Boundary Element Research Articles

Experiments and FE Modeling on the Seismic Behavior of Partially Precast Steel-Reinforced Concrete Squat Walls

This paper proposed an innovative precast steel-reinforced concrete (PPSRC) squat wall to simplify on-site construction. In PPSRC squat shear walls, the hollowly precast RC wall panel can be assembled on-site through the pre-erected steel shapes, and the boundary cores will be filled using fresh concrete together with the slab system. The seismic performance of PPSRC squat walls, influenced by different construction techniques (cast-in-place vs. precast) and steel ratios, was examined through pseudo-static experiments on three specimens. Some key performance indicators, including hysteretic behavior, skeleton curves, stiffness degradation, energy dissipation, and load-carrying capacity, were analyzed in detail. The test results indicated that all the PPSRC squat walls failed in typical shear failure, and no significant slippage between the precast and fresh concrete sections was observed during the loading process, indicating that the composite action could be fully achieved via the novel throat connectors. In addition, the PPSRC squat walls could achieve comparable seismic performance compared with that of cast-in-place SRC shear walls (the peak load of the PPSRC squat wall only increased by 0.26% compared with the control specimen), and the load-carrying capacity and deformability could be enhanced by increasing the steel ratio in the boundary elements. Finally, an elaborate finite element model was developed and validated using ABAQUS software. The parametric analysis of the concrete strengths of precast and cast-in-place parts and the axial load was conducted further to investigate the seismic performance of PPSRC squat walls.

Improving EEG Forward Modeling Using High-Resolution Five-Layer BEM-FMM Head Models: Effect on Source Reconstruction Accuracy

Electroencephalographic (EEG) source localization is a fundamental tool for clinical diagnoses and brain-computer interfaces. We investigate the impact of model complexity on reconstruction accuracy by comparing the widely used three-layer boundary element method (BEM) as an inverse method against a five-layer BEM accelerated by the fast multipole method (BEM-FMM) and coupled with adaptive mesh refinement (AMR) as forward solver. Modern BEM-FMM with AMR can solve high-resolution multi-tissue models efficiently and accurately. We generated noiseless 256-channel EEG data from 15 subjects in the Connectome Young Adult dataset, using four anatomically relevant dipole positions, three conductivity sets, and two head segmentations; we mapped localization errors across the entire grey matter from 4,000 dipole positions. The average location error among our four selected dipoles is ∼5mm (±2mm) with an orientation error of ∼12∘ (±7∘). The average source localization error across the entire grey matter is ∼9mm (±4mm), with a tendency for smaller errors on the occipital lobe. Our findings indicate that while three-layer models are robust under noiseless conditions, substantial localization errors (10–20mm) are common. Therefore, models of five or more layers may be needed for accurate source reconstruction in critical applications involving noisy EEG data.

Time-dependent electromagnetic scattering from dispersive materials

Abstract This paper studies time-dependent electromagnetic scattering from obstacles that are described by dispersive material laws. We consider the numerical treatment of a scattering problem in which a dispersive material law, for a causal and passive homogeneous material, determines the wave–material interaction in the scatterer. The resulting problem is nonlocal in time inside the scatterer and is posed on an unbounded domain. Well-posedness of the scattering problem is shown using a formulation that is fully given on the surface of the scatterer via a time-dependent boundary integral equation. Discretizing this equation by convolution quadrature in time and boundary elements in space yields a provably stable and convergent method that is fully parallel in time and space. Under regularity assumptions on the exact solution we derive error bounds with explicit convergence rates in time and space. Numerical experiments illustrate the theoretical results and show the effectiveness of the method.

Uncertainty quantification of 3D acoustic shape sensitivities with generalized [formula omitted]-order perturbation boundary element methods

This paper presents a novel perburbation-based method for uncertainty quantification of acoustic fields and their shape sensitivities. In this work, the frequencies of impinging acoustic waves are regarded as random variables. Taylor’s series expansions of acoustic boundary integral equations are derived to obtain nth-order derivatives of acoustic state functions with respect to frequencies. Acoustic shape sensitivity is obtained by directly differentiating acoustic boundary integral equation with respect to shape design variables, and then the nth-order derivatives of shape sensitivity with respect to random frequencies are formulated with Taylor’s series expansions. Based on the nth-order perturbation theory, the statistical characteristics of acoustic state functions and their shape sensitivities can be evaluated. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed algorithm.

Deep Learning‐Driven Modeling of Dynamic Acoustic Sensing in Biomimetic Soft‐Robotic Pinnae

ABSTRACTBiological function often depends on complex mechanisms of a dynamic, time‐variant nature. An example is certain bat species (horseshoe bats—Rhinolophidae) that use intricate pinna musculatures to execute a variety of pinna deformations. While prior work has indicated the potential significance of these motions for sensory information encoding, it remains unclear how the complex time‐variant pinna geometries could be controlled to enhance sensory performance. To address this issue, this work has investigated deep neural network models as digital twins for biomimetic pinnae. The networks were trained to predict the acoustic impacts of the deformed pinna geometries. A total of three network architectures have been evaluated for this purpose using physical numerical simulations (boundary element method) as ground truth. The networks predicted the acoustic beampattern function from pinna shape or even directly from the states of actuators that were used to deform the pinna shapes in simulation. Inserting prior knowledge in the form of beam‐shaped basis functions did not improve network performance. The ability of the networks to produce beampattern predictions with low computational effort (in about three milliseconds each) should lend itself readily to supporting learning methods such as deep reinforcement learning that require many such functional evaluations.

Numerical investigation of the effects of short-crested irregular waves on the performance of a floating power capture platform

This paper presents a novel power capture platform concept consisting of a semi-submersible platform and multiple point-absorber wave energy converters (WECs). The primary objective of the current study is to investigate the dynamic behavior of the power capture platform under short-crested irregular wave conditions. A spreading function is used to modify the JONSWAP spectrum into a wave spectrum that accounts for both frequency and direction. To ensure the reliability of the numerical analysis, three-dimensional potential flow theory and boundary element method (BEM) are utilized to perform mesh convergence analysis and hydrodynamic validation of the platform and WEC models. Time-domain simulations are conducted to evaluate the effects of wave directionality on the platform motion, mooring line tension, and power absorption of the WEC array. In addition, three models, “single WEC”, “WEC array” and “fixed power capture platform” are defined. The influence of hydrodynamic interactions and platform motion are predicted by comparing the power absorption of individual WEC, WEC row, and WEC array among these models. The results show that the effects of wave directionality on the performance of the floating power capture platform cannot be ignored. The findings of this study may provide some insights into the design of power capture platforms. Meanwhile, it is recommended to determine the wave characteristics of the target operational area in advance, in order to find out the optimal design for system stability and power absorption.

EFFECT OF NONUNIFORM POROSITY IN CURVED BREAKWATER ON WATER WAVES

Abstract Assuming linear theory, the phenomenon of scattering of waves by a circular arc shaped barrier with nonuniform porosity is studied. The water region is considered to be of infinite or finite depth. Based on a judicious application of Green’s integral theorem, the corresponding boundary value problem is reduced to a hypersingular integral equation of second kind. The boundary element method and the collocation method are adopted to solve the hypersingular integral equation, and we ensure a good matching of the solutions obtained by the two methods. The reflection coefficient and energy dissipation are evaluated by using the solution of the integral equation which is then studied graphically. Different choices of distributions of pores on the barrier are considered, and we observe that the nonuniform porosity of the barrier has significant effect on the reflected wave and the energy dissipation.

Evaluating interseismic deformation patterns in the North Tabriz Fault (Iran) using enhanced fitting of velocity field and analysis of surface deformation

Understanding the mechanisms and locations of interseismic strain accumulation along faults is essential for assessing earthquake hazards. However, the mechanical response during the transition from deep fault locking to creep behavior remains uncertain. Estimating the slip deficit within these transition zones is challenging. This study challenges the assumption of a constant depth distribution of interseismic slip rate along the fault over time and proposes variable locking depths as an alternative model. By rejecting the constant locking depth assumption, singularity issues during stress theorem resolution are resolved. To address this, we employ a methodology considering creep propagation within a fully elastic medium. This approach incorporates long-term deformation resulting from viscoelastic flow in the upper mantle and lower crust. Including viscoelastic effects improves the fit to interseismic deformation rates, yielding lower locking depths compared to fully elastic models. To conduct the investigation, the GPS velocity field is recovered using the forward problem and the boundary element method. Subsequently, a physics-based inversion approach, deep interseismic creep, is employed to determine interseismic deformation patterns on a strike-slip fault. Furthermore, this study examined the correlation between the dislocation parameters and their relationship, as well as established the probability distributions associated with each faulting parameter. This research highlights the importance of considering variable locking depths in understanding interseismic strain accumulation and the transition to creep behavior along faults. The findings contribute to improved earthquake hazard assessment and mitigation strategies by providing valuable insights into fault behavior mechanics along the North Tabriz Fault.

Numerical search for the effective thermal conductivity of cracked media

Spacecraft parts accumulate damage during operation and defects that are invariably present even in new designs may grow. This leads to changes in the behavior of individual parts of the space vehicle and, consequently, to the risk of fracture. A more accurate assessment of spacecraft safety requires internal defects to be included in the material models under consideration. One of the main hazardous effects on space objects is multiple temperature heating and cooling due to periodic action of solar rays. This paper presents a study of thermal conduction of media containing cracks. It is carried out with the help of a technique developed by the authors to determine the effective thermal conductivity of materials and based on approximate numerical solution of the steady-state thermal conduction problem for a three-dimensional medium with cracks by the boundary element method. This technique allows to obtain the distribution of the temperature field and heat flux density at any point of the body under consideration, as well as to calculate the effective parameters of materials with high accuracy at relatively low calculation time using ordinary personal computers of average power. The basis of the numerical method presented in this paper is the decomposition of the desired solution into a series of some pre-calculated analytical solutions of the heat conduction equations. The dependence of the effective thermal conductivity on the density of thermally insulated cracks was considered. The formula of this dependence is proposed. Verification of the proposed methodology was carried out by comparing the numerical results of a number of problems with the results of other authors.

A novel direct interpolation boundary element method formulation for solving diffusive–advective problems

The capability of dealing with the advective transport term constitutes a challenging issue for the performance of the majority of the numerical techniques, which significantly lose their precision with the increasing in the relative magnitude of this term. Recently, a new boundary element technique called direct interpolation (DIBEM) has emerged, mainly characterized by the approximation of the entire kernel of the remaining domain integrals. The DIBEM model has been successfully applied to several scalar field problems and recently applied to certain diffusive–advective problems with superior accuracy compared to dual reciprocity formulation (DRBEM). Using DIBEM, a broader range of precise responses for flows with higher Peclet numbers can be reached beyond a lower computational cost due to the simplicity of its matrix operations. These advantages are due DIBEM concept that employs a simple interpolation procedure to approximate the kernel of the advective domain integral. However, it was noticed that in some physical scenarios with spatial variation in the velocity field, the accuracy of DIBEM did not have the same quality observed in other applications. Therefore, this work presents a new DIBEM model so that the integral equations include the explicit calculation of spatial derivatives and simultaneously solve the variation of the divergent velocity field if this is not zero. Conversely, reactive and source terms were also included to expand numerical comparisons. Thus, in the proposed examples, the results of two DIBEM models, the standard (DIBEM-S) and the new, so-called alternative model (DIBEM-A), are compared with DRBEM and also with available analytical solutions.

Self-propulsion performance prediction in calm water based on RANS/TEBEM coupling method

This paper proposes a hybrid RANS/TEBEM method to conduct self-propulsion prediction in calm water with accuracy and improve its efficiency by means of larger time step. In the coupling procedure, the rotating propeller is represented by time-averaged, spatial inhomogeneous body force field obtained from the potential flow solver based on Taylor Expansion Boundary Element Method (TEBEM) in RANS simulation. Effective wake is evaluated by subtracting induced velocities computed by potential solver from total velocities in RANS solver at a coupling plane upstream of propeller plane. The influence of coupling plane position and grid density on the numerical results is also investigated. Through KCS and KVLCC2 cases, it is shown that the predicted value of propeller revolution speed is within 4% of the experimental value, verifying the robustness and reliability of this method.

Boundary-element analysis of the noise scattering for urban aerial mobility vehicles: Solver development and assessment

Abstract Urban aerial mobility (UAM) vehicles with multi-propeller configurations have attracted considerable attention in recent years. However, previous investigations have mainly focused on the aerodynamic noise from individual propellers, with limited focus on the fuselage's sound scattering effects which can alter the far-field noise directivity. In this work, an efficient boundary element solver for sound scattering was developed to fill this gap. The solver employs hierarchical matrices to save computational cost. The benchmark examples showed high accuracy and good scalability. A representative vehicle model was then chosen, the propeller noise was simulated using rotating sources. Results show that the shielding effect in the fuselage/propeller configuration can produce an apparent noise reduction and redirect sound-energy distribution, suggesting the importance of considering the fuselage in low-noise UAM development.

A simple, effective and high-precision boundary meshfree method for solving 2D anisotropic heat conduction problems with complex boundaries

A simple, effective and high-precision boundary meshfree method called virtual boundary meshfree Galerkin method (VBMGM) is used to tackle 2D anisotropic heat conduction problems with complex boundaries. Temperature and heat flux are expressed by virtual boundary element method. The virtual source function is constructed through the utilization of radial basis function interpolation. Calculation model diagram and discrete model diagram of real boundaries, and schematic diagram of VBMGM are demonstrated. Using Galekin method and considering boundary conditions, the integral equation and the discrete formula of VBMGM are given in detail. The benefits of the Galerkin, meshfree, and boundary element methods are all presented in VBMGM. Seven numerical examples of general anisotropic heat conduction problems (including three numerical examples with complex boundaries and four numerical examples with mixed boundary conditions) are computed and contrasted with precise solutions and different numerical methods. The computation time of each example is given. The number of degrees of freedom used in many examples is half or less than that of the numerical method being compared. The suggested method has been demonstrated to be effective and high-precision for solving the 2D anisotropic heat conduction problems with complex boundaries.

Optimal electrode placements for localizing premature ventricular contractions using a single dipole cardiac source model

IntroductionThe inverse problem of electrocardiography describes non-invasively the electrical activity of the heart using potential recordings from tens to hundreds of torso electrodes. Regrettably, the use of numerous electrodes poses a challenge to its integration into routine clinical practice. MethodsOptimal electrode placements, ranging from 8 to 112 electrodes, were derived from the singular values of the transfer matrices computed for all feasible positions of a single dipole cardiac source across 12 patients with unique geometrical characteristics from the Bratislava dataset. The transfer matrices were computed using the boundary element method. Subsequently, these optimal electrode placements were used to compute the inverse solution for localizing the origin of premature ventricular contraction (PVC) with a single dipole cardiac source. The localization error (LE) was computed as the Euclidean distance between the true PVC origin, obtained through an invasive radiofrequency ablation, and the inverse solution. This enabled a direct comparison of LE computed for each optimal electrode placement with that from the full 128-electrode set. ResultsResults showed that subsets of electrodes, particularly 32 to 112, provided comparable localization accuracy (LE of 30.5 ± 15.0 mm and 26.8 ± 12.6 mm) to the full 128-electrode set (LE of 27.2 ± 11.5 mm). High errors were observed with 8 and 16-electrode placements (LE of 48.6 ± 21.3 mm and 41.0 ± 18.3 mm). ConclusionPrecise PVC localization can be achieved using strategically positioned subsets of electrodes, offering advantages in reduced preparation time, enhanced patient comfort, and improved cost-effectiveness of body surface potential mapping.

Mechanics-based machine learning for failure classification of load-bearing walls

This paper presents novel methodologies that combine analytical mechanics with artificial intelligence to classify the failure mode of reinforced concrete walls under lateral loading. The adequacy of existing approaches is examined, including design equations and established machine learning algorithms, against experimental datasets consisting of 330 specimens. Findings indicate that the machine learning algorithms outperform the empirical design equations in terms of failure mode classification; however, the former lacks physical interpretability. To address this limitation, a new concept is proposed by integrating analytical and computational platforms for identifying attributes that dominate the failure characteristics of the walls. Non-dimensional features are derived and substituted into the machine learning algorithms. The aspect ratio of the walls and the amount of vertical rebars in boundary elements are found to be salient factors when categorizing failure modes, followed by the amount of horizontal rebars in the web. Through the application of decision boundaries stemming from the mechanics-based machine learning protocol, design recommendations are suggested to effectively classify the failure mode of load-bearing walls.

Boundary Element Method for Viscous Flow through Out-phase Slip-patterned Microchannel under the Influence of Inclined Magnetic Field

Abstract In this paper, we investigate the impact of an inclined magnetic field of uniform intensity on viscous, incompressible pressure-driven Stokes flow through a slip-patterned, rectangular microchannel using the boundary element method based on the stream function-vorticity variables approach. The present investigation focuses only on the out-phase slip patterning of the microchannel walls. We address two scenarios of slip patterning, specifically large and fine slip patterning, which are determined by the periodicity of the patterning. We utilized the no-slip and Navier’s slip boundary conditions in an alternative manner on the walls. The Stokes equations govern the viscous flow through a microchannel. We assume a very small magnetic Reynold’s number to eliminate the equation of induced magnetic field in the present study. We analyzed the impact of considered dimensionless hydrodynamic parameters, including the Hartman number (Ha), inclination angle (θ) of the magnetic field, and the slip length (ls ) on fluid dynamics. In the case of fine slip, we observed significant variations in both velocity and pressure gradient, in contrast to large slip patterning. Fine slip patterning significantly increases the shear stress at slip regimes, while large slip periodicity significantly reduces it at no-slip regimes. The present investigation has several notable implications, such as regulation and advancement of mixing and heat transmission within microfluidic systems.

A Contact Mechanics Model for Surface Wear Prediction of Parallel-Axis Polymer Gears.

As surface wear is one of the major failure mechanisms in many applications that include polymer gears, lifetime prediction of polymer gears often requires time-consuming and expensive experimental testing. This study introduces a contact mechanics model for the surface wear prediction of polymer gears. The developed model, which is based on an iterative numerical procedure, employs a boundary element method (BEM) in conjunction with Archard's wear equation to predict wear depth on contacting tooth surfaces. The wear coefficients, necessary for the model development, have been determined experimentally for Polyoxymethylene (POM) and Polyvinylidene fluoride (PVDF) polymer gear samples by employing an abrasive wear model by the VDI 2736 guidelines for polymer gear design. To fully describe the complex changes in contact topography as the gears wear, the prediction model employs Winkler's surface formulation used for the computation of the contact pressure distribution and Weber's model for the computation of wear-induced changes in stiffness components as well as the alterations in the load-sharing factors with corresponding effects on the normal load distribution. The developed contact mechanics model has been validated through experimental testing of steel/polymer engagements after an arbitrary number of load cycles. Based on the comparison of the simulated and experimental results, it can be concluded that the developed model can be used to predict the surface wear of polymer gears, therefore reducing the need to perform experimental testing. One of the major benefits of the developed model is the possibility of assessing and visualizing the numerous contact parameters that simultaneously affect the wear behavior, which can be used to determine the wear patterns of contacting tooth surfaces after a certain number of load cycles, i.e., different lifetime stages of polymer gears.

Framework of acoustic analysis and shape optimization for three-dimensional doubly periodic multilayered structures

In this research, a framework of acoustic analysis and shape optimization, based on isogeometric boundary element method (IGA-BEM), is proposed for three-dimensional doubly periodic multilayered structures. The study addresses a gap in the literature by focusing on the shape optimization of such structures, which has not been extensively explored previously. The interface between different acoustic media is an infinite doubly periodic surface, which can be constructed by an open non-uniform rational B-splines. A periodic IGA-BEM is developed for the sound field analysis of the doubly periodic multilayered structure, in which the Ewald method is used to accelerate the calculation of periodic Green function. Furthermore, the shape derivative of the doubly periodic multiple boundaries is derived by imposing boundary perturbation and using the adjoint variable method. The control points of the NURBS surfaces are defined as the shape design variables, and all shape sensitivities can be quickly calculated by discretizing the shape derivative formula. Finally, in according with shape sensitivities, the corresponding shape optimization problem is solved by the method of moving asymptotes, so that the optimized shape design can be obtained. A series of numerical examples validates the accuracy and applicability of the proposed approaches.

Research on the prediction method of wing structure noise based on the combination of conditional generative adversarial neural network and numerical methods

This paper presents a technique for predicting noise generated by airfoil structures that combines deep learning techniques with traditional numerical methods. In traditional numerical methods, accurately predicting the noise of airfoil structures requires significant computational resources, making it challenging to perform low-noise optimization design for these structures. To expedite the prediction process, this study introduces Conditional Generative Adversarial Networks (CGAN). By replacing the generator and discriminator of CGAN with traditional regression neural network models, the suitability of CGAN for regression prediction is ensured. In this study, the data computation was accelerated by expanding the kernel function in the traditional boundary element method using a Taylor series. Based on the resulting data, an alternative predictive model for wing structure noise was developed by integrating Conditional Generative Adversarial Networks (CGAN). Finally, the effectiveness and feasibility of the proposed method are demonstrated through three case studies.

A Novel BEM for the Hydrodynamic Analysis of Twin-Hull Vessels with Application to Solar Ships

A novel Boundary Element Method (BEM) is presented for predicting the hydrodynamic behavior of twin-hull vessels, traveling at low speeds, aiming to quantify the benefits of integrating solar technology onboard. In particular, the power requirements of an electric 33 m long twin-hull ship are examined. The study discusses the placement of solar panels on deck and assesses their utilization in terms of real-time energy generation, aiming to extend the autonomy range while also reducing carbon emissions. The discussed methodology predicts the power needs by considering various operational variables, design specifications and hydrodynamic principles. In addition, it addresses the viability and possible advantages of integrating solar technology onboard and provides preliminary estimates regarding the extent to which solar energy may compensate for power needs, based on several factors, including the velocity, the prevailing sea state and the incident solar irradiance. The results provide useful information regarding the utilization of solar energy in the shipping sector, in addition to advancing sustainable maritime propulsion.