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.

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.

THE COUPLING METHOD OF FINITE ELEMENTS AND BOUNDARY ELEMENTS FOR RADIATION PROBLEM

The paper presents the variational formulation and well posedness of the coupling method offinite elements and boundary elements for radiation problem. The convergence and optimal errorestimate for the approximate solution and numerical experiment are provided.

COUPLING OF FINITE ELEMENT AND BOUNDARY ELEMENT METHODS FOR THE SCATTERING BY PERIODIC CHIRAL STRUCTURES

Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R^3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and nonhomogeneous. In this paper, variational formulations coupling finite element methods in the chiral medium with a method of integral equations on the periodic interfaces are studied. The well-posedness of the continuous and discretized problems is established. Uniform convergence for the coupling variational approximations of the model problem is obtained.

MULTIGRID ALGORITHM FOR THE COUPLING SYSTEM OF NATURAL BOUNDARY ELEMENT METHOD AND FINITE ELEMENT METHOD FOR UNBOUNDED DOMAIN PROBLEMS

In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.

THE COUPLING METHOD FOR TORSION PROBLEM OF THE SQUARE CROSS-SECTION BAR WITH CRACKS

By coupling natural boundary element method (NBEM) with FEM based on domain decomposition, the torsion problem of the square cross-sections bar with cracks have been studied, the stresses of the nodes of the cross-sections and the stress intensity factors have been calculated, and some distribution pictures of the stresses have been drawn. During computing, the effect of the relaxed factors to the convergence speed of the iterative method has been discussed. The results of the computation have confirmed the advantages of the NBEM and its coupling with the FEM.

Time-domain Finite Element Method for Transient Electric Field and Transient Charge Density on Dielectric Interface

This paper is devoted to solving the transient electric field and transient charge density on the dielectric interface under the electroquasistatic(EQS)field conditions with high accuracy.The proposed method is suitable for both 2-D and 3-D applications.Firstly,the governing equations represented by scalar electric potential are discretized by the nodal finite element method(FEM)in space and the finite difference method in time.Secondly,the transient constrained electric field equation on the boundary(TCEFEB)is derived to calculate the normal component of the transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface.Finally,a 2-D numerical example is employed to demonstrate the validity of the proposed method.Furthermore,the comparisons of the numerical accuracy of the proposed method in this paper with the existing FEMs for electric field intensity and charge density on the dielectric interface are conducted.The results show that the numerical accuracy of the proposed method for calculating the normal component of transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface is close to that of nodal electric potential and an order of magnitude higher than those of existing FEMs.

Application of semi-analytical finite element method coupled with infinite element for analysis of asphalt pavement structural response

A specific computational program SAFEM was developed based on semi-analytical finite element （FE） method for analysis of asphalt pavement structural responses under static loads. The reliability and efficiency of this FE program was proved by comparison with the general commercial FE software ABAQUS. In order to further reduce the computational time without decrease of the accuracy, the infinite element was added to this program. The results of the finite-infinite element coupling analysis were compared with those of finite element analysis derived from the verified FE program, The study shows that finite-infinite element coupling analysis has higher reliability and efficiency.

Methodology for Comparing Coupling Algorithms for Fluid-Structure Interaction Problems

The multi-physics simulation of coupled fluid-structure interaction problems, with disjoint fluid and solid domains, requires one to choose a method for enforcing the fluid-structure coupling at the interface between solid and fluid. While it is common knowledge that the choice of coupling technique can be very problem dependent, there exists no satisfactory coupling comparison methodology that allows for conclusions to be drawn with respect to the comparison of computational cost and solution accuracy for a given scenario. In this work, we develop a computational framework where all aspects of the computation can be held constant, save for the method in which the coupled nature of the fluid-structure equations is enforced. To enable a fair comparison of coupling methods, all simulations presented in this work are implemented within a single numerical framework within the deal.ii [1] finite element library. We have chosen the two-dimensional benchmark test problem of Turek and Hron [2] as an example to examine the relative accuracy of the coupling methods studied;however, the comparison technique is equally applicable to more complex problems. We show that for the specific case considered herein the monolithic approach outperforms partitioned and quasi-direct methods;however, this result is problem dependent and we discuss computational and modeling aspects which may affect other comparison studies.

Improved Simulation Method for Soil-Geogrid Interaction of Reinforced Earth Structure in FEM

The interaction between geogrid and soil is crucial for the stability of geogrid-reinforced earth structure. In finite element （FE） analysis, geogrids are usually assumed as beam or truss elements, and the interaction between geogrid and soil is considered as Coulomb friction resistance, which cannot reflect the true stress and displacement developed in the reinlbrcement. And the traditional Lagrangian elements used to simulate soil always become highly distorted and lose accuracy in high-stress blocks. An improved geogrid model that can produce shear resistance and passive resistance and a soil model using the Eulerian technique, in combination with the coupled Eulerian-Lagrangian （CEL） method, are used to analyze the interaction between geogrid and soil of reinforced foundation test in ABAQUS. The stress in the backfill, resistance of geogrid, and settlement of foundation were computed and the results of analysis agree well with the experimental results. This simulation method is of referential value for FE analysis of reinforced earth structure.

Coupled BEM-FEM Analysis of the Large-Diameter Cylinder Structure System

A method of coupled BEM-FEM analysis for the elastic spatial structure system is presented. It can be applied to the calculation of the stress and deformation of the large-diamater cylinder structure system and it is suitable for symmetric or non-symmetric structures under the distributed or concentrated load. Numerical examples show that the proposed method and computer program BEFEM are quite efficient in the analysis of the large-diameter cylinder structure problems in ocean engineering.

Cavity noise sensitivity analysis of tire contour design factors and application of contour optimization methodology

Cavity resonance noise of passenger car tires is generated by interacting excitation between a tire structure and the fill gas (air), and generally lies in a frequency range of 200?250 Hz. As such, this noise is strongly perceived and may be a serious source of driver annoyance. Thus, many studies regarding the cavity noise mechanism and its reduction have already been conducted. In this work, a vibro-acoustic coupled analysis was conducted between a tire structure and air cavity. Using this analysis, we can more accurately simulate the tire noise performance in the region of the cavity resonance frequency. An analysis of the effects of variation of tire contour design factors was conducted, using design-of-experiments methods. Finally, a multi-objective optimization was performed using in-house codes to reduce the cavity noise level while minimizing the loss of other performances, such as diminished ride comfort and handling caused by the variations of contour. As a result of this optimization, an optimized contour shape was derived, which satisfied the multi-objective performances.

DYNAMIC RESPONSE OF UNDERGROUND STRUCTURES BY TIME DOMAIN SBEM AND SFEM

The dynamic interaction problems of three-dimensional lineqr elastic structures with arbitrary shaped section embedded in a homogeneous, isotropic and linear elastic half space under dynamic disturbances are numerically solved. The numerical method employed is a combination of the time domain semi-analytical boundary element method (SBEM) used for the semi-infinite soil medium and the semi-analytical finite element method (SFEM) used for the three-dimensional structure. The two methods are combined through equilibrium and compatibility conditions at the soil-structure interface. Displacements, velocities, accelerations and interaction forces at the interface between underground structure and soil medium produced by the diffraction of wave by an underground structure for every time step are obtained. In dynamic soil-structure interaction problems, it is advantageous to combine the SBEM and the SFEM in an effort to produce an optimum numerical hybrid scheme which is characterized by the main advantages of the two methods. The effects of the thickness, the ratio of length and diameter of underground structure and the soil medium on dynamic responses are discussed.

Numerical Simulation on the Resistance Performance of Ice-Going Container Ship Under Brash Ice Conditions

Ice resistance prediction is a critical issue in the preliminary design of ships navigating brash ice conditions, which is closely related to the safety of a ship to navigate encounter brash ice, and has significant effects on the kinds of propellers and motor power needed. In research on this topic, model tests and full-scale tests on ships have thus far been the primary approaches. In recent years, the application of the finite element method(FEM) has also attracted interest. Some researchers have conducted numerical simulations on ship–ice interactions using the fluid–structure interaction(FSI) method. This study used this method to predict and analyze the resistance of an ice-going ship, and compared the results with those of model ship tests conducted in a towing tank with synthetic ice to discuss the feasibility of the FEM. A numerical simulation and experimental methods were used to predict the brash ice resistance of an ice-going container ship model in a condition with three concentrations of brash ice(60%, 80%, and 90%). A comparison of the results yielded satisfactory agreement between the numerical simulation and the experiments in terms of both observed phenomena and resistance values, indicating that the proposed numerical simulation has significant potential for use in related studies in the future.

Transient Hydroelastic Response of VLFS by FEM with Impedance Boundary Conditions in Time Domain

A time-dependent finite element method (FEM) is developed to analyze the transient hydroelastic responses of very large floating structures (VLFS) subjected to dynamic loads. The hydrodynamic problem is formulated based on the linear theory of fluid and the structural response is analyzed based on the thin plate theory. The FEM truncates the unbounded fluid domain by introducing an artificial boundary surface, thus defining a finite computational domain. At this boundary surface an impedance boundary conditions are applied so that no wave reflections occur. In the proposed scheme, all of the procedures are processed directly in time domain, which is efficient for nonlinear analyses of structure floating on unbounded fluid. Numerical results indicate acceptable accuracy of the proposed method.

Simulation of the Whole Process of Ship-Bridge Collision

The simulation of the whole ship-bridge collision process can be effectively carried out by nonlinear dynamic finite element method. Based on the simple description of the theory, a scenario of a 40000 DWT oil tanker colliding with a bridge across the Yangtze River is designed for simulation. The technology of structure modeling and the determination of related parameters are introduced. The deformation of the bulb bow, the history,of collision force change, the exchange of collision energy and the stress distribution. of the bridge pier-are described in detail, which: are of great value to bridge design and bridge pier damage estimation. mechanical characters in the process of ship-bridge collision are described. More accurate results can be produced by finite element method than that by empirical formulas and simplified analytical methods.

An Integrated Structural Strength Analysis Method for Spar Type Floating Wind Turbine

An integrated structural strength analysis method for a Spar type floating wind turbine is proposed in this paper,and technical issues related to turbine structure modeling and stress combination are also addressed.The NREL-5MW ＂Hywind＂ Spar type wind turbine is adopted as study object.Time-domain dynamic coupled simulations are performed by a fully-coupled aero-hydro-servo-elastic tool,FAST,on the purpose of obtaining the dynamic characteristics of the floating wind turbine,and determining parameters for design load cases of finite element calculation.Then design load cases are identified,and finite element analyses are performed for these design load cases.The structural stresses due to wave-induced loads and wind-induced loads are calculated,and then combined to assess the structural strength of the floating wind turbine.The feasibility of the proposed structural strength analysis method for floating wind turbines is then validated.

Numerical Approximation of Port-Hamiltonian Systems for Hyperbolic or Parabolic PDEs with Boundary Control

We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.

A Kinematic Thermal Model for Descending Slabs with Velocity Boundary Layers

Kinematic models compute the temperature distribution by prescribing a constant convergent velocity for the subducting slab,resulting in an artificial velocity discontinuity,which may accelerate the heating of subducting slabs.For the purpose to moderate the influence of such artificial discontinuity, we construct a 2D thermal model for subduction zones with a velocity boundary layer,within which the velocities decrease linearly with the distance from the interfaces of slabs.Temperatures are calculated

Adaptive mesh refinement immersed boundary method for simulations of laminar flows past a moving thin elastic structure

One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions,especially for flows past a stationary thin elastic structure where large deformations occur.High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body.Hence,in this work,an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses.In this algorithm,adaptive mesh refinement(AMR)is integrated with immersed boundary finite element method(IBFEM)with two-stage pressure-velocity corrections.Despite successive interpolation of the flow field by IBM,the governing equations were solved using a fixed structured mesh,which significantly reduces the computational time associated with mesh reconstruction.The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface.AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface.The AMR-IBFEM algorithm is first verified by comparing the drag coefficient,lift coefficient,and Strouhal number for a benchmark case(laminar flow past a circular cylinder at Re=100)and the results showed good agreement with those of other researchers.The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction.The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian(ALE)algorithm for elastic thin boundaries.It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy(error of-0.02%)with only-1%of the computational time for simulations with full mesh refinement.