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 transcript:

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, J. T. Chen and K. H. Chen National Taiwan Ocean University Kun Shan University T , 25, :35~12:05

海洋大學力學聲響振動實驗室 2 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

海洋大學力學聲響振動實驗室 3 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

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

海洋大學力學聲響振動實驗室 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.

海洋大學力學聲響振動實驗室 6 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

海洋大學力學聲響振動實驗室 7 Neumann problem Dirichlet problem Relation between MFS and RMM Interior problem Exterior problem Kernel functions Introduction of MFS

海洋大學力學聲響振動實驗室 8 Relation between MFS and RMM Single-layer Potentials Double-layer Potentials Laplace problem Introduction of MFS

海洋大學力學聲響振動實驗室 9 Relation between MFS and RMM d=0 Introduction of MFS Convention MFS RMM

海洋大學力學聲響振動實驗室 10 Relation between MFS and RMM Introduction of RMM =0

海洋大學力學聲響振動實驗室 11 Introduction of Method of Fundamental Solutions Introduction of RMM

海洋大學力學聲響振動實驗室 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

海洋大學力學聲響振動實驗室 13 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

海洋大學力學聲響振動實驗室 14 RMM for solving multiply-connected-domain problems Source point Collocation point Laplace problem

海洋大學力學聲響振動實驗室 15 RMM for solving multiply-connected-domain problems Source point Collocation point Laplace problem

海洋大學力學聲響振動實驗室 16 RMM for solving multiply-connected-domain problems Source point Collocation point Laplace problem

海洋大學力學聲響振動實驗室 17 RMM for solving multiply-connected-domain problems Construction of influence matrices

海洋大學力學聲響振動實驗室 18 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

海洋大學力學聲響振動實驗室 19 Application on multiply-connected-domain problems Antiplane piezoelectricity problem

海洋大學力學聲響振動實驗室 20 Application on multiply-connected-domain problems Decomposition of the problem

海洋大學力學聲響振動實驗室 21 Application on multiply-connected-domain problems Inclusion Matrix Antiplane piezoelectricity problems

海洋大學力學聲響振動實驗室 22 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

海洋大學力學聲響振動實驗室 23 Application on multiply-connected-domain problems Nm -2 Cm -2 CV -1 m -1 Nm -2 Antiplane piezoelectric problems with multiple inclusions

海洋大學力學聲響振動實驗室 24 Application on multiply-connected-domain problems Case 1: Single inclusion

海洋大學力學聲響振動實驗室 25 Application on multiply-connected-domain problems Case 1: Single inclusion

海洋大學力學聲響振動實驗室 26 Application on multiply-connected-domain problems Nm -2 Cm -2 CV -1 m -1 Nm -2 Antiplane piezoelectric problems with multiple inclusions

海洋大學力學聲響振動實驗室 27 d Application on multiply-connected-domain problems Case 2: Two inclusions

海洋大學力學聲響振動實驗室 28 Application on multiply-connected-domain problems d=10 d=1d=0.1 Case 2: Two inclusions

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

海洋大學力學聲響振動實驗室 30 Outlines Literature review Relation between MFS and RMM RMM for solving multiply-connected- domain problems Application on antiplane piezoelectricity problems Numerical examples Conclusions

海洋大學力學聲響振動實驗室 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.

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