Boundary Element Technique Research Articles

Nonuniform Charge Effects in Protein−Protein Interactions

Two phenomena reduce the electrostatic repulsion between protein molecules in solution: charge heterogeneity (patchiness) and charge fluctuation. In this work, the electrostatic interaction energy for two protein molecules is computed as a function of separation and orientation. The results are based on solutions of the linearized Poisson−Boltzmann equation for an arbitrary prescribed surface charge distribution. A boundary element technique yields a numerical solution for the electrostatic potential on the protein surface that is then used to compute the reversible charging work. The results indicate that the two mechanisms act in a complementary fashion. Correlations in charge fluctuations reduce the net charge on the molecules and produce a long-range effect, while charge patchiness becomes significant at separations smaller than the Debye length. Both effects are included in a DLVO-type interaction potential that is used to match published second virial coefficients of lysozyme. Compared to earlier studies, the best-fit values of the effective Hamaker constant are much less sensitive to ionic strength and in better agreement with estimates based on Lifshitz theory.

THE EFFECT OF STRUCTURAL ELASTICITY ON THE EFFICIENCY OF NOISE BARRIERS

The efficiency of noise barriers is usually estimated neglecting their elastic behaviour. In this paper, the total vibro-acoustical response of simple barriers is considered. A variational approach with a boundary-element technique is used. It is a generalization of an existing formalism developed for the study of two-dimensional acoustical problems. The case of straight and thin barriers is studied. It is found that, at low frequencies, their vibrations can modify their insertion losses by several decibels.

Three-dimensional electromagnetic modeling of fiber-core effects on the coupling characteristics of weakly fused tapered fiber-optic couplers

Based on the full-wave formulations, which combine the finite element method add the boundary element technique, and the step-like approximation method, a three-dimensional (3-D) electromagnetic modeling approach is proposed in this work to investigate the fiber-core effects on the coupling characteristics of the weakly fused tapered couplers. We find the fiber cores have significant effects on the mode field patterns, coupling coefficients, and birefringence for the coupler with large normalized frequencies. The influence of the fiber cores on the coupling behavior for the real couplers, such as 3 dB power dividers, polarization beam splitters, and wavelength demultiplexing/multiplexing couplers, are also studied in 3-D view. It is found that the effects of fiber-cores in the weakly fused tapered couplers have to be considered for accurately modelling their coupling behavior, although the model with no core assumption can predict the trend of the coupling characteristics for the real couplers.

Fracture evolution during indentation of a brittle elastic solid

This paper examines the problem of crack extension during the indentation of a brittle elastic half-space by a cylindrical punch with a smooth flat contact surface. The paper develops a procedure for locating the point of nucleation of the crack within the brittle elastic solid and employs a boundary element technique to locate the progress of crack evolution as the force on the punch is increased. The numerical results illustrate the influence of the extent of crack development on the load–displacement relationship for the indentor. Copyright © 2000 John Wiley & Sons, Ltd.

A heuristic approach to microcracking and fracture for ceramics with statistical consideration

Microcracking damage and toughening are examined for ceramics. These effects have been found to depend on the material microstructure and macrocrack growth. Isotropic damage, attributed to random distribution of microcrack location, length and orientation can be associated with a disordered microstructure and a non-uniform residual stress field. When the applied stress is the main cause of cracking, the microcrack distribution is no longer random such as a system of quasi-parallel cracks. To highlight the effect of crack interaction, discrete models are advanced where damage is simulated by a distribution of microcracks. The dilute concentration assumption is invoked to simplify the analysis. The two-dimensional discrete model is based on a phenomenological approach that is statistical in character. Interactions of microcracks and with a macrocrack are considered by means of a boundary element technique (A. Brencich, A. Carpinteri, Int. J. Fracture 76 (1996) 373–389; A. Brencich, A. Carpinteri, Eng. Fract. Mech. 59 (1998) 797–814) where both isotropic and anisotropic damage could be treated. Comparisons with other results are made to show that the model can be applied to analyse the fracture behaviour of different materials.

Stress analysis of two-dimensional perforated plates using boundary element alternating method

In this paper, the boundary element alternating method (BEAM) is developed to study the stress concentration of a two-dimensional (2D) perforated plate. This method involves the iterative superposition between the boundary element solution of a bounded plate without holes and the analytical solution of an infinite 2D plate with a circular hole subjected to arbitrary normal and shear loading until the required boundary conditions of the original problem are satisfied. Excellent agreements between the solutions of the present simplified procedure and the numerical methods (conventional finite element and boundary element techniques) are observed and show the advantages of the proposed method.

Vector potential integral formulation for eddy-current probe response to cracks

A boundary integral vector potential formulation has been developed to evaluate eddy-current interactions with three-dimensional finite cracks in conductors. The approach is compared with an electric field integral equation method also used for solving crack problems in eddy-current nondestructive evaluation. An important advantage of the vector potential integral formulation is that the kernel has a weak singularity, but a drawback is that two unknown functions must be found on the crack surface. One of these functions, the current dipole density, represents the effect of the crack in terms of an induced source, and the other function is a solution of the two-dimensional Laplace equation. By contrast, the source density alone is needed for a complete solution of the electric field integral equation. In order to determine the surface Laplacian for finite cracks of arbitrary shape, a general numerical solution utilizing the boundary element technique is introduced. Numerical predictions of the eddy-current probe response to a crack give good agreement with experimental measurements, supporting the validity of the formulation.

Simulation of a mold‐cooling process for gas‐assisted injection molded parts designed with a top rib on the gas channel

AbstractThe same CAE model used for the filling and packing stage in the gas‐assisted injection molding (GAIM) process simulation was also applied to simulate the cooling phase. This was made possible by using the line source method for modeling cooling channels. The cycle‐averaged and cyclic transient mold cavity surface temperature distribution within a steady cycle was calculated using the three‐dimensional modified boundary element technique similar to that used in conventional injection molding. The analysis results for GAIM plates of a semicircular gas channel design attached with a top rib are illustrated and discussed. It was found that the difference in cycle‐averaged mold wall temperatures may be as high as 10°C, and within a steady cycle, part temperatures may also vary by about 15°C. The conversion of the gas channel into equivalent circular pipe and further simplification into two‐node elements using the line source method not only affects the mold wall temperature calculation very slightly but also reduces the computer time by 93%. This indicates that it is feasible to achieve an integrated process simulation for GAIM under one CAE model, resulting in great computational efficiency for industrial application.

Integration of High Resolution EEG and Functional Magnetic Resonance in the Study of Human Movement-Related Potentials

Cortical sources of human movement-related potentials (i.e. unilateral finger extension) were modeled using functional magnetic resonance imaging (fMR) data as a constraint of a linear inverse source estimation from highly sampled (128 channels) EEG data. Remarkably, this estimation was performed within realistic subject's MR-constructed head models by boundary element techniques. An appropriate figure of merit served to set the optimal amount of fMR constraints. With respect to standard linear inverse source estimates, fMR-constrained ones presented increased spatial detail and provided a more reliable timing of activation in bilateral sensorimotor cortical regions of interest.

Derivation of feasibility conditions in engineering problems under parametric inequality constraints with classical Fourier elimination

Fourier (or Motzkin or even Fourier–Motzkin) elimination is the classical and equally old analogue of Gaussian elimination for the solution of linear equations to the case of linear inequalities. Here this approach (and two standard improvements) is applied to two engineering problems (involving numerical integration in fracture mechanics as well as finite differences in heat transfer in the parametric case) with linear inequality constraints. The results (solvent systems of inequalities including only the related parameters) concern the feasibility conditions (existential quantifier-free formulae) so that the satisfaction of the original system of linear inequality constraints can be possible (for appropriate values of the variables in it). Further applications, e.g. to singular integral equations and to the boundary and finite element techniques in computational mechanics and engineering, are also possible. The computer algebra system Maple V has been used and a related elementary procedure for Fourier elimination was prepared and is displayed. The competitive Weispfenning elimination approach can also be used instead. The present results constitute an extension of the already available applications of computer algebra software to the classical approximate–numerical methods traditionally employed in engineering and are also related to computational quantifier elimination techniques in computer algebra and applied logic. Copyright © 2000 John Wiley & Sons, Ltd.

Computer prediction of misaligned welded joints

Experimental tests have shown that misalignment can reduce the fatigue strength of welded joints significantly. Further theoretical investigations are also required to understand the behavior of these joints. In the present study, boundary element technique together with the hypersingular boundary integral equation are employed to estimate the notch stress concentration factors at the surface. These are then used to predict the fatigue life. The addressed variable is the root crack length, or partial penetration depth, which can be accurately modeled by boundary element method. It is shown that there is a good correlation between the previous experimental results and the present theoretical results.

Dynamic soil–structure interaction analysis via coupled finite-element–boundary-element method

In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element–Boundary-Element technique (FE–BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil–structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as dam–foundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam–foundation interaction.

Closed-form integration of singular terms for constant, linear and quadratic boundary elements. Part 1. SH wave propagation

One of the most important aspects in the application of boundary element techniques to wave propagation problems is the accurate representation of the singular terms at the points of application of the virtual loads. It is current practice to carry out this task by means of numerical quadrature. This paper presents an analytical evaluation of the singular integrals for constant, linear and quadratic boundary elements involving SH waves, the results of which are then used to model inclusions in a two-dimensional acoustic medium illuminated by dynamic anti-plane line sources. Finally, the BEM results are compared with the known analytical solutions for cylindrical inclusions.

An inverse problem in estimating interfacial cracks in bimaterials by boundary element technique

An inverse elasticity problem by utilizing both the regularization method (RM) and the conjugate gradient method (CGM) is presented for estimating the interfacial cracks (including location and shape) of a bimaterial from the measurement of displacements at discrete locations internal to the domain and parallel to the interface. The present algorithm in determining the interfacial cracks is totally different from the conventional one. The comparisons of using the conjugate gradient method and commonly used regularization method are discussed systematically, moreover, the advantages and disadvantages in applying the large matrix (LM) and small matrix (SM) formulations are also examined. To the author's knowledge the present work is the first of its kind. Finally, the effects of the measurement errors on the inverse solutions are discussed. Results show that the present inverse algorithms are not sensitive to measurement errors. The CGM is recommended because it is straightforward, LM formulation is better than SM formulation without the consideration of computer time. Copyright © 1999 John Wiley & Sons, Ltd.

An inverse problem in estimating interfacial cracks in bimaterials by boundary element technique

An inverse problem in estimating interfacial cracks in bimaterials by boundary element technique

Stress analysis of the multiple circular holes with the rhombic array using alternating method

This paper presents the alternating method to study the stress distributions of the multiple circular holes with the rhombic pattern in the infinite domain. For the purposes of the efficiency and simplicity, one must use an analytical solution for a single circular hole in an infinite domain, subjected to the arbitrary traction on the circle boundary. Then, the analytical solution correlates with a successive iterative superposition process capable of satisfying the prescribed boundary conditions in the plane problems with the multiple holes. Comparisons between the solutions of the present procedure and the conventional boundary element technique demonstrate the accuracy and the advantages. Effects of the number of holes and the spaces on the stress concentration factors also are evaluated in detail herein.

A unified time domain surface impedance concept for both linear and non-linear skin effect problems

A new time-domain boundary element technique for calculation of the magnetic field and temperature distribution in the skin layer of conductors of isotropic material with general BH-curve and /spl sigma/(T) relationship is proposed. The formulation consists of the surface integral equation for the scalar magnetic potential and the time-domain surface impedance boundary condition (SIBC) for the normal component of the magnetic field. The SIBC is obtained in the form of 1-D nonlinear diffusion equations for the magnetic field and temperature inside the conductor normal to its surface. The number of integral equations is the same for 2-D and 3-D problems. The technique requires the same computational expenses as solving the problem in the well-known perfect electrical conductor limit. Numerical examples are also considered.

Two surface element formulations in the time domain for the calculation of sound fields in cavities with varying boundary conditions

Two different surface element formulations are presented which apply the equivalent source method in the time domain. The first method uses planar surface elements. The boundary condition of the cavity surface in the form of a prescribed impedance is fulfilled by using monopole elements (i.e., layers of free-field radiating monopoles with a uniform signal over the element). The second method is based on the Kirchhoff–Helmholtz integral. While the traditional boundary element technique uses the free-field Green’s functions, here a set of specialized Green’s functions is applied which is adapted to the cavity geometry. This set of functions fulfills the boundary conditions for the cavity with rigid walls. In this way the Kirchhoff–Helmholtz integral is simplified substantially and only areas of the surface with nonrigid boundary conditions have to be included in the calculations. Advantages and disadvantages of both formulations are highlighted, and results from both methods are compared for rooms of different complexity.

Finite element and boundary elements for underground input to SEA calculations

In order to study underground structures with a SEA model, special care must be given to ground loading which affects the behavior of the walls. The use of more precise techniques such as finite elements and boundary element techniques enables a description of complex phenomena and the computation of input to the SEA model. Therefore, several aspects have been analyzed: effect of type and position of source, type of ground, size and shape of the foundation, influence of the superstructure (size and type). Applications to the case of railway type situations are given. The source can be either on the surface or in the ground resulting in the generation of different types of waves.

An efficient indirect boundary element technique for multi-frequency acoustic analysis

An efficient indirect boundary element technique for multi-frequency acoustic analysis