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海洋大學力學聲響振動實驗室 1 Regularized meshless approach for antiplane piezoelectricity problems with multiple inclusions J. H. Kao,

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Presentation on theme: "海洋大學力學聲響振動實驗室 1 Regularized meshless approach for antiplane piezoelectricity problems with multiple inclusions J. H. Kao,"— Presentation transcript:

1 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 1 Regularized meshless approach for antiplane piezoelectricity problems with multiple inclusions J. H. Kao, J. T. Chen and K. H. Chen National Taiwan Ocean University Kun Shan University T0406 11, 25, 2006 10:35~12:05

2 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 2 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

3 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 3 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

4 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 4 Literature review Bleustein, 1968, antiplane piezoelectric dynamics problem. Pak, 1992, single circular inclusion, analytical solution, alternative method. Honein, 1995, two circular inclusions.

5 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 5 Literature review Chen and Chiang, 1997, solitary cavity or rigid inclusion, conformal mapping technique. Chao and Chang, 1999, double inclusions, complex variable theory. Wu et al., 2000, two circular inclusions, conformal mapping and the theorem of analytic continuation.

6 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 6 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

7 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 7 Neumann problem Dirichlet problem Relation between MFS and RMM Interior problem Exterior problem Kernel functions Introduction of MFS

8 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 8 Relation between MFS and RMM Single-layer Potentials Double-layer Potentials Laplace problem Introduction of MFS

9 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 9 Relation between MFS and RMM d=0 Introduction of MFS Convention MFS RMM

10 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 10 Relation between MFS and RMM Introduction of RMM =0

11 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 11 Introduction of Method of Fundamental Solutions Introduction of RMM

12 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 12 Relation between MFS and RMM Source points Collocation points Kernel functions MFS RMM fictitious boundary Real boundary Single-layer potentials Double-layer potentials Double-layer potentials Compared RMM with MFS

13 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 13 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

14 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 14 RMM for solving multiply-connected-domain problems Source point Collocation point Laplace problem

15 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 15 RMM for solving multiply-connected-domain problems Source point Collocation point Laplace problem

16 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 16 RMM for solving multiply-connected-domain problems Source point Collocation point Laplace problem

17 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 17 RMM for solving multiply-connected-domain problems Construction of influence matrices

18 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 18 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

19 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 19 Application on multiply-connected-domain problems Antiplane piezoelectricity problem

20 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 20 Application on multiply-connected-domain problems Decomposition of the problem

21 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 21 Application on multiply-connected-domain problems Inclusion Matrix Antiplane piezoelectricity problems

22 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 22 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

23 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 23 Application on multiply-connected-domain problems Nm -2 Cm -2 CV -1 m -1 Nm -2 Antiplane piezoelectric problems with multiple inclusions

24 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 24 Application on multiply-connected-domain problems Case 1: Single inclusion

25 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 25 Application on multiply-connected-domain problems Case 1: Single inclusion

26 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 26 Application on multiply-connected-domain problems Nm -2 Cm -2 CV -1 m -1 Nm -2 Antiplane piezoelectric problems with multiple inclusions

27 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 27 d Application on multiply-connected-domain problems Case 2: Two inclusions

28 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 28 Application on multiply-connected-domain problems d=10 d=1d=0.1 Case 2: Two inclusions

29 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 29 Application on multiply-connected-domain problems d=1 d=10 d=0.1 d=0.01 d=0.02 Case 2: Two inclusions

30 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 30 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

31 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 31 Conclusions Only the boundary nodes on the physical boundary are required by using proposed method. The proposed method can regularize singularity by using subtracting and adding-back technique. A systematic approach to solve the antiplane piezoelectricity problems with multiple inclusions was proposed successfully by using the regularized meshless method.

32 海洋大學力學聲響振動實驗室 http://msvlab.hre.ntou.edu.tw 32 The end Thanks for your attentions. Your comment is much appreciated. You can get more information on our website. http://msvlab.hre.ntou.edu.tw

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