論文 / 著書情報
Article / Book Information
題目(和文)

高速な時間領域境界要素法及びその非線形超音波シミュレーションへの適用

Title(English)

Fast time-domain boundary element method and its application tononlinear ultrasonic simulation

著者(和文)

丸山泰蔵

Author(English)

Taizo Maruyama

出典(和文)

学位:博士(工学),学位授与機関:東京工業大学,
報告番号:甲第10240号,授与年月日:2016年3月26日,
学位の種別:課程博士,
審査員:廣瀬 壮一,天谷 賢治,三上 貴正,アニール ワイジェ,中村 隆志,斎藤 隆泰

Citation(English)

Degree:Doctor (Engineering),
Conferring organization: Tokyo Institute of Technology,
Report number:甲第10240号,
Conferred date:2016/3/26,
Degree Type:Course doctor,Examiner:,,,,,

学位種別(和文)

博士論文

Category(English)

Doctoral Thesis

種別(和文)

論文要旨

Type(English)

Summary

Powered by T2R2 (Tokyo Institute Research Repository)

（博士課程）Doctoral Program論 文 要 旨ＴＨＥＳＩＳ ＳＵＭＭＡＲＹ

専攻：
Department of

情報環境学（社会・環境系）

学生氏名：
Student’s Name

丸山 泰蔵

専攻

申請学位（専攻分野）： 博士
Academic Degree Requested

指導教員（主）：Academic Advisor(main)

Doctor of

教授（工学）

廣瀬壮一

指導教員（副）：Academic Advisor(sub)要旨（英文 800 語程度）
Thesis Summary （approx.800 English Words ）In this dissertation, a convolution quadrature time-domain boundary element
method (CQ-BEM) has been accelerated using a fast multipole method (FMM) and a rapid
convolution algorithm for solving large-scale wave problems. The author has applied theproposed fast CQ-BEM to numerical simulations of nonlinear ultrasonic testing (NLUT)
based on the contact acoustic nonlinearity (CAN). He also investigated causes andcharacteristics of the nonlinear phenomenon from obtained numerical results.
This dissertation is organized by the following seven chapters:
Chapter 1 [Introduction]
The previous studies on the NLUT based on CAN and time-domain BEM including
the CQ-BEM were reviewed in Chapter 1. The author then mentioned the importance andrequirement of theoretical approach to nonlinear ultrasonic phenomena. He also pointed out
the limitations of conventional time-domain BEM for wave problems. The organization ofthis dissertation is also described in this chapter.
Chapter 2 [Convolution Quadrature Time-domain Boundary Element Method (CQ-BEM)]
Although the time-domain BEM is considered as the most appropriate numericalmethod for the nonlinear ultrasonic simulation, the conventional one in which a collocation
method is used for time discretization has disadvantages in its numerical stability.
Therefore, as the solution of this issue, the CQ-BEM based on implicit Runge-Kutta scheme(IRK-based CQ-BEM) has been proposed. Its important aspects were presented throughnumerical examples for three-dimensional (3-D) acoustic wave problems. Then, the author
pointed out that the computational complexity of the IRK-based CQ-BEM is large, andapplication of acceleration techniques is often required.
Chapter 3 [Acceleration of CQ-BEM]
The IRK-based CQ-BEM has disadvantages in its computational cost, and theoriginal computational and memory complexities are 𝑂(𝑁 2 𝑀2 ), where 𝑁 and 𝑀 denote thenumbers of time steps and elements, respectively. Therefore, the acceleration of CQ-BEM
for 3-D acoustic and elastic wave problems using the FMM and rapid convolution algorithm
have been presented in Chapter 3. As the result of acceleration, the computational andmemory complexities could be reduced to 𝑂(𝑁𝑀log𝑁log𝑀) and 𝑂(𝑁𝑀), respectively. The
accuracy and efficiency of fast CQ-BEM were also confirmed by solving wave problems
numerically.
Chapter 4 [3-D Simulation of Higher-harmonic Waves Due to an Interface Crack]
From Chapter 4, the application of IRK-based CQ-BEM to nonlinear ultrasonicsimulation has been discussed. The 3-D simulation of nonlinear ultrasonic waves due to aninterface crack with contact boundary conditions between two semi-infinite elastic solids,
has been performed in Chapter 4. This problem can be considered as the wave scattering by
a nonlinear imperfection on a bi-material interface. The appropriate boundary element
formulation for this problem has been proposed in order to accurately compute thetangential velocity of displacement which is included in the nonlinear boundary conditions.
The author carried out some numerical simulations of the higher-harmonic generation inNLUT and validated the numerical model of interface crack through obtained numericalresults.
Chapter 5 [2-D Simulation of Nonlinear Ultrasonic Waves Due to Interior and Surface
Breaking Cracks]
Some 3-D nonlinear ultrasonic simulations were performed in Chapter 4. Since theboundary element formulation was developed for an interface crack between two semiinfinite elastic solids, not only the boundary elements of interface crack but the ones of bimaterial interface were also required. Thus, it is difficult to conduct long-time analyses andto confirm the sub-harmonic generation using the method owing to its computational cost.
In Chapter 5, therefore, 2-D long-time analyses of nonlinear ultrasonic generation byinterior and surface breaking cracks have been implemented by the non-accelerated CQBEM. Complex shape and arrangement of cracks were considered because the multiple
reflection of bulk waves is significant to the sub-harmonic generation in view of the previous
researches. Moreover, the nearly stationary vibration fields must be investigated to confirm
the sub-harmonic generation.
From numerical results, the author succeeded in the numerical simulation of subharmonic generation and investigated the relationship between the nonlinear sub-harmonicresonance and frequency response characteristic of the linear system. It was also found thatthe behavior of sub-harmonic generation due to a surface breaking crack is different fromthat due to interior cracks.
Chapter 6 [3-D Simulation of Nonlinear Ultrasonic Waves Due to Interior Cracks]
The 3-D simulation of nonlinear ultrasonic waves due to interior cracks has been
conducted by the fast CQ-BEM, which is presented in Chapter 3, in order to investigate
dimensional effects in the sub-harmonic generation. In practice, the shape and arrangementof cracks have 3-D geometry, and it is important to evaluate the dimensional effect.
Therefore, the numerical method that was developed in Chapter 5, has been extended to the3-D crack problem.
From numerical results, it was confirmed that the sub-harmonic generation iscaused under the similar conditions to the 2-D cases. However, the dimensional effect issignificant to the characteristic of sub-harmonic generation, and it was hard to observe thesub-harmonic generation compared with the 2-D case.
Chapter 7 [Final Remarks]
The author stated the conclusions of this dissertation and mentioned the future prospects.

備考 : 論文要旨は、和文 2000 字と英文 300 語を 1 部ずつ提出するか、もしくは英文 800 語を 1 部提出してください。
Note : Thesis Summary should be submitted in either a copy of 2000 Japanese Characters and 300 Words (Engｌish) or 1copy of 800
Words (English).
注意：論文要旨は、東工大リサーチリポジトリ（T2R2）にてインターネット公表されますので、公表可能な範囲の内容で作成してください。
Attention: Thesis Summary will be published on Tokyo Tech Research Repository Website (T2R2).