Finite element solution for electromagnetic scattering from two-dimensional bodies

The problem of scattering from bodies in free space is formulated using a differential equation approach. The finite element mesh extends outward into the far field region of the scattering body, where the outer boundary condition is evaluated using the asymptotic expression for the scattered field. Numerical results for two scattering bodies are presented and discussed. Non-physical, standing waves appear in the results due to the inadequacy of the outer boundary condition in fulfilling the radiation condition for the scattered field. The differential equation approach does not appear to be competitive with integral equation approaches for thin bodies, but seems promising for handling scattering from thick inhomogeneous bodies into which the field penetrates.     

Three-dimensional thermo-elastoplastic analysis by triple-reciprocity boundary element method

In general, internal cells are required to solve thermo-elastoplastic problems using a conventional boundary element method (BEM). However, in this case, the merit of the BEM, which is ease of data preparation, is lost. The triple-reciprocity BEM can be used to solve two-dimensional thermo-elastoplasticity problems with a small plastic deformation without using internal cells. In this study, it is shown that three-dimensional thermo-elastoplastic problems with heat generation can be solved by the triple-reciprocity BEM without using internal cells. Initial strain and stress formulations are adopted and the initial strain or stress distribution is interpolated using boundary integral equations. A new computer program is developed and applied to solve several problems.     

Spherical wave scattering by slender bodies

The problem of the scattering of a spherical acoustic wave by rigid slender bodies of revolution is investigated theoretically from a formalism based on the matched asymptotic expansion method. It is an extension of a formulation that was originally derived for incident plane waves with the so-called slender-body approximation. Simple and practical formulas are obtained for the scattered pressure in the near- and far-fields: they are valid at low and medium frequencies when the reduced wavenumber Ka is less or of the order of unity. Computations of the monostatic and bistatic angular distributions for a spheroid are presented to illustrate the sensitivity of the scattered field with respect to the distance source and observation point.     

Three-dimensional unsteady heat conduction analysis by triple-reciprocity boundary element method

The conventional boundary element method (BEM) requires a domain integral in heat conduction analysis with heat generation or an initial temperature distribution. In this paper it is shown that the three-dimensional heat conduction problem can be solved effectively using the triple-reciprocity BEM without internal cells. In this method, the distributions of heat generation and initial temperature are interpolated using integral equations and time-dependent fundamental solutions are used. A new computer program was developed and applied to solving several problems.     

Three-dimensional unsteady thermal stress analysis by triple-reciprocity boundary element method

The conventional boundary element method (BEM) requires a domain integral in unsteady thermal stress analysis with heat generation and/or an initial temperature distribution. In this paper, it is shown that the three-dimensional unsteady thermal stress problem can be solved effectively using the triple-reciprocity boundary element method without internal cells. In this method, the distributions of heat generation and initial temperature are interpolated using integral equations and higher order time-dependent fundamental solutions. A new computer program was developed and applied for solving several test problems.     

Application of the boundary element method to elastic wave scattering by irregular defects

A time-harmonic boundary element formulation for elastic wave scattering in 3D is adapted to ultrasonic NDE. Defect classes addressed are volumetric voids and inclusions, and crack-like elliptical voids. For axisymmetric flaws, comparisons are made with method of optimal truncation (MOOT) and transition-matrix calculations. Comparison to experiment is made for more general shapes. For crack-like voids, comparisons are made with the Kirchhoff, geometric theory of diffraction (GTD), and quasistatic asymptotic approximations. The efficiency and usefulness of the boundary element method (BEM) in finding the bounds of applicability of these approximate theories are demonstrated. An example of a flaw characterization technique based on intermediate frequency scattering data simulated by BEM is given. The ability of BEM to handle nonplanar incident fields, as described by a transducer beam model, is shown. Other computational and modeling efficiencies of the BEM are noted.     

Time-domain analysis of electromagnetic wave fields by boundary integral equation method

Time-domain analysis of electromagnetic wave fields is popularly performed by the Finite Difference Time-Domain method. Then the Boundary Integral Equation Method (BEM) still has advantage comparing with FDM or FEM type scheme in open boundary problems, moving boundary problems and coupled problems of charge particle and electromagnetic fields. However, the time-domain boundary integral equation method still do not well developed, numerical instability in long time range calculations frequently appear except for special cases. In this paper, a stable scheme of the time-domain boundary integral equation method is presented and numerical example of particle accelerator wake fields is shown.     

Isotropic scattering by penetrable cylinders

Isotropic scattering is considered for infinite cylinders thin in the sense that ka < 1, although ?k'a? and cross-sectional shape can be arbitrary within limits (k and k' are, respectively, free-space and interior propagation constants, and a is a characteristic dimension of the cylinder). For circular cylinders, scattering width is found to saturate at its perfectly conducting value, and absorption width is found to peak, when skin depth becomes comparable with cylinder diameter. For a variety of cylinders with and without edges, both scattering and absorption widths are then found to be effectively identical to those of the circular cylinder with equal cross-sectional area. A new analytical formula is obtained for high but not infinite conductivity, and the connection with scattering cross sections of corresponding finite cylinders is discussed.     

Three-dimensional piezoelectric boundary element analysis of transversely isotropic half-space

In this paper, we present a boundary element method (BEM) solution technique for studying the three-dimensional transversely-isotropic piezoelectric half-space problems. The use of mixed alternative point force solutions for half and full-space problems presented are necessary to overcome the computation difficulties especially in the calculation of the derivatives with respect to z. Infinite boundary elements are introduced to model the surface of the half-space only when stresses at the internal points are required to be evaluated. The integration over the infinite boundary elements is bounded and some limitations of the infinite element construction are relaxed. Closed-form solutions for uniformly distributed mechanical and electrical loads acting on a circular area on the surface of half-space are derived. This theoretical work serves as a good verification tool for numerical computation. In this paper, the numerical and theoretical results show good agreement. Numerical analysis via the finite element method (FEM) is also carried out using the commercial solver ANSYS. These FEM results are used to verify against the accuracy of the BEM solution. Finally, numerical results for the case of Hertzian pressure applied to an imperfect half-space are presented. The effects of the coupled mechanical–electrical influences as well as the presence of voids are examined. This work was supported by NTU Academic Research Funds. The finite element simulation using the ANSYS code was conducted by Mr. Ji Ren. Also, the authors wish to acknowledge the journal editor and anonymous reviewers for their helpful suggestions and comments leading to improvement of the paper.     

Three-dimensional magnetic field analysis method using scalarpotential formulated by boundary element method

A computational method for magnetic fields formulated by a BEM (boundary element method) has been developed. In the method, a reduced scalar potential is selected as an unknown variable to simplify the calculation of the boundary conditions. Its use requires a high numerical accuracy of the potential gradient. Conventional BEM does not provide this, because numerical element integration for the singular kernal causes a large error. To overcome this difficulty, a highly accurate numerical integration scheme is proposed based on the BEM, and it is applied to magnetic field problems. Calculation results for a spherical permeable material in a problem proposed by the Institute of Electrical Engineers of Japan (the problem of a magnetic field generated by a coil) agreed with the exact solution and the experimental data within 5%     

A new boundary element formulation for wave load analysis

A new boundary element (BEM) formulation is proposed for wave load analysis of submerged or floating bodies. The presented formulation, through establishing an impedance relation, permits the evaluation of the hydrodynamic coefficients (added mass and damping coefficients) and the coefficients of wave exciting forces systematically in terms of system matrices of BEM without solving any special problem, such as, unit velocity or unit excitation problem. It also eliminates the need for scattering analysis in the evaluation of wave exciting forces. The imaginary and real parts of impedance matrix give, respectively, added mass and damping matrices whose elements describe the fluid resistance against the motion of the body. The formulation is explained through the use of a simple fluid-solid system under wave excitations, which involves a uniform fluid layer containing a solid cylindrical body. In the formulation, the solid body is taken first as deformable, then, it is specialized when it is rigid. The validity of the proposed method is verified by comparing its result with those available in literature for rigid submerged or floating bodies.     

Three-dimensional analysis of magnetic field distortion of ferromagnetic beam-plates by the boundary element method

Magnetoelastic buckling of a ferromagnetic beam-plate has been experimentally and theoretically studied by many investigators. A great discrepancy between the experimental results and the theoretical predictions has stimulated related studies. It has been supposed that the discrepancy could be attributed to the finite size of the test piece; this case has not yet been solved exactly, or even numerically. In this study the boundary element method is applied to solve for the magnetic field distribution around the finite specimen.     

Three-dimensional crack problem analysis using boundary element method with finite-part integrals

A set of hypersingular integral equations of a three-dimensional finite elastic solid with an embedded planar crack subjected to arbitrary loads is derived. Then a new numerical method for these equations is proposed by using the boundary element method combined with the finite-part integral method. According to the analytical theory of the hypersingular integral equations of planar crack problems, the square root models of the displacement discontinuities in elements near the crack front are applied, and thus the stress intensity factors can be directly calculated from these. Finally, the stress intensity factor solutions to several typical planar crack problems in a finite body are evaluated. This revised version was published online in August 2006 with corrections to the Cover Date.     

A three-dimensional boundary element formulation for the elastoplastic analysis of cracked bodies

In this paper a general boundary element formulation for the three-dimensional elastoplastic analysis of cracked bodies is presented. The non-linear formulation is based on the Dual Boundary Element Method. The continuity requirements of the field variables are fulfilled by a discretization strategy that incorporates continuous, semi-discontinuous and discontinuous boundary elements as well as continuous and semi-discontinuous domain cells. Suitable integration procedures are used for the accurate integration of the Cauchy surface and volume integrals. The explicit version of the initial strain formulation is used to satisfy the non-linearity. Several examples are presented to demonstrate the application of the proposed method. © 1998 John Wiley & Sons, Ltd.     

Three-dimensional contact mechanics analysis of crack problems using the boundary element method

In this paper, a formulation based on the iterative-load incremental approach for the three-dimensional frictional contact mechanics analysis of fracture problems using the boundary element method (BEM), is presented. Special crack front elements are employed to provide a quick and direct means of obtaining the stress intensity factor. The veracity of the formulation is demonstrated with four crack problems. Three of these problems involve crack closure under bending loads, and the fourth is that of a pin-loaded rectangular plate with corner cracks at the pin-hole. The computed BEM solutions are compared, where possible, with those available in the literature, and there is generally good agreement between them. The numerical examples serve also to illustrate the need for a proper contact mechanics treatment to obtain accurate stress intensity factors for such problems.     

Transient analysis of three-dimensional wave propagation using the boundary element method

In the past the time domain solution of the wave equation has been limited to simplified problems. This was due to the limitations of analytical methods and the capacity of computers to manipulate and store ‘large’ blocks of spatial information. With the advent of ‘super computers’ the ability to solve such problems has significantly increased. This paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method. The technique presented will allow the definition of a domain, the input of impedance conditions on the domain's surface, the specification of inputs on the surface, and the specification of initial conditions within the domain. It will produce a complete solution of the wave equation inside the domain. The techniques are demonstrated using a program with a boundary element formulation of Kirchhoff's equation. The elements used are triangular and compatible.     

Time-domain boundary element analysis of elastic wave interaction with a crack

The mathematical formulation of the problem of transient wave interaction with a crack in a homogeneous, isotropic, linearly elastic solid has been reduced to the solution of an integral equation over the insonified crack face. The integral equation relates the unknown crack-opening displacement, which depends on time and position, to the incident wave field. The integral equation has been solved numerically by a time-stepping method in conjunction with a boundary element discretization of the crack surface. For normal incidence of a longitudinal step-stress wave on a penny-shaped crack, results as functions of time have been obtained for the crack-opening displacement, the elastodynamic Mode-I stress intensity factor and the scattered far-field.     

Numerical analysis of low-frequency electromagnetic scattering from axially symmetric bodies using an inductance matrix

We have proposed a numerical method for calculating low-frequency electromagnetic scattering from axially symmetric conducting bodies with and without apertures. The surface of the perfectly conducting scatterer is modeled by a set of inductively coupled coil elements, and the current in each coil element is computed by solving an inductance matrix equation. A disadvantage of a conventional method for a scatterer with apertures is discussed. Scattering from various axially symmetric conducting bodies with or without apertures is calculated and the resulting fields are in good agreement with those obtained by finite-element method.     

Reduced forward operator for electromagnetic wave scattering problems

The paper describes a reduced forward operator for solving electromagnetic scattering problems using a volume integral equation in conjunction with a conjugate gradient fast Fourier transform scheme. The reduction is obtained by decoupling of the interaction between the locations in the spatial computational domain at which there is non-zero contrast and those positions at which there is zero contrast. The decoupling is achieved by multiplication of the kernel by a diagonal matrix whose entries reflect the presence or absence of contrast at the associated point. Analysis supported by numerical experiments shows that the conjugate gradient algorithm applied to the reduced system converges more rapidly than when it is applied to the original system