Boundary Element Approach Research Articles

Wave reflection and transmission in a piezomagnetic right-angle plane with irregular boundaries: a boundary element approach

Wave reflection and transmission in a piezomagnetic right-angle plane with irregular boundaries: a boundary element approach

A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields

Objective. Commonly used cable equation approaches for simulating the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or ‘whole’ finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons. Approach. Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank–Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin–Huxley axons and spherical cells in multiple brain stimulation scenarios. Main Results. Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is simplified, and the relative placement of devices and cells can be varied without the need to generate a new mesh. Significance. Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

Mathematical analysis and numerical simulations for a nonlinear Klein Gordon equation in an exterior domain

In this study, the finite propogation speed properties investigated for a two dimensional exterior problem defined by nonlinear Klein-Gordon equation. Under some assumptions on the initial data and the nonlinearity, the solution is shown to have a finite propogation speed. Furthermore, it is demonstrated that the problem has a unique solution, and accurate numerical solutions have been produced by the use of the dual reciprocity boundary element approach with linear radial basis functions.

РАСПАРАЛЛЕЛИВАНИЕ ВЫЧИСЛЕНИЙ НА ГРАФИЧЕСКОМ ПРОЦЕССОРЕ ДЛЯ УСКОРЕНИЯ ГРАНИЧНО-ЭЛЕМЕНТНЫХ РАСЧЕТОВ В МЕХАНИКЕ

In solving problems of computer modeling using various methods, accuracy and computational efficiency questions always arise. This study explores the application of two modifications of the boundary element method to solve the problem of potential distribution within a closed two-dimensional domain with a uniform potential distribution on its boundary. The first modification involves using three nonlinear shape functions instead of one. The second modification applies the Galerkin method to the boundary element approach with three nonlinear shape functions. The essence of this modification lies in the fact that the system of equations is formulated in integral form over the entire boundary element, rather than at collocation points. In addition to this, the paper describes and investigates the advantages and disadvantages of the smoothing modification applied to these approaches. Since the influence matrix consists of independently computable elements, parallelization of calculations using NVIDIA CUDA technology has been proposed to enhance computational efficiency, significantly accelerating the calculation of interaction matrix. The choice of this technology is advantageous due to the prevalence of NVIDIA graphics accelerators in almost every personal computer or laptop, as well as it is easy to use. The study presents an approach to the application of this technology and demonstrates the results, showing the acceleration of parallelized calculations which show the dependence on the number of boundary elements. A comparison of the efficiency of the selected technology when applied to two methods, collocation and Galerkin, is also presented, indicating a significant speedup of up to 22 times by computing the influence matrix of the boundary elements.

The acoustic radiation analysis of SFGP conical shell

The shell of revolution made of sandwich functionally graded material (SFGM) has broad applications in engineering. Pores are inevitable in processing SFGM, making it complex for the vibro-acoustic characteristics of the structure. To analyze the acoustic radiation mechanism of sandwich functional gradient porous materials (SFGP) shells deeply, a theoretical model for vibro-acoustic coupling of SFGP shells based on a semi-analytical approach is proposed. The spectral boundary element approach is used to simulate the sound field while the energy method is utilized for representing the structural field. The substructure scheme is introduced, resulting in a uniform division of both the structural field and the sound field into several segments. Similarly, both the displacement and sound pressure are depicted in an identical manner, with the meridional direction expanded using the Legendre series and the circumferential direction expanded using the Fourier series. By introducing the virtual work done by the sound pressure, the structural and sound fields are coupled to form the vibro-acoustic coupling equation, which is solved using the strong coupling approach. The present method exhibits outstanding convergence and precision, showcasing a strong agreement in vibro-acoustic response results when compared to prior research. Since the conical shell is one of the most widely applicable shells of revolution, this paper takes the conical shell as the research object to study. Following the proposed methodology, we delve into the examination of the roles played by various circumferential wave number modes in influencing the vibro-acoustic response of SFGP conical shells. Building upon this groundwork, an investigation is conducted into the influence of factors such as material gradient index, porosity, and pore distribution on the vibro-acoustic characteristics of SFGP conical shells.

Preliminary Modeling of Coupled Motion Response for Floating Crane and Suspended Module by Using Boundary Element Approach and Empirical Model

Preliminary Modeling of Coupled Motion Response for Floating Crane and Suspended Module by Using Boundary Element Approach and Empirical Model

Stochastic Vibrations of a System of Plates Immersed in Fluid Using a Coupled Boundary Element, Finite Element, and Finite Difference Methods Approach.

The main objective of this work is to investigate the natural vibrations of a system of two thin (Kirchhoff-Love) plates surrounded by liquid in terms of the coupled Stochastic Boundary Element Method (SBEM), Stochastic Finite Element Method (SFEM), and Stochastic Finite Difference Method (SFDM) implemented using three different probabilistic approaches. The BEM, FEM, and FDM were used equally to describe plate deformation, and the BEM was applied to describe the dynamic interaction of water on a plate surface. The plate's inertial forces were expressed using a diagonal or consistent mass matrix. The inertial forces of water were described using the mass matrix, which was fully populated and derived using the theory of double-layer potential. The main aspect of this work is the simultaneous application of the BEM, FEM, and FDM to describe and model the problem of natural vibrations in a coupled problem in solid-liquid mechanics. The second very important novelty of this work is the application of the Bhattacharyya relative entropy apparatus to test the safety of such a system in terms of potential resonance. The presented concept is part of a solution to engineering problems in the field of structure and fluid dynamics and can also be successfully applied to the analysis of the dynamics of the control surfaces of ships or aircraft.

Time domain boundary element modeling of coupled interaction between ocean wave and elastic bridge pier

High-rising bridge pylons or piers in coastal site are flexible enough to induce obvious interaction effect against ocean waves which could alter the dynamic properties and affect the resultant structural response. This study proposes a time domain boundary element approach to investigate the instantaneous coupled interaction between ocean wave and flexible structure with arbitrary geometry. The boundary element theory is integrated with Euler-Bernoulli element following a time integration scheme. The simple Green function associated with perturbation expansion is employed to build the time-invariant hydrodynamic matrix and Newmark method with additional numerical damping is used to integrate the structural response. The proposed approach is validated against both of a benchmark experiment and a previous frequency-domain approach. The interaction effects on structural dynamic properties as well as simultaneous structural response, wave run-up and surface pressure are characterized. The computational efficiency and stability are discussed. Results show that interaction effect might alter the fundamental period and damping ratio and affects the structural response considerably. The proposed approach shows both favorable accuracy and efficiency and could provide more transient information which is absent in previous frequency domain approaches.

Sensitivity analysis of structural-acoustic fully-coupled system using isogeometric boundary element method

In many engineering challenges, the whole interaction between the structural domain and the acoustic domain must be taken into account, particularly for the acoustic analysis of thin structures submerged in water. The fast multipole boundary element approach is used in this work to simulate the external acoustic domain and the finite element method is used to describe the structural components. To improve coupling analysis accuracy, discontinuous higher-order boundary components are created for the acoustic domain. The isogeometric boundary element method (IGABEM) discretizes unknown physical fields by using CAD spline functions as basis functions. IGABEM is inherently compatible with CAD and can perform numerical analysis on CAD models without having to go through the time-consuming meshing process required by traditional FEM/BEM and volume parameterization in isogeometric finite element methods. IGABEM’s power in tackling infinite domain issues and combining CAD and numerical analysis is fully used when it is applied to structural form optimization of three-dimensional external acoustic problems. The structural-acoustic design and optimization procedures benefit from the use of structural-acoustic design sensitivity analysis because it may provide information on how design factors affect radiated acoustic performance. This paper provides adjoint operator-based equations for sound power sensitivity on structural surfaces and direct differentiation-based equations for sound power sensitivity on arbitrary closed surfaces surrounding the radiator. Numerical illustrations are provided to show the precision and viability of the suggested approach.

Spectral wave explicit weak-scattering approach for higher harmonic wave loads and ringing response of flexible monopile

This paper presents an accurate potential decomposition strategy for wave–structure interactions, known as the spectral wave explicit weak-scattering approach, where the entire original problem is divided into incident and scattered components. The incident component is evaluated using spectral models in advance; hence, only the scattered component is to be solved via a higher-order boundary element approach. The proposed coupled model is validated using published experimental and computational fluid dynamics results for wave interactions with a vertical cylinder. The results obtained are consistent with wave elevations and wave loads for regular waves and focused wave groups. A finite-element numerical model is applied to measure the severity of structural responses. Fluid–structure interactions are simulated by converting the obtained pressures into equivalent nodal forces, and new nodal velocities are converted into boundary conditions. The ringing response of a bottom-fixed monopile due to moderately steep focused wave groups is discussed based on various focal positions relative to the monopile, incident wave conditions, and damping ratios. The time–frequency characteristics of the ringing phenomenon are successfully revealed via wavelet analyses.

Employing Boundary Element Approach With Genetic Algorithm to Increase Travel Range of Repulsive Actuators

The design of repulsive electrostatic actuators having enlarged travel range is achieved by combining the boundary element approach and a genetic algorithm. The boundary element method enables calculating the electrostatic forces without time consuming finite element simulations. Once a static equation that uses a model of effective lumped mass solves the travel ranges, the GA maximizes travel ranges by optimizing the dimensional parameters. The effectiveness of the scheme is demonstrated with extensive experimental results showing the travel ranges of a micro out-of-plane actuator are increased by up to 190%. The developed platform can improve the signal-to-noise ratios and the performance of general multi-electrode systems.

Squeeze lubrication between soft solids: A numerical study

Squeezing a lubricating film between viscoelastic solids is a process with many applications, ranging from biomechanics to industrial engineering. The problem is addressed by means of an innovative numerical strategy coupling a finite difference solver for the lubricant fluid dynamics and a Boundary Element approach, which provides the deformation field in the solid. Results show marked differences compared to classical elasto-hydrodynamic lubrication (EHL): Pressure and film thickness depend, in fact, on the material viscoelastic relaxation, peaking at the two edges of the lubricated contact area. This implies, also for the minimum and central thickness values, time-dependent trends that significantly deviate from EHL solution and, thus, point out the necessity of accounting for the actual viscoelastic rheology of the lubricated solids.

Influence of Imperfect Interface of Anisotropic Thermomagnetoelectroelastic Bimaterial Solids on Interaction of Thin Deformable Inclusions

Abstract This work studies the problem of thermomagnetoelectroelastic anisotropic bimaterial with imperfect high-temperature conducting coherent interface, whose components contain thin inclusions. Using the extended Stroh formalism and complex variable calculus, the Somigliana-type integral formulae and the corresponding boundary integral equations for the anisotropic thermomagnetoelectroelastic bimaterial with high-temperature conducting coherent interface are obtained. These integral equations are introduced into the modified boundary element approach. The numerical analysis of new problems is held and results are presented for single and multiple inclusions.

A novel isogeometric boundary element approach for solving phase change problems with the level set method

In this study a new algorithm is proposed for numerically solving phase change problems. The algorithm (PTE-IGBEM) integrates the precise time domain expanding method (PTE) and the isogeometric boundary element method (IGBEM). The governing equations are transformed into recursive form by expanding the variables within the time period. The domain integral is transformed into boundary integral by the dual reciprocity method (DRM). An adaptive checking scheme is used to determine the number of expanding items required for a time period. In addition, the level set method (LSM) is used to capture the trajectory of the front separating the solid and liquid phases. Several classical examples are given to demonstrate the accuracy and robustness of the algorithm.

Numerical modeling of injection-induced earthquakes based on fully coupled thermo-poroelastic boundary element method

In recent years, there has been a substantial increase in the induced seismicity associated with geothermal systems. However, understanding and modeling of injection-induced seismicity have still remained as a challenge. This paper presents a two-dimensional fully thermo-hydro-mechanical (THM) coupled boundary element approach to characterize the fault response to forced fluid injection and assess the effect of different injection protocols on seismic risk mitigation as well as permeability enhancement. The laboratory-derived rate-and-state friction law was used to capture the frictional paradigm observed in mature faults produced in granite rocks. All phases of stick-slip cycles, including aseismic slip, propagation of dynamic rupture, and interseismic periods, were simulated. The modeling results showed that the residual values of effective normal stress and static shear stress after a particular event completely dominate the constitutive behavior of fault friction during the next seismic event. The seismic energy analyses indicated that there is a negative correlation between the seismic magnitude and the total injected volume, such that a prolonged monotonic injection eventually results in the steady slip, rather than the seismic slip. Several fluid injection protocols were designed based on a volume-controlled (VC) approach and traffic light systems (TLS) to explore their effectiveness on the seismic risk mitigation and permeability enhancement. The results showed that cyclic injection based on TLS is the most effective approach for irreversible permeability enhancement of faults through promoting slow and steady slips. Our numerical simulations also revealed that fluid extraction (backflow-fixing bottom hole pressure at atmospheric pressure), regardless of the injection style, can considerably reduce the seismicity-related risks by preventing the fast-accelerated fracture slip during the post-injection stage. This study presents novel insights into modeling the rate-and-state governed faults exposed to forced fluid injection, and provides useful approaches for shear stimulation of faults with reduced seismic risks.

Scattering attenuation of transient SH-wave by an orthotropic gaussian-shaped sedimentary basin

• Scattering attenuation of transient SH -wave. • Orthotropic Gaussian-shaped sedimentary basin. • Time-domain boundary element method. • Illustrating the responses in time and frequency domains. • Isotropy-factor, wave angle, and geometrical effect of sedimentary basin. The surface motion of an orthotropic Gaussian-shaped sedimentary basin embedded in a linear elastic half-space was successfully obtained under transient SH -wave propagation. In the use of the time-domain boundary element approach, a simple model was developed only by discretizing the interface. To achieve better convergence of the response, an attenuation rule was implemented with the assistance of the reduction exponential function applied in the boundary integral equations. After a brief overview of the method, the heterogonous sub-structured basin model was created and decomposed into two parts to satisfy the modified continuity conditions based on the normal direction at the interface node position. Then, the coupled matrices were temporarily solved at each time-step to obtain the boundary values. The developed computer code was tested by solving a validation example. Finally, to illustrate the valley surface response in the time/frequency-domain, a general sensitivity analysis was performed by considering the parameters of frequency, shape-ratio, isotropy-factor, and wave angle in the form of snapshots, seismograms, and amplification patterns. The results showed that the effect of orthotropic anisotropy was very efficient on the ground response and different seismic patterns on the surface of sedimentary basins were extracted by changes in the quantity of this parameter.

A boundary element approach for the evaluation of SSI effects in presence of pile foundations under steady-state conditions

Simplified procedures, capable of predicting the main effects of soil-structure interaction (SSI), involving minimum computational effort are desired in engineering practice. Besides, user-friendly approaches can be incorporated into guidelines or practical recommended procedures. Nevertheless, approximate solutions need to be carefully validated through rigorous analytical or numerical methods, as well as by the comparison with experimental results or field measurements. In the case of piles, the flexibility of the soil-foundation system plays a fundamental role in structural design and the evaluation of the pile group effects still represents a crucial task in practical problem. In this paper, a Boundary Element approach based on the Stiffness Matrix Method (Kausel in Fundamental solutions in elastodynamics. A compendium, Cambridge University Press, England, 2006) is employed to investigate the key features of SSI, by comparison with the actual field data collected by Stewart et al. (Empirical evaluation of inertial soil-structure interaction effects. Rep. No. PEER-98/07, Pacific Earthquake Engineering Research Center, 1998) from instrumented sites and structures.

Crack nucleation and propagation modeling for lubricated spur gear contacts of rough surfaces

In this study, a rolling contact fatigue model for lubricated gear contacts of rough surfaces is proposed, considering both crack nucleation and propagation stages. A boundary element approach is implemented to describe surface roughness topography effect on near surface stress concentration, with surface tractions yielded from mixed EHL analysis. A fatigue criterion is employed to find crack nucleation position and life. Assuming mode II crack opening mechanism, stress intensity factor range is determined and used to arrive crack propagation life. Through comparisons to experiments, model capability is demonstrated. Simulation results show important roughness effect on crack propagation as well as crack nucleation.

РАСЧЕТЫ ДЕЙСТВИЯ СИЛЫ НА ПОРОУПРУГОЕ ТРЕХФАЗНОЕ ПОЛУПРОСТРАНСТВО

The mathematical formulation of the boundary value problem in the images of the linear three-dimensional isotropic dynamic theory of poroelasticity is given when the material of the medium is partially saturated. The poroelastic medium is represented by a model of a heterogeneous material consisting of a phase of an elastic matrix and two phases of fillers – liquid and gas filling the pore system. A method for the numerical inversion of the Laplace transform is described. The description of the boundary-element approach is given. A regularized boundary integral equation is given. A discrete analogue of the boundary integral equation is written down. The discrete analog is parametrized by the complex variable of the Laplace integral transform. As an example, the problem of the action of a vertical force uniformly distributed on a square area on a partially saturated poroelastic half-space is considered. The choice of the computational boundary-element model made it possible to obtain verified numerical results. The effect of saturation on the amplitudes of the nonstationary wave response and on the velocities of the response waves is noted. The behavior of the wave response with an isotropic, homogeneous, poroelastic half-space moving away from the loading source is demonstrated. The problem of the action of a vertical force on a partially saturated poroelastic half-space weakened by a cubic cavity is considered. The influence of half-space attenuation on the wave surface response is analyzed. There is an analysis of the influence of depth on the dynamic wave response, as well as the influence of the phase of the poroelastic material.

Bem2d.jl: A quadratic co-location two-dimensional boundary element approach to quasi-static faulting problems with gravity and non-planar topography

Linear elastic boundary element models are commonly used tools to understand the mechanics of earthquake cycle processes and their contribution to the growth of tectonic structures. Here we describe a two-dimensional plane strain linear elastic boundary element approach to earthquake cycle and tectonic processes based on the displacement discontinuity method. This approach integrates an analytic solution for coincident interactions using three node quadratic elements and the classic particular integral approach to uni-directional gravity. Three node quadratic elements are more accurate than classical constant displacement elements and enable the exact representation displacements, stresses and tractions on elements subject to slip gradients. We demonstrate the recovery of analytic solutions and illustrate the combined effects of faulting and gravitational body forces in the presence of topographic relief.