-die forming.

COUPLED SIMULATION OF 3D ELECTRO-MAGNETO-FLOW FIELD IN HALL-HEROULT CELLS USING FINITE ELEMENT METHOD

Two full 3D steady mathematical models are developed by finite element method （FEM） to calcalate coupled physics fields. the electro-magnetic model is built and solved first and so is the fluid motion model with the acquired electromagnetic force as source body forces in Navier-Stokes equations. Effects caused by the ferromagnetic shell, busbar system around, and open boundary problem as well as inside induced current were considered in terms of the magnetic field. Furthermore, a new modeling method is found to set up solid models and then mesh them entirely with so-called structuralized grids, namely hex-mesh. Examples of 75kA prebaked cell with two kinds of busbar arrangements are presented. Results agree with those disclosed in the literature and confirm that the coupled simulation is valid. It is also concluded that the usage of these models facilitates the consistent analysis of the electric field to magnetic field and then flow motion to the greater extent, local distributions of current density and magnetic flux density are very much dependent on the cell structure, the steel shell is a shield to reduce the magnetic field and flow pattern is two dimensional in the main body of the metal pad.