M. Kitahara

Boundary-integral equation method for elastodynamic scattering by a compact inhomogeneity

The set of singular integral equations which relates unknown fields on the surface of the scatterer to a time-harmonic incident wave is solved by the boundary element method. The general method of solution is discussed in some detail for scattering by an inclusion. Results are presented for a spherical cavity, and for a soft and a stiff spherical inclusion. Fields on the surface of the scatterer are compared with previous results obtained by different methods. Back-scattered and forward-scattered displacement fields are presented, both as a function of position at fixed frequency, and as a function of frequency at fixed position. The quasi-static approximation is briefly discussed.

Application of the boundary integral equation (BIE) method to transient response analysis of inclusions in a half space

Abstract Transient scattering of elastic waves by inclusions in a half space is investigated by the boundary integral equation (BIE) method. The formulation of BIE presented here is based on the Fourier transform method, and involves the analysis of transformed problems and the reconstitution of transient solutions by Fourier inversion. After the BIE has been solved numerically in the transformed domain, the transient wave fields are obtained with the help of the fast Fourier transform (FFT) algorithm. After confirmation of the accuracy of the present method, some numerical examples are shown for various inclusions in a half space, such as a cavity, an elastic inclusion, and a fluid inclusion.

Neural Network for Crack-Depth Determination from Ultrasonic Backscattering Data

A neural network approach has been developed to determine the depth of a surface breaking crack in a steel plate from ultrasonic backscattering data. The network is trained by the use of a feedforward three-layered network together with a back-propagation algorithm for error corrections[1,2]. The signal used for crack insonification is a mode converted 45° transverse wave. The plate containing a surface breaking crack is immersed in water and the crack is insonified from the opposite uncracked side of the plate. A numerical analysis of the backscattered field is carried out based on elastic wave theory, by the use of the boundary element method. The numerical data are calibrated by comparison with experimental data. The computed backscattered field provides synthetic data for the training of the network. The training data have been calculated for cracks with specified increments of the crack depth. The performance of the network has been tested on experimental data for cracks of different depths than used for network training.

Coupling of numerical Green's matrix and boundary integral equations for the elastodynamic analysis of inhomogeneous bodies on an elastic half-space

Abstract A coupled system of integral equations (of the domain and boundary types) is formulated for the elastodynamic response analysis of a locally inhomogeneous body on a homogeneous elastic half-space. The method uses the fundamental solution for homogeneous elastostatics in the inhomogeneous domain owing to the lack of a fundamental solution in inhomogeneous elastodynamics. The integral representation of displacements in the inhomogeneous domain is formulated with the help of this elastostatic fundamental solution by considering the term induced by the inhomogeneity of materials and the acceleration term as the body force term. Then the Greens matrix is obtained numerically from this integral representation and combined with the ordinary boundary integral equations, which are valid in the exterior homogeneous half-space. Some numerical examples show the efficiency and the versatility of this coupled method.

Elastodynamic analysis of inhomogeneous anisotropic bodies

Abstract The integral equation method is presented for elastodynamic problems of inhomogeneous anisotropic bodies. Since fundamental solutions are not available for general inhomogeneous anisotropic media, we employ the fundamental solution for homogeneous elastostatics. The terms induced by material inhomogeneity and inertia force are regarded as body forces in elastostatics, and evaluated in the form of volume integrals. The scattering problems of elastic waves by inhomogeneous anisotropic inclusions are investigated for some test cases. Numerical results show the significant effects of inhomogeneity and anisotropy of materials on wave propagations.

Backscatter from a Spherical Inclusion with Compliant Interphase Characteristics

In studies of scattering by an inclusion it is generally assumed that the inclusion is perfectly bonded to the surrounding matrix material. The actual bond between two materials is, however, generally effected by a thin layer, which may be called an interphase, rather than an interface. It is well known that the mechanical behavior of such an interphase may significantly influence the overall mechanical behavior of a solid containing inclusions.

Neural Network Approach to the Inverse Problem of Crack-Depth Determination from Ultrasonic Backscattering Data

A neural network approach has been developed to determine the depth of a surface breaking crack in a steel plate from ultrasonic backscattering data. The network is trained by the use of a feedforward three-layered network together with a back-propagation algorithm for error corrections[1,2]. Synthetic data are employed for network training. The signal used for crack insonification is a mode converted 45° transverse wave. The plate with a surface breaking crack is immersed in water and the crack is insonified from the opposite uncracked side of the plate. A numerical analysis of the backscattered field is carried out based on elastic wave theory, by the use of the boundary element method. The numerical data are calibrated by comparison with experimental data. The numerical analysis provides synthetic data for the training of the network. The training data have been calculated for cracks with specified increments of the crack depth. The performance of the network has been tested on other synthetic data and experimental data which are different from the training data.

A Neural Network Applied to Crack Type Recognition

In these years, a lot of numerical analyses based on elastic wave propagation theory have been carried out in the field of non-destructive evaluation, and responses under various conditions have been accumulated as analytical solutions. By using these results of analysis as a knowledge base, accurate informations about cracks, such as types, sizes, shapes, locations and directions, is expected to be obtained.

Scattering Characteristics of a Partially Debonded Compliant Inclusion-Matrix Interphase

Scattering characteristics have been calculated for a spherical inclusion with partially debonded interphase conditions. Three scattering characteristics of the scattered field have been selected for investigation: 1) the frequency response at a fixed point, 2) the scattered field at a fixed frequency along an observation line, and 3) the radiation pattern. The compliant interphase between the inclusion and the surrounding elastic matrix has been modeled by a layer of distributed springs which offers resistance to relative displacements in the two tangent and the normal directions. Two basic assumptions are made for the spring model of the interphase: 1) The springs are linear, and 2) The interphase is very thin so that the effect of inertia of the interphase can be neglected. These assumptions are acceptable in the low frequency range. The partial debonding of the interphase is modeled by setting the spring constants (defined per unit area) equal to zero along part of the interphase.

Crack Parameter Characterization by a Neural Network

A neural network with binary outputs is presented to determine the angle and the depth of a surface-breaking crack from ultrasonic backscattering data. The estimation procedure is divided into two steps: n n1. n nThe angle of the crack is estimated in the range from 10 to 70 degrees with a precision of 5 degrees. To improve the accuracy of estimation, information on the integral of the backscattered signal is utilized. n n n n n2. n n2. When the angle of the crack has been estimated, the depth of the crack is determined with a precision of 0.5mm in the range from 2.0mm to 4.0mm. This determination is achieved by employing sets of neural networks corresponding to various angles of the crack.