Two-dimensional Boundary Element Method Research Articles

The analyticity of the Neumann kernel and an associated quadrature problem in two-dimensional boundary element methods

The purpose of this paper is to point out that in most practical situations, the Neumann kernel of two-dimensional potential theory is an analytic function of its arguments. Consequently, standard quadrature methods may normally be used for all element integrals in boundary element collocation methods involving the Neumann kernel. We illustrate this for a simple numerical example.

Development of expert system for BEM analysis. (1st Report. BEM modelling by using object-oriented representation of knowledge).

The Boundary element method (BEM) is a useful engineering tool for structural analysis but there are various strategies to obtain the accurate solutions. We developed an expert system for two-dimensional elastostatic BEM analysis on the engineering work station (EWS). This system supports the input of shapes and boundary condition, modelling, BEM analysis, error estimation, adaptive meshing and post-processing. This paper describes the development of the user interface and the expert system for BEM modelling and meshing, which are developed by using object-oriented programming and representing of knowledge. It is found that the object-oriented representation of knowledge is very useful in the design of user interface and expert system in this study.

Analysis of the Dynamic Stress Concentration Factor by the Two-Dimensional Boundary Element Method

Two-dimensional impulsive stresses are analyzed by the boundary element method with the Laplace transformation and the numerical inverse transformation using the fast Fourier transformation. The condition of the stability between the length of the element and the time step is given by the analysis. The validity of the condition is confirmed by the numerical results. Under the consideration of this condition, the dynamic stress concentration factors of the circular hole, the elliptic hole and the elliptic notch in a strip are obtained from the surface forces and the tangential derivatives of surface displacements. It is shown that the dynamic stress concentrations are approximately ten percent larger than the static ones.

Laminated eddy-current type solenoid coil for alternating high magnetic field

The authors describe the performance and characteristics of two kinds of multilayered eddy-current-type intense AC magnetic field generators: the laminated plate coil type and the whirled coil type. The first is suitable for use with low voltage and high current in a comparatively high-frequency range, and the second is suitable for use with high voltage and low current in a low-frequency range, e.g., for commercial use. These multilayered devices have a very simple structure, and the intense magnetic field region can be controlled by the number of stacks. The distributions of the magnetic-flux density and the eddy-current density are analyzed by two-dimensional boundary-element methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A method identifying defects by inverse analysis using boundary element method.

In this paper, the defect with noncircular shape in a two-dimensional structural component is identified by using the complex method incorporated into the two-dimensional elastic boundary element method. The method for searching for the defect is that the norm of boundary displacement, defined as the sum of the square of the difference between experimental values and numerical solutions, becomes minimum when the assumed defect coincides with the real one. The complex method is used to find the defect shape and position with minimal norm by iteratingly modifying the fictitious defect boundary within some constraint conditions without calculating derivatives. The procedure of defect identification is discussed under several numerical examples, and it is shown that the present method is efficient and accurate in searching for the real defect.

Characteristics of Acoustic Field inside Cavitation Tunnel

At present it is usual that the propeller cavitation noise characteristics are evaluated from the measured results at the cavitation tunnel through the scaling laws. However, the test section boundary of the cavitation tunnel is made of plural materials such as stainless steel and acrylic observation window. From this fact, it is predicted that the reflection effect of the boundary is significant and should be removed before the scaling-up to the fullscale. As the first step to this goal, the sound pressure distribution inside the cavitation tunnel was measured and compared with the calculated results by the two-dimensional Boundary Element Method (BEM) in order to argue the effectiveness of BEM for predicting the acoustic field inside the cavitation tunnel.The measurement was carried out using monotone sound to evaluate the acoustic field purely. The sound pressure emitted from a B&K 8100 hydrophone was received by a B&K 8103 hydrophone array. The sound pressure distribution in the transverse section was calculated by a two-dimensional BEM to argue the possibility of BEM application to the theoretical prediction of the tunnel acoustic field. Since the distance attenuation of the sound pressure in the experiment is three-dimensional, the comparison of the sound pressure level is not meaningful. However, since the reflection at the side boundary is considered dominant because of the tunnel test section configuration and the interaction of the sound pressure is mainly determined by the distance (phase) difference, it is considered that the calculated pattern of the sound pressure distribution, i. e. positions of the peaks, can be compared with the experiment. In the research, it was particularly examined what kind of boundary conditions should be given at the tunnel walls.The results obtained were as follows : (1) The measured sound pressure distribution in both the transverse and longitudinal sections showed some loops and nodes. This result showed that the reflection effect of test section boundary was very significant. This effect increased with frequency.(2) The comparison with the experiment showed that calculated pattern of the sound pressure distribution agreed well if we adopted the boundary condition where the loops and nodes of the sound pressure amplitude respectively appeared at the boundaries between the water and the stainless steel and between the acrylic window and the air. This result could be elucidated from the acoustic impedance values of water, stainless steel, acrylic resin and air. It is concluded from this result that BEM is an effective procedure to predict the acoustic field inside the cavitation tunnel theoretically if the precise boundary condition is adopted.

Mold Cooling System Design Using Boundary Element Method

Cooling system design in injection molding industries is of great importance because it significantly affects productivity and the quality of the final part. It would thus be very helpful for mold designers to be able to use a computer aided design tool in determining locations of cooling channels and process conditions to achieve uniform cooling and minimum cooling time. Towards this goal, the Boundary Element Method (BEM) has been applied to develop a system of computer aided cooling system design programs: (a) an interactive design program using a two-dimensional BEM and (b) a cooling analysis program using a three-dimensional BEM. In the present work, the injection molding cooling process is simplified by quasi-steady-state heat transfer in terms of cycle-averaged temperature. In this regard, a cycle-averaged heat transfer coefficient between a mold and polymeric material has been introduced for a cycle-averaged boundary condition. In the present paper, discussion centers on the fundamental modeling of the cooling process and the features of the BEM mold cooling design systems.

Boundary element method taking into account external power source

A formulation for solving two-dimensional magnetic field problems making use of boundary integral equations to extend the application of T. Nakata and N. Takashi's (1982) finite-element method including the external power source has been developed. The development of the method of analysis has made it easy to calculate practical magnetic field problems using the boundary-element method. The same procedure of the boundary-element formulation may be applied to three-dimensional magnetic field problems by using this two-dimensional boundary-element method. >

Analysis of the dynamic stress concentration factor by the two-dimensional boundary element method.

Two-dimensional impulsive stresses are analyzed by the boundary element method with the Laplace transformation and the numerical inverse transformation using the fast Fourier transformation. The condition of the stability between the length of the element and the time step is given by the analysis. The validity of the condition is confirmed by the numerical results. Under the consideration of this condition, the dynamic stress concentration factors of the circular hole, the elliptic hole and the elliptic notch in a strip are obtained from the surface forces and the tangential derivatives of surface displacements. It is shown that the dynamic stress concentrations are approximately ten percent larger than the static ones.

Analytic integration of integrals involved by the two-dimensional boundary element method using straight elements

An alternative recurrence formula is presented to evaluate analytically the integrals involved by two-dimensional potential problems solved with the boundary element method. The formula applies to straight elements but the degree of the shape functions used to model the variation of the unknowns is not limited. This implies that singular elements can also be considered.

Analytic integration of integrals involved by the two-dimensional boundary element method using straight elements

Analytic integration of integrals involved by the two-dimensional boundary element method using straight elements

The two-dimensional boundary integral equation method in elasticity with a consistent boundary formulation

The two-dimensional boundary element method is re-developed using a consistent formulation for traction and displacement on the boundary - displacements are assumed to vary quadratically with are length and traction are assumed to vary linearly with arc lenght. It is shown that, relative to an inconsistent model of ‘higher’ order, (a) the consistent model provides equivalent accuracy with lower required computational times when the input boundary data is traction data, (b) the consistent model provides equivalent accuracy with dramatically reduced computational times when the input boundary data is displacement data. Hence, it is clear that any HYBRID scheme employing experimentally determined boundary displacement data should use a consistent boundary element model.

An Analysis of Large Strain Viscoplasticity Problems Including the Effects of Induced Material Anisotropy

This paper examines the modeling of large shearing of solids that exhibit induced anisotropy during inelastic deformation. The “traditional” approach uses integration of material rates of certain tensors which are obtained from Jaumann rates of these tensors delivered by a material constitutive model. This leads to erroneous results (spurious oscillations) in a simple shear example. Several previous authors have suggested resolutions to this dilemma based on modification of the constitutive model — usually based upon changing the interpretation of the tensor rates delivered by a constitutive model. This paper draws attention to another aspect of the modeling process — that of obtaining the components of tensors such as the Cauchy stress in a global, space-fixed basis, from the objective rates of these tensors as delivered by the material constitutive model. In essence, it is suggested here that the elastic rotation rather than the spin should be used to achieve the above objective. The rotation idea is first discussed in the context of a simple shear example. This philosophy is then incorporated in a general purpose two-dimensional boundary element method (BEM) formulation and computer program. Numerical results for the simple shear problem, using the rotation idea, are obtained both by direct integration and from the general BEM computer program.

Shallow Trenches and Propagation of Surface Waves

The effect of the placement of shallow trenches of semi-circular or rectangular shape in the path of propagation of surface waves is studied. The ground is represented as a linear elastic halfplane, the vehicle as a point load vibrating in a wide range of frequencies, and an open air trench is interposed between the vehicle and the receiver. A two-dimensional direct boundary element method approach defined in the frequency domain is used to numerically investiate this problem. The results obtained indicate that trenches are beneficial in reducing the amplitude of vibration only in a narrow band around the mid-frequency range and in all other cases a large amplification of the dynamic signal is obtained. The actual shape of the trench is of minor importance.