Boundary Element Software Research Articles

Sound power from coupled structures using elementary radiators

Sound power measurements are of interest in numerous applications, and several methods are available for obtaining the sound power of a system. A recent method that has been developed, referred to as the Vibration-Based Sound Power (VBSP) method, utilizes vibration measurements obtained from a Scanning Laser Doppler Vibrometer (SLDV). The VBSP method has previously been used to obtain the sound power radiated from flat plates, cylindrical shells and curved plates. This paper will present further developments to extend VBSP measurements to multiple coupled structures and investigate the acoustic coupling effects that may exist. Two coplanar flat plates separated by a distance d were modeled using the boundary element method. The sound power was determined within the boundary element software and the structural velocities were also exported and processed using the VBSP method. Computational and experimental results will be shown to demonstrate abilities and limitations for the VBSP method to accurately determine the radiated sound power for coupled structures. [Funding for this work was provided by the National Science Foundation (NSF).]

Stress analysis of composites with interfacial bridged cracks and damaged zones

Stress analysis of composite structures with bridged cracks and damaged zones is performed with the direct boundary integral equations method in axisymmetric formulation. It is assumed that: a) the crack faces interact in some zones behind of the cracks edges (bridged zones); b) these zones width can be comparable to the whole crack size; c) adjacent parts of the structure can be connected by mechanical ligaments (including interfaces ahead of cracks fronts) and the relative displacements of these parts can occur under the loading (these zones consider as damaged zones). The boundary element software to solve axisymmetric problems of elasticity with interfacial bridged cracks and damaged zones was developed. The results for different properties of composite materials and bonds are presented. Applications the bridged crack approach to modeling of cracks self-healing is remarked.

Accelerated Calderón preconditioning for Maxwell transmission problems

We investigate a range of techniques for the acceleration of Calderón (operator) preconditioning in the context of boundary integral equation methods for electromagnetic transmission problems. Our objective is to mitigate as far as possible the high computational cost of the barycentrically-refined meshes necessary for the stable discretisation of operator products. Our focus is on the well-known PMCHWT formulation, but the techniques we introduce can be applied generically. By using barycentric meshes only for the preconditioner and not for the original boundary integral operator, we achieve significant reductions in computational cost by (i) using “reduced” Calderón preconditioners obtained by discarding constituent boundary integral operators that are not essential for regularisation, and (ii) adopting a “bi-parametric” approach [1,2] in which we use a lower quality (cheaper) H-matrix assembly routine for the preconditioner than for the original operator, including a novel approach of discarding far-field interactions in the preconditioner. Using the boundary element software Bempp (www.bempp.com), we compare the performance of different combinations of these techniques in the context of scattering by multiple dielectric particles. Applying our accelerated implementation to 3D electromagnetic scattering by an aggregate consisting of 8 monomer ice crystals of overall diameter 1 cm at 664 GHz leads to a 99% reduction in memory cost and at least a 75% reduction in total computation time compared to a non-accelerated implementation.

BESLE: Boundary element software for 3D linear elasticity

BESLE is the first available parallel open-source code to analyse the mechanical behaviour of heterogeneous materials using the boundary element method (BEM) in 3D and in both an elastostatic and elastodynamic setting. Unlike all the other codes that are presently available, the software presented here is capable of simulating both isotropic and anisotropic materials comprised of single or multiple domains. Furthermore, the user-interface has been designed to provide a convenient way for configuring simulations involving many complex material constituents. Results are described by the displacement and traction fields, also, the stress and strain tensors are available for post-processing. BESLE is largely implemented in Fortran-MPI, but some of the sub-packages are based on other languages such as C and C++, and as such a the software is best used on a multi-core architecture where the parallelisation can be fully exploited. The main features and functionality of BESLE are presented here, and the User's Guide, available from the repository listed below, gives further details and outlines how users can carry out bespoke simulations. Program summaryProgram Title: BESLECPC Library link to program files:https://doi.org/10.17632/vx4vg47hzg.1Developer's repository link:https://github.com/Afgr1087/BESLE_v1.0.gitLicensing provisions: GPL-v3.0Programming language: Fortran 90, C++/CExternal libraries: LAPACK [1], BLAS [2], SCOTCH [3], ScaLAPACK [4], MUMPS [5], Voro++ [6], Triangle [7]Nature of problem: The solution of 3D elasticity models of heterogeneous materials is often arduous owing to the complexity of the underlying system of partial differential equations. Some analyses that require intensive computation are solids under quasi-static, inertial, and high-rate loading (all of which are treated by BESLE).Solution method: BESLE provides a strategy to configure and solve complex problems of 3D heterogeneous solids using the elastostatic and elastodynamic formulations of the boundary element method (BEM). Moreover, it provides flexible means create surface meshes, to impose both Neumann and Dirichlet boundary conditions, and comes with a material database for fast parameterisation. It allows large scale problems to be treated in a straightforward framework. The mechanical behaviour of isotropic and anisotropic bodies which can include several domains, each comprised of heterogeneous materials with a diverse range of constitutive properties and complex morphologies, is feasibly analysed.Additional comments including restrictions and unusual features: Fortran is limited in the size of arrays that can be allocated. Thus, for very large problems the number of degrees of freedom in the discretised system can exceed that allowed in Fortran, even if the machine has a large amount of RAM. To avoid over-allocation we have added functionality to check whether BESLE, and it's underlying Fortran code, will be able to handle the requisite number of degrees of freedom in advance of a calculation being executed. In the event that this limitation will be approached, BESLE will return an error message advising that the number of entries required will exceed 70% of the limit imposed by Fortran.

Analysis and Research on the Influence of Sonar Dome on Ship’s Underwater Electrostatic Field

This paper firstly analyzes the influence of the sonar dome on the ship’s underwater electrostatic field in theory, and then uses boundary element software to simulate and analyze this kind of influence. It is found that the sonar dome can be used as a cathode to participate in the electrochemical corrosion of ships, forming a “propeller-hull-sonar dome” corrosion system. In this case, the “dubble compensation anode” method is proposed in order to control the electric field signature, and the effectiveness of this method is verified by the boundary element simulation software.

A new magnetic modeling method for magnetic levitation rotary table

Precision machining fields require the worktable to have a large-scale multi-degree-of-freedom motion capability. In order to provide a more accurate magnetic model for the control strategy decoupling process and the size parameter optimization design process of the maglev rotary table. This paper proposes a new magnetic modeling method based on the Two-Dimensional Harmonic method. Different from the existing harmonic method, this method simultaneously considers the tangential and radial magnetic field changes of circumferential magnetic array. And it eliminates the edge effect of the magnetic flux density distribution in the radial aperiodic direction. The magnetic force and torque are solved by the Lorenz integral formula and the Gaussian quadrature method. In order to verify the accuracy of the TDH method, the boundary element software RadiaTM is used for simulation, and a prototype is made for measurement. The experimental results shown that this method reduced the maximum error of the radial edge magnetic field from 104.19% to 3.29%. And it improved the calculation accuracy of magnetic force and torque by 60.74% and 84.39% respectively. This method does not rely on special example, and is beneficial to cross-platform applications. It is more suitable for realizing the magnetic modeling of the maglev rotary table with both rotational motion and large-stroke translational motion.

Optimization study of a catenary mooring system for a spar floating wind turbine based on its hydrodynamic responses

In this article, selecting an appropriate mooring system for the spar platform of a wind turbine consisting of chain–cable–chain is investigated based on a meta-heuristic method. A boundary element software is applied to hydrodynamics analysis, and the numerical results are verified by experimental results. According to the characteristics of the experimental mooring system, an appropriate chain is selected for the prototype model, and then a mooring system consisting of chain–cable–chain replaces the chain-based mooring system. Environmental forces have been applied by the conditions of the Caspian Sea. Analysis is done in time domain for irregular wave spectrum of Joint North Sea Wave Project. For the cable in the middle, seven lengths in the range of 30–210 m were considered. The simulations showed that in the cable length of 180 m, the structure exhibits a proper behavior. Also, in order to increase the reliability of the anchor, a portion of the initial chain was reduced and was added to the anchor chain; for this purpose, five different chain lengths from 25 to 65 m have been considered. The results show that for the heave, roll, pitch, and yaw degrees of freedom, the minimum structure oscillation happens in the length of 25 m, finally considering the proper behavior of the structure in the length of 25 m; this length of chain was added to the anchor chain.

Product Algebras for Galerkin Discretisations of Boundary Integral Operators and their Applications

Operator products occur naturally in a range of regularised boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp, we have implemented a complete operator algebra that depends on knowledge of the domain, range, and test space. The aim was to develop a way of working with Galerkin operators in boundary element software that is as close to working with the strong form on paper as possible, while hiding the complexities of Galerkin discretisations. In this article, we demonstrate the implementation of this operator algebra and show, using various Laplace and Helmholtz example problems, how it significantly simplifies the definition and solution of a wide range of typical boundary integral equation problems.

Semi-Analytical Solution of Magnetic Force and Torque for a Novel Magnetically Levitated Actuator in Rotary Table

This article proposes a fast and accurate semi-analytical calculation method of magnetic force and torque in the magnetically levitated rotary table. Benefited from the high computation efficiency and accuracy, the solution is suitable for the optimization and real-time control of the magnetically levitated system. Different with the existing harmonic method for modeling the magnetic field produced by the circular magnet array in the rotary table, the gaps in circular permanent magnet array are taken into account for the force and torque computation in this article. With the obtained magnetic flux density distribution, the magnetic force and torque can be acquired via the coordinate transformation and Lorenz integral law. Then, the numerical integral method is used to calculate the exact results of complex Lorentz integrals. Finally, the effectiveness and accuracy of the semi-analytical solution are verified by a boundary element software named Radia. Compared with the existing solutions, the new semi-analytical method is more accurate and suitable for the magnetically levitated actuator in the rotary table.

A New Multi-Objective Optimization Method of Magnetic Levitation Planar Motor

This paper proposes a fast and accurate electromagnetic optimization method for magnetic levitation planar motors (MLPMs). With the purpose of achieving the maximum force with the minimum power dissipation and cost, a multi-objective optimization is adopted for the MLPM. Furthermore, in order to improve the precision and reduce the computational burden, the levitation force expression in the objective function is analyzed through the numerical model. This model is built by the magnetic charge method and the Gaussian quadrature and implemented in parallel computation. According to the optimal objective, an intelligent optimization algorithm—particle swarm optimization (PSO)—is used to undertake the optimization variables of the planar motor for a global optimal solution. The precision and effectiveness of the proposed method are validated by both the finite-element method (FEM) commercial software COMSOL and a boundary element software program named Radia. The comparative results with other optimization methods are also presented to highlight the performance of the proposed optimization method.

Hydrodynamic Analysis of Partially Filled Liquid Tanks Subject to 3D Vehicular Manoeuvring

This paper is concerned with liquid sloshing in a partially filled container due to 3‐dimensional vehicle motion. The liquid sloshing is described by a set of linear modal equations derived from the potential flow theory, which can be applied to liquid sloshing induced by arbitrary combination of lateral, longitudinal, and rotational excitations. The sloshing force and moment are expressed with a set of hydrodynamic coefficients that are determined by the linear velocity potential. These coefficients can be precalculated and incorporated into the motion equations of the vehicle system so that a fully coupled vehicle‐sloshing model is available. In addition, we propose an approach to calculate the hydrodynamic coefficients using the outputs of commercial frequency‐domain boundary element software in order to maximize the efficiency of modelling and computation. The accuracy of the proposed model is examined by comparison with available CFD and model test data in the literature. The case of a road tanker encountering a road bump during acceleration/braking is investigated. Results show that the tank rotational motion will affect the amplitude and the sloshing force, and neglecting tank rotation may lead to underestimation of the sloshing force magnitude.

Calderón preconditioning of PMCHWT boundary integral equations for scattering by multiple absorbing dielectric particles

We consider the simulation of electromagnetic scattering by single and multiple isotropic homogeneous dielectric particles using boundary integral equations. Galerkin discretizations of the classical Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) boundary integral equation formulation provide accurate solutions for complex particle geometries, but are well-known to lead to ill-conditioned linear systems. In this paper we carry out an experimental investigation into the performance of Calderón preconditioning techniques for single and multiple absorbing obstacles, which involve a squaring of the PMCHWT operator to produce a well-conditioned second-kind formulation. For single-particle scattering configurations we find that Calderón preconditioning is actually often outperformed by simple “mass-matrix” preconditioning, i.e. working with the strong form of the discretized PMCHWT operator. In the case of scattering by multiple particles we find that a significant saving in computational cost can be obtained by performing block-diagonal Calderón preconditioning in which only the self-interaction blocks are preconditioned. Using the boundary element software library Bempp (www.bempp.com) the numerical performance of the different methods is compared for a range of wavenumbers, particle geometries and complex refractive indices relevant to the scattering of light by atmospheric ice crystals.

Three-dimensional BEM for transient dynamic analysis of piezoelectric and anisotropic elastic solids

A boundary element approach based on the Green's functions in integral representation and the convolution quadrature method is presented. Proposed approach is designed for analyzing 3D initial boundary-value problems of the dynamics of general anisotropic elastic and piezoelectric linear homogeneous solids with mixed boundary conditions. Numerical modelling of transient dynamics of elastic anisotropic and piezoelectric three-dimensional solids is carried out to demonstrate the potential of the developed boundary element software. Obtained solutions are compared with the corresponding FEM results and results of the dynamic experiment. A numerical technique based on the exact Laplace-domain boundary integral equations for the direct approach of 3D linear theories of anisotropic elasticity and piezoelectricity is employed. The BEM scheme is constructed using the collocation method and the convolution quadrature method in the form of a stepping method for numerical inversion of integral Laplace transform. Results of the stepped BE-modelling of the problems when a transient force is acting on 3D piezoelectric and anisotropic elastic homogeneous solids are presented.

A simple approach to the numerical simulation with trimmed CAD surfaces

In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its simplicity and ease of implementation into existing Finite Element (FEM) or Boundary Element (BEM) software. The method is first verified with classical test examples in structural mechanics. Then two practical applications are presented one using the FEM, the other the BEM, that show the applicability of the method.

The influence of manufacturing method on the running-in of gears

Striving for higher gear transmission efficiency by using a low-viscosity transmission lubricant affects the lubricant film thickness. To keep the Λ-ratio (the ratio between the film thickness and the surface roughness) intact, more effort must be put on the surface topography. This paper presents a study of how running-in affects the dry elastic contact area ratio in spur gears using real surface topographies from three common manufacturing methods (green-shaving, honing, and grinding). The test gears were manufactured in case-hardened steel, similar to 20MnCrS5. Surface topography measurements were used as input to a contact analysis boundary element software program. An important hypothesis used in this work is that the dry elastic contact area ratio, i.e. the ratio between real and nominal contact area, can be used as a measure of the contact conditions in gears. It is concluded that running-in differs significantly for the studied manufacturing methods and that the dry elastic contact area ratio gives a consistent description of these changes. The shaved gears have the highest dry elastic contact area ratio after running in, where the ground gears have the lowest dry elastic contact area ratio. The increase in dry elastic contact area ratio is about 30 per cent for the shaved gears, 12 per cent for the honed gears and less than 5 per cent for the ground gears. Extreme value parameters, such as Rp and Rz, showed relatively good correlation to dry elastic contact area ratio. However no genuine correlation could be found between dry elastic contact area ratio and two-dimensional (2D) surface roughness parameters. Furthermore, traditional gear metrology form parameters do not serve as a good measure on the changes occurring during the running-in.

A New Numerical Analysis for Cracks Emanating from a Surface Semi-Spherical Cavity in an Finite Elastic Body

Due to the stress concentration effect around the hole, cracks are likely to initiate at the hole under the action of fatigue loading. This paper is specifically concerned with cracks emanating from a surface semi-spherical cavity in a finite body by using the boundary element software FRANC3D developed by a fracture mechanics investigation group of Cor-nell University. The numerical results can reveal the effect of the geometry of the surface cavity on the stress intensity factors.

Perpendicular Recording with Reduced Skew Angle Sensitivity

A detailed analysis to the problem of skew angle sensitivity in perpendicular magnetic recording is presented. A proposed analytical model is supported by numerical simulations with a commercial boundary element software program. According to the presented equivalent magnetic circuit model, a single pole recording head with a laminated composition involving two layers of different magnetic materials could be used to localize adequately strong magnetic field in the vicinity of the trailing edge of the recording head. It is shown that the recording field generated under each lamination layer is proportion to the relative magnetic permeability of the respective layer. Such localization of the magnetic flux results in substantially reduced skew angle sensitivity.

A numerical analysis for cracks emanating from a surface semi-spherical cavity in an infinite elastic body by FRANC3D

This note is specifically concerned with cracks emanating from a surface semi-spherical cavity in an infinite body (see Fig. 1) by using the boundary element software FRANC3D developed by a fracture mechanics investigation group of Cornell University. The numerical results can reveal the effect of the geometry of the surface cavity on the stress intensity factors.

Hybrid numerical and analytical solutions for acoustic boundary problems in thermo-viscous fluids

The present work aims at contributing to the investigation of methods to solve some classes of problems of acoustic propagation in thermo-viscous fluids, in unbounded or bounded media. The focus here is on thermal and vortical diffusion at the boundaries, which have to be considered for an accurate description of the acoustic field in small fluid-filled cavities and ducts. Existing boundary element or finite element acoustic software does not include these phenomena, as they are not compatible with the basic equations involved. A methodology is given to solve such problems when using this software, introducing a hybrid method which combines both numerical solutions and analytical solutions (for the fields inside the boundary layers). A detailed application is presented to validate the process using a boundary elements method.

FEM and BEM in the context of information retrieval

Numerical techniques such as, first of all, the finite element and boundary element methods are frequently used today in research as well as in many industry applications. The output of finite element and boundary element literature and development of software, has been growing during last three decades. Today, it is almost impossible to be up-to-date with all the relevant information. At present, we have an excess of information––the term “information fatigue syndrome” will soon be a recognized medical condition. The author presents, by means of information from his database, the progress of both numerical techniques in their theoretical developments and practical usage for the period of last 30 years. The topics included: finite element and boundary element literature and software with emphasis on structural and solid mechanics. Some pointers for classical, printed, and for modern, on-line, information retrieval are given.