Transient implicit wave propagation dynamics with the method of finite spheres

Kim, Ki-Tae; Bathe, Klaus‐Jürgen

doi:10.1016/j.compstruc.2016.05.016

Cited by 35 publications

(7 citation statements)

References 34 publications

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“…There have been many prior researches that used dispersive behavior of elastic waves for non-destructive evaluation (NDE) of various structural elements [11][12][13][14][15]. The IE test is an NDE method that uses dispersion of transient elastic waves for evaluation delamination defects in plate-like concrete structures.…”

Section: Theoretical Background Of Iementioning

confidence: 99%

Evaluation of Delamination in Concrete by IE Testing Using Multi-Channel Elastic Wave Data

Kee

Lee

Candelaria

2019

Sensors

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The main objectives of this study are to develop a non-destructive test method for evaluating delamination defects in concrete by the Impact-echo test using multi-channel elastic wave data and to verify the validity of the proposed method by experimental studies in the laboratory. First, prototype equipment using an eight-channel linear sensor array was developed to perform elastic wave measurements on the surface of the concrete. In this study, three concrete slab specimens (1500 mm (width) by 1500 mm (length) by 300 mm (thickness)), with simulated delamination defects of various lateral dimensions and depth, were designed and constructed in the laboratory. Multi-channel elastic wave signals measured on the three concrete specimens were converted to the frequency-phase velocity image by using the phase-shift method. A data processing method was proposed to extract the dominant propagating waves and non-propagating waves from the dispersion images. The dominant wave modes were used to evaluate delamination defects in concrete. It was demonstrated that the surface wave velocity values were useful for characterizing the shallow delamination defects in concrete. In addition, the peak frequency of non-propagating wave modes extracted from the dispersion images gives information on the lateral dimensions and depths of the delamination defects. This study also discussed the feasibility of combined use of the results from propagating and non-propagating wave modes to better understand the information on delamination defects in concrete. As will be discussed, the multi-channel elastic wave measurements enable more accurate, consistent, and rapid measurements and data processing for evaluation of delamination defects in concrete than the single-channel sensing method.

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Section: Theoretical Background Of Iementioning

confidence: 99%

Evaluation of Delamination in Concrete by IE Testing Using Multi-Channel Elastic Wave Data

Kee

Lee

Candelaria

2019

Sensors

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“…Moreover, the basis (or shape) functions in the MFS are easier to construct than the basis functions in other meshfree methods, such as the moving least squares shape functions, 9 since inverting matrices is not necessary. The MFS has been applied thus far only to problems posed in media with homogeneous material properties 14‐16,62‐71 . In this work we choose an approach based on Lagrange multipliers and extend the MFS to problems for which discontinuous gradients are present in the solution.…”

Section: Introductionmentioning

confidence: 99%

Acoustic scattering in nonhomogeneous media and the problem of discontinuous gradients: Analysis and inf‐sup stability in the method of finite spheres

Nicomedes

Bathe

Moreira

et al. 2021

Numerical Meth Engineering

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In this paper we focus on a meshfree formulation for the solution of time‐harmonic acoustic scattering problems and verify the stability of the procedure. The sound waves propagate in nonhomogeneous media, giving rise to discontinuities in the gradients of the pressure field across the interfaces between regions of different material properties. Meshfree methods usually do not reproduce accurately the discontinuities in a numerical solution. We overcome this issue by introducing Lagrange multiplier fields defined at the interfaces in order to treat the discontinuities in the gradients of the pressure field. The method does not depend on any kind of adjustable parameter. We show by a numerical study of the applicable inf‐sup conditions that the resulting mixed formulation leads to well‐posed problems. The use of the proposed method is illustrated in the solution of a number of problems of wave propagation through nonhomogeneous media.

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“…The importance of numerical solution of wave problems is clear to engineers and physicists; thus, it may go without saying that the necessity of improvement of the available numerical tools is still felt by many researchers (see, for instance, the work of Kim and Bathe for the latest history). Some well‐known numerical tools, such as the finite element method (FEM) or the boundary element method (BEM), are nowadays available for such a purpose.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The type of interpolation is one of the major issues in methods using spatial discretization, such as the FEM, and this is the main reason that some pioneering scientists recommend the use of meshless methods. 1,24,25 In sum, the use of frequency domain may seem cumbersome not only because of the computational expense in spatial solution, either in the FEM or the BEM, but also because the actual solution in time needs inverse transformation, which is time consuming and needs deliberate steps. 26,27 Nevertheless, when it comes to transient solution, along with the issues relating to the time-marching algorithms, [28][29][30][31] nearly the same aforementioned issues are discernible, which now appear in the form of numerical anisotropy and period-elongation, for instance.…”

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confidence: 99%

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A robust time‐space formulation for large‐scale scalar wave problems using exponential basis functions

Movahedian

Boroomand

Mansouri

2018

Numerical Meth Engineering

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Summary In this paper, a new effective boundary node method is presented for the solution of acoustic problems, directly in time domain, using exponential basis functions. Unlike many other methods using boundary information, the final coefficient matrix is sparse. The formulation is well suited for domains whose extent is relatively larger than the distance traveled by the acoustic wave in an increment of time. The exponential basis functions used satisfy the time‐space governing equation. This helps to choose a relatively large time increment and a moderate number of boundary points, which leads to reduction of computation time. The computation is performed incrementally using a weighted residual in time. Through a series of numerical examples, it is shown that the method, when combined with a domain decomposition strategy, is effectively capable of solving various 1‐ to 3‐dimensional acoustic problems.

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Transient implicit wave propagation dynamics with the method of finite spheres

Cited by 35 publications

References 34 publications

Evaluation of Delamination in Concrete by IE Testing Using Multi-Channel Elastic Wave Data

Evaluation of Delamination in Concrete by IE Testing Using Multi-Channel Elastic Wave Data

Acoustic scattering in nonhomogeneous media and the problem of discontinuous gradients: Analysis and inf‐sup stability in the method of finite spheres

A robust time‐space formulation for large‐scale scalar wave problems using exponential basis functions

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