Hybrid Finite Element-boundary Element Method Research Articles

Experimental and numerical investigation on the vibro-acoustic characteristics of periodic rib stiffened plate based on band gap theory

This study presents a novel method for analyzing the vibration and noise from the periodic rib stiffened plate (PRSP). For the first time, the band gap theory was combined with hybrid finite element-boundary element method (FE-BEM) to predict the vibro-acoustic characteristics of this structure and guide its vibration and noise reduction design from the perspective of bending wave propagation. The excitation test was carried out simultaneously to verify the rationality and accuracy of the proposed method. Then, the acoustic contribution analysis was conducted and the influence of structural design parameters on bending wave bandgap and noise reduction effect was discussed in detail. The results show that there are alternating passbands and stopbands for bending waves propagating in PRSP, making the vibro-acoustic responses in different frequency bands exhibit distinct differences as well. Increasing the base plate thickness and decreasing the rib spacing are conducive to widen the bandgaps and reduce the noise radiation, which are the decisive factors affecting the vibro-acoustic characteristics of PRSP. While the rib thickness has little effect, this provides a new approach for vibration mitigation and acoustic optimization in steel bridges.

Interval and subinterval perturbation finite element-boundary element method for low-frequency uncertain analysis of structural-acoustic systems

Uncertainties exist widely in the structural-acoustic systems, due to the physical imperfections, model inaccuracies and system complexities. To deal with the uncertainties, the interval perturbation and subinterval perturbation techniques, for the first time, are extended and integrated into the hybrid finite element-boundary element method (IPFEM/BEM) in this work. Firstly, the structural part of structural-acoustic systems is modeled using finite element method (FEM) and acoustic cavity is modeled by boundary element method (BEM). Then the interval perturbation technique is introduced to establish the interval perturbation equations of the system. For large uncertainty levels, the interval of parameters is divided into smaller sub-intervals to improve the accuracy of proposed IPFEM/BEM (sub-interval perturbation finite element-boundary element method, SIPFEM/BEM). The proposed IPFEM/BEM and SIPFEM/BEM are verified by two numerical examples. The results obtained by IPFEM/BEM, SIPFEM/BEM and Monte-Carlo method are compared. It is found that IPFEM/BEM and SIPFEM/BEM is reliable for the frequency response analysis of structural-acoustic systems with small or large uncertain levels.

Extracting energy while reducing hydroelastic responses of VLFS using a modular raft wec-type attachment

This paper presents the use of a modular raft Wave Energy Converter (WEC)-type attachment at the fore edge of a rectangular Very Large Floating Structure (VLFS) for extracting wave energy while reducing hydroelastic responses of the VLFS under wave action. The proposed modular attachment comprises multiple independent auxiliary pontoons (i.e. modules) that are connected to the fore edge of the VLFS with hinges and linear Power Take-Off (PTO) systems. For the hydroelastic analysis, the auxiliary pontoons and the VLFS are modelled by using the Mindlin plate theory while the linear wave theory is used for modelling the fluid motion. The analysis is performed in the frequency domain using the hybrid Finite Element-Boundary Element (FE-BE) method. Parametric studies are carried out to investigate the effects of pontoon length, PTO damping coefficient, gap between auxiliary pontoons, and incident wave angle on the power capture factor as well as reductions in the hydroelastic responses of the VLFS with the modular attachment. It is found that in oblique waves, the modular attachment comprising multiple narrow pontoons outperforms the corresponding rigid attachment that consists of a single wide pontoon with respect to the power capture factor and the reduction in the deflection of the VLFS. In addition, it is possible to have a considerable gap between pontoons without significantly compromising the effectiveness of the modular attachment.

Oblique Wave-Induced Responses of A VLFS Edged with A Pair of Inclined Perforated Plates

This paper is concerned with the hydroelastic responses of a mat-like, rectangular very large floating structure (VLFS) edged with a pair of horizontal/inclined perforated anti-motion plates in the context of the direct coupling method. The updated Lagrangian formulae are applied to establish the equilibrium equations of the VLFS and the total potential formula is employed for fluids in the numerical model including the viscous effect of the perforated plates through the Darcy’s law. The hybrid finite element-boundary element (FE-BE) method is implemented to determine the response reduction of VLFS with attached perforated plates under various oblique incident waves. Also, the numerical solutions are validated against a series of experimental tests. The effectiveness of the attached perforated plates in reducing the deflections of the VLFS can be significantly improved by selecting the proper design parameters such as the porous parameter, submergence depth, plate width and inclination angle for the given sea conditions.

Nonlinear analysis for ship-generated waves interaction with mooring line/riser systems

A time-domain hybrid finite element-boundary element (FE-BE) method is developed to investigate nonlinear interaction between ship waves and slender structures. The ship waves are modeled in the context of the three-dimensional potential theory including ship steady state motion, and the velocity potential are computed using a higher-order boundary element method (HOBEM). A special global coordinate-based FEM rod model, when using catenary solution as an initial static profile, is employed in the accurate analysis of slender structures. The internal flow is incorporated in the numerical model by adding a new term to the effective tension formulation while both the seabed support and friction effect are performed by using a nonlinear quadratic spring and a Coulomb friction model. The numerical model is verified with the published experimental and numerical results for the ship waves generation and dynamic responses of mooring line/riser. Numerical simulations are executed to determine the dynamic behavior of two example slender structures such as multi-component mooring line and deepwater steel catenary riser under ship waves. Then the coupled analysis program is applied for a truss Spar with its mooring lines subjected to ship waves, wind-generated waves and their combined action, respectively. The dependence of the top node tensions of the slender structures on ship path, ship speed, ship distance, internal flow and seabed friction, is also examined.

Large-Scale Eddy-Current Analysis of Conductive Frame of Large-Capacity Inverter by Hybrid Finite Element-Boundary Element Method

This paper reports a large-scale eddy-current analysis of conductive frame of large-capacity inverter. The eddy-current loss obtained by the electromagnetic field analysis is used as a heat source for the thermal analysis. Then, the suitable configuration of the frame for the suppression of temperature increase is investigated and designed. The hybrid finite-element and boundary-element (FE-BE) method is very suitable for the analysis of a complicated-shaped frame because it does not require mesh division for a free space and can easily treat eddy current. For the reduction of large computational costs, the fast multipole method (FMM) is introduced. Furthermore, in order to improve the convergence characteristic of iterative methods for system matrix, we develop the application of the IDR(s) method to the minor iterative preconditioning technique (MIP) and evaluate the performance. Finally, some numerical results that demonstrate the effectiveness of the developed method are presented.

積層鉄芯ベンチマークモデルの提案とその高精度磁界解析

This paper describes a benchmark model proposed for the clarification of the characteristic of various methods for modeling the laminated iron core. In order to obtain a reference solution of the benchmark model, a large-scale nonlinear magnetostatic field analysis with a fine mesh enough to represent the microscopic structure of the laminated iron core is carried out by using the hybrid finite element-boundary element (FE-BE) method combined with the fast multipole method (FMM) based on diagonal forms for translation operators. The computational costs and accuracy of two kinds of the homogenization methods are discussed comparing the reference solution. As a consequence, it is verified that the homogenization methods can analyze magnetic fields in laminated iron core within acceptable computational costs.

Erratum

Correction to: "Large-Scale Analysis of Eddy-Current Problems by the Hybrid Finite Element-Boundary Element Method Combined With the Fast Multipole Method"

Large-scale analysis of eddy-current problems by the hybrid finite element-boundary element method combined with the fast multipole method

This paper shows large-scale eddy-current analysis by a hybrid finite-element and boundary-element (FE-BE) method. We introduce the fast multipole method (FMM) into the two kinds of hybrid FE-BE formulations developed by ourselves. To achieve more reduction of CPU time, we propose a novel preconditioning technique suitable for the hybrid FE-BE methods with the FMM. Furthermore, we improve the FMM calculation process in the hybrid method using magnetic field intensity. Some numerical results that demonstrate the effectiveness of these approaches are also presented

Transient analysis of thin layers for the magnetic field shielding

The thin layer technique is extended to the analysis of passive shields for the mitigation of pulsed magnetic fields. The interface conditions between the two sides of the shell are determined by discretizing the diffusion equation along the shell thickness. The proposed formulation is validated by comparison with a standard hybrid finite element-boundary element method solution. Finally, some applications on problems related to industrial and laboratory environments are presented

Large-scale Magnetic Field Analysis by the Hybrid Finite Element-Boundary Element Method Combined with the Fast Multipole Method

This paper describes large-scale magnetic field analysis by means of the hybrid finite element-boundary element (FE-BE) method. The FE-BE method is well-suited for solving open electromagnetic field problems that comprise movement, non-linear media and eddy current. In general, however, large memory and computational costs are required due to the dense blocks in the system matrix generated by the BE part of the hybrid formulation. To overcome the above difficulties, we introduce the fast multipole method (FMM) to the FE-BE formulation developed by ourselves. Furthermore, we propose a novel preconditioning technique suitable for the hybrid FE-BE method with the FMM. Some numerical results that demonstrate the effectiveness of the proposed approach are also presented.

Preconditioned iterative solvers for complex and unsymmetric systems of equations resulting from the hybrid FE-BE method

A complex and unsymmetric system of equations has to be solved when the hybrid finite element/boundary element (FE-BE) method is applied to harmonic eddy currents. In this paper the performance of preconditioned iterative solvers for complex and unsymmetric systems of equations are numerically investigated. It is significant to adopt an incomplete LU decomposition preconditioner of a higher fill-in level to accelerate the convergence rate. For nonlinear problems it is suggested to use a symbolic decomposition in preconditioning for a further performance improvement.

A hybrid finite element-boundary element method for the analysis of diffractive elements

Abstract We apply a two-dimensional hybrid finite element-boundary element method to the analysis of diffractive optical elements (DOEs). We use the finite element method to solve Helmholtz's equation in the interior of a DOE and use the boundary element method, a Green's function approach, to determine the fields exterior to the DOE. We couple the two methods at the DOE surface by enforcing field continuity conditions. We validate our implementation by comparing its results to the analytic solution for diffraction from a dielectric cylinder and to the scalar solution for far-field diffraction from a dielectric slab. We use the hybrid method to analyse the diffraction from an eight-level phase lens and a binary-phase lens that has subwavelength features.

A hybrid finite element-boundary element method for the analysis of diffractive elements

Abstract We apply a two-dimensional hybrid finite element-boundary element method to the analysis of diffractive optical elements (DOEs). We use the finite element method to solve Helmholtz's equation in the interior of a DOE and use the boundary element method, a Green's function approach, to determine the fields exterior to the DOE. We couple the two methods at the DOE surface by enforcing field continuity conditions. We validate our implementation by comparing its results to the analytic solution for diffraction from a dielectric cylinder and to the scalar solution for far-field diffraction from a dielectric slab. We use the hybrid method to analyse the diffraction from an eight-level phase lens and a binary-phase lens that has subwavelength features.

Iterative hybrid finite element-boundary element method for the analysis of induction heating system with nonlinear charge

The iterative hybrid finite element-boundary element method is applied for the analysis of induction heating systems with rotational symmetry in unbounded free space. A mathematical boundary is defined arbitrarily in free space to enclose the system. The finite elements formulation is applied for the interior region and the boundary integral formulation is applied on the boundary using the response function excited by a circular line current. A quasistatic magnetic field problem is solved in terms of the magnetic vector potential. A ferromagnetic charge of nonlinear magnetic properties is considered. An iterative technique is used to correct the permeability values and the effect of nonlinearity is calculated. The accuracy of the method is verified with measurements of practical induction heating systems.

Hybrid finite element-boundary element method for nonlinear electromagnetic problems

The paper deals with the application of the hybrid finite element-boundary element method in the computation of linear and nonlinear magnetostatic field with a vector potential for 2D and with a scalar potential for 3D problems. The nonlinear part of the domain is solved by finite elements, while in the linear part of the domain, the boundary elements are used. Different boundary formulations are developed to overcome the coupling problems. "Mixed" boundary elements are coupled with linear finite elements, for both 2D and 3D problems. Typical examples are presented: electrical motor and the IEEJ model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of Composite Materials by a Hybrid FE-BE Method.

The hybrid finite element-boundary element method was applied to solve the two dimensional problem of composite materials. The method combines the differential and integral approaches and gives specific advantages to analyze the system which includes different materials. In this paper, the base matrix of the composite material was modeled using the boundary element method, while the fibers imbedded in the matrix were represented using the finite-element method. Two-dimensional elastic problems were solved to demonstrate the effectiveness of this method in the analysis of composite materials. It was shown that the solutions with high accuracy can be obtained by the hybrid FE-BE method using far smaller degrees of freedoms compared with the finite-element method.

Efficient vectorial hybrid FE-BE method for electromagnetic scattering problem

In this paper block circulant boundary meshes are introduced to 3-dimensional electromagnetic scattering problem to overcome the excessive storage requirement of the hybrid finite element-boundary element method. In addition, edge elements are incorporated for this vectorial hybrid method. This boundary mesh makes use of axi-symmetry to produce block circulant boundary element matrices, and results in up to 64-fold reduction in matrix storage. To demonstrate its efficiency this hybrid scheme is applied to a time-harmonic electromagnetic scattering from a double-layered dielectric sphere.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The calculation of the impedance of an induction plasma installation by a hybrid finite-element boundary-element method

A hybrid finite-element, boundary-element (FE-BE) analysis in a RF induction plasma is developed to predict the current distribution in an inductor and a plasma and to calculate the impedance of an entire installation. The electromagnetic and heat transfer equations are solved by the FE method inside the plasma, and the BE method is used to calculate the boundary conditions. To preserve the sparse and positive definite matrix structure of the FE method, an iterative algorithm is used to solve the coupled matrix equations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Regular polyhedra for storage efficient hybrid FE-BE method

Boundary meshes using regular polyhedra are devised to reduce storage requirements in hybrid FE-BE (finite-element-boundary-element) analysis in three dimensions. Storage reduction rates of the boundary matrix are investigated for five regular polyhedral meshes. The boundary meshes make use of the symmetry of regular polyhedra and reduce storage requirements of the boundary element matrices up to a factor of 90 in the case of a dodecahedron, which may be enough to secure an advantage over the pure element approach. Impedance/admittance matrices also have the same storage reduction, and may be precalculated to form a database for later use. To demonstrate its efficiency, a magnetostatic problem is solved using this dodecahedral mesh and compared with its exact solution. >