scholarly journals An Improved Implementation of Time Domain Elastodynamic BIEM in 3D for Large Scale Problems and its Application to Ultrasonic NDE

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
Hitoshi Yoshikawa ◽  
Naoshi Nishimura
Keyword(s):  
Time Domain ◽  
Large Scale ◽  
Scattering Problem ◽  
Time Integration ◽  
Simple Wave ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Computational Time ◽  
Integration Algorithm ◽  
Ultrasonic Nde

This paper discusses a three dimensional implementation of boundary integral equation method (BIEM) for large scale time domain elastodynamic problems and its application to ultrasonic nondestructive evaluation (NDE). We improve the time integration algorithm of the BIEM in order to reduce the required computational time. We show the e±ciency of the proposed method by applying it to a simple wave scattering problem and to a more realistic crack determination problem related to ultrasonic NDE.

The inverse elastic scattering by an impenetrable obstacle and a crack

2020 ◽  
Author(s):  
Jianli Xiang ◽  
Guozheng Yan
Keyword(s):  
Mixed Type ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Operator ◽  
Integral Equation Method ◽  
Factorization Method ◽  
Boundary Integral ◽  
Far Field ◽  
Direct Scattering ◽  
Time Harmonic

Abstract This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by a mixed-type scatterer, which is given as the union of an impenetrable obstacle and a crack. We develop the modified factorization method to determine the shape of the mixed-type scatterer from the far field data. However, the factorization of the far field operator $F$ is related to the boundary integral matrix operator $A$, which is obtained in the study of the direct scattering problem. So, in the first part, we show the well posedness of the direct scattering problem by the boundary integral equation method. Some numerical examples are presented at the end of the paper to demonstrate the feasibility and effectiveness of the inverse algorithm.

Diffraction of elastic waves from object in layer with slightly corrugated surface

2017 ◽  
Vol 23 (9) ◽  
pp. 1249-1262 ◽  
Author(s):  
Khaled M Elmorabie ◽  
Rania R Yahya
Keyword(s):  
Elastic Waves ◽  
Perturbation Technique ◽  
Scattering Problem ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Harmonic Load ◽  
Frequency Range ◽  
Corrugated Surfaces ◽  
Geometrical Shapes ◽  
Diffraction Of Elastic Waves

This work is concerned with the influence of corrugated surfaces on waves diffracted from an object in an elastic layer. A boundary value problem is formulated to simulate an anti-plane problem for a harmonic load acting on the upper surface of the layer. By using the boundary integral equation method and the perturbation technique, the considered problem is reduced to a pair of integral equations. By constructing the Green’s function, the scattering problem in a one-mode frequency range is solved. To check the validity of the proposed technique, several numerical examples for different geometrical shapes of the corrugated bottom are presented.

scholarly journals Lagrangian meshfree finite difference particle method with variable smoothing length for solving wave equations

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878924 ◽  
Author(s):  
Sheng Wang ◽  
Yong Ou Zhang ◽  
Jing Ping Wu
Keyword(s):  
Finite Difference ◽  
Wave Equations ◽  
Time Integration ◽  
Simple Wave ◽  
Domain Size ◽  
Particle Method ◽  
Computational Time ◽  
Integration Scheme ◽  
Smoothed Particle ◽  
Support Domain

In a Lagrangian meshfree particle-based method, the smoothing length determines the size of the support domain for each particle. Since the particle distribution is irregular and uneven in most cases, a fixed smoothing length sometime brings too much or insufficient neighbor particles for the weight function which reduces the numerical accuracy. In this work, a Lagrangian meshfree finite difference particle method with variable smoothing length is proposed for solving different wave equations. This pure Lagrangian method combines the generalized finite difference scheme for spatial resolution and the time integration scheme for time resolution. The new method is tested via the simple wave equation and the Burgers’ equation in Lagrangian form. These wave equations are widely used in analyzing acoustic and hydrodynamic waves. In addition, comparison with a modified smoothed particle hydrodynamics method named the corrective smoothed particle method is also presented. Numerical experiments show that two kinds of Lagrangian wave equations can be solved well. The variable smoothing length updates the support domain size appropriately and allows the finite difference particle method results to be more accurate than the constant smoothing length. To obtain the same level of accuracy, the corrective smoothed particle method needs more particles in the computation which requires more computational time than the finite difference particle method.

Nonlinear Reaction Forces on Oscillating Bodies by a Time-Domain Panel Method

1996 ◽  
Vol 40 (04) ◽  
pp. 288-302
Author(s):  
P. J. F. Berkvens ◽  
P. J Zandbergen
Keyword(s):  
Time Domain ◽  
Domain Boundary ◽  
Reaction Force ◽  
Integral Equation Method ◽  
Order Theory ◽  
Boundary Integral ◽  
Second Order ◽  
The Body ◽  
Triple Frequency ◽  
Force Signal

An outline of a time-domain boundary integral equation method (with second-order accuracy) for bodies floating on a fluid is given. It includes the full nonlinear dynamics of a potential flow with a free surface. To validate the method, a partially immersed body is forced to oscillate at a small amplitude for each of three modes. Relevant components of the reaction force on the body are integrated separately, thereby enhancing the accuracy of the hydrodynamic coefficients determined from this force signal. Linear frequency-domain results in a range of frequencies agree well with the present ones for the square, excellently for the circle. Nonlinear fluid-body interaction is simulated for a vertically oscillating square with amplitudes up to 80% of its draft. The force dependence on the motion amplitude provides a confirmation of second-order theory. Furthermore, the triple-frequency force component shows a pronounced cubic dependence on the amplitude.

Scattering in a Shallow Ocean with an Elastic Seabed

1997 ◽  
Vol 05 (04) ◽  
pp. 403-431 ◽  
Author(s):  
R. P. Gilbert ◽  
Zhongyan Lin
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Near Field ◽  
Scattering Problem ◽  
Sufficient Conditions ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Parallel Computer ◽  
Hankel Transformation ◽  
Necessary And Sufficient

In this paper the boundary integral equation method is used to solve a scattering problem in a shallow ocean with an elastic seabed. The Hankel transformation and Mittag–Leffler decomposition were used to construct the propagating solution for both far-field and near-field. In particular, necessary and sufficient conditions are found for the existence of the propagating solution. Using the propagating solution, the scattering problem is recast as a boundary integral equation. A numerical algorithm is developed for solving this boundary integral equation and its implementation on a T3D parallel computer is used to compute an illustrative example.

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