National Taiwan Ocean University Research Hubhttps://scholars.ntou.edu.twThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 20 Jul 2024 16:57:51 GMT2024-07-20T16:57:51Z50711Analytical solutions for the Laplace problem of an eccentric annular domainhttp://scholars.ntou.edu.tw/handle/123456789/23691Title: Analytical solutions for the Laplace problem of an eccentric annular domain
Authors: Chen, Jeng-Tzong; Lee, Ying-Te; Tai, Wei -Chen; Tsao, Mei-Na
Abstract: Boundary value problems including a source and no source for an eccentric annular domain are both revisited in this paper. Instead of using complex variables, the null-field boundary integral equation in conjunction with the degenerate kernel is employed to analytically solve the problem. Due to the geometry of the eccentric domain, the fundamental solution is expanded to the degenerate kernel under the bipolar coordinates. Once the degen-erate kernel is found, the boundary integral equation is nothing more than a linear algebraic system. The so-lutions derived by using the present method have been compared with those done by using the complex variables. The potential field of the problems are plotted to show the validity of the present method.
Sun, 01 Jan 2023 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/236912023-01-01T00:00:00ZSupport motion of a finite bar with a viscously damped boundaryhttp://scholars.ntou.edu.tw/handle/123456789/23630Title: Support motion of a finite bar with a viscously damped boundary
Authors: Chen, Jeng-Tzong; Kao, Hao-Chen; Lee, Jia-Wei; Lee, Ying-Te
Abstract: In this paper, we extended the previous experience to solve the vibration problem of a finite bar with a viscously damped boundary and the support motion on the other side. Two analytical methods, the mode superposition method in conjunction with the quasi-static decomposition method and the method of diamond rule based on the method of characteristics, were employed to derive two analytical solutions. One is a series solution by using the mode superposition method. The other is an exact solution by using the method of diamond rule. The non-conservative system with an external damper is solved straightforward by using the method of diamond rule to avoid the complex-valued eigen system. Agreement is made well. Both advantages and disadvantages of two methods were discussed.
Thu, 17 Nov 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/236302022-11-17T00:00:00ZA systematic approach for potentials on closely packed cells using the null-field boundary integral equation in conjunction with the degenerate kernel and eigenfunction expansionhttp://scholars.ntou.edu.tw/handle/123456789/22010Title: A systematic approach for potentials on closely packed cells using the null-field boundary integral equation in conjunction with the degenerate kernel and eigenfunction expansion
Authors: Lee, Ying-Te; Kao, Jeng-Hong; Chou, Yen-Ting; Chen, Jeng-Tzong
Abstract: A systematic approach based on the null-field integral formula is used to determine the electric potential of a tissue with many cells stimulated by remote electric fields. When the cells are very close to each other, the problem becomes nearly singular and the accuracy of the solution deteriorates. However, in the proposed approach, the highly accurate results are obtained because the separable kernel (degenerate kernel) and eigenfunction expansion are introduced to capture the geometry property in the integral formulation. Only boundary nodes are required instead of boundary elements to satisfy the boundary conditions or interface conditions. The proposed approach could be seen as one kind of meshless and semi-analytical methods. In addition, the error just stems from the number of truncation terms of the eigenfuntion expansion and the convergence rate of exponential order is better than the linear order of the conventional boundary element method. For the problem of closely packed cells, the boundary density of sharp variation could be accurately simulated or captured by increasing the number of terms of eigenfunctions. Finally, the acceptable results are shown to see the efficiency and accuracy of the proposed approach by the given numerical examples including one, three and twenty cells.
Fri, 01 Jul 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/220102022-07-01T00:00:00ZStudy on the interaction between a screw dislocation and circular holes or rigid inclusions by using the angular basis function in conjunction with bipolar coordinateshttp://scholars.ntou.edu.tw/handle/123456789/21855Title: Study on the interaction between a screw dislocation and circular holes or rigid inclusions by using the angular basis function in conjunction with bipolar coordinates
Authors: Chen, Jeng-Tzong; Kao, Shing-Kai; Tai, Wei-Chen; Lee, Ying-Te; Lee, Jia-Wei; Chou, Yen-Ting
Abstract: In this paper, the degenerate kernel in conjunction with the bipolar coordinates is employed to solve the anti-plane problems of interaction between a screw dislocation and circular holes or rigid inclusions. Once the degenerate kernel of the angular basis function (ABF) is provided in terms of the bipolar coordinates, the analytical solution for cases of one or two circular holes and rigid inclusions can be derived. Not only the radial basis function (RBF) but also the ABF is used. First, the observer objectivity of the degenerate kernel in terms of the bipolar coordinates is examined numerically. A special case, one circular hole or rigid inclusion, is considered to demonstrate the validity of the present approach. Finally, the cases containing two circular holes and two circular rigid inclusions were examined. The comparison between available results and ours is well done. Besides, for the solutions of two holes and rigid inclusions, it is interesting to find that the present method provides an analytical solution with a series form of explicitly determined coefficients, while the coefficients provided by the complex variable need to be determined using the recursive formulae.
Tue, 26 Apr 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/218552022-04-26T00:00:00ZSupport motion of a finite bar with an external springhttp://scholars.ntou.edu.tw/handle/123456789/21554Title: Support motion of a finite bar with an external spring
Authors: Chen, Jeng-Tzong; Kao, Hao-Chen; Lee, Ying-Te; Lee, Jia-Wei
Abstract: In this paper, we gave the vibration analysis of a finite bar with an external spring on one side and the support motion on the other side. Two analytical methods, the mode superposition method in conjunction with the quasi-static decomposition method and the method of characteristics using the diamond rule, were employed to solve this problem. Both advantages and disadvantages of two methods were discussed. It is interesting to find that the mode superposition method can capture the silent area in terms of sum of an infinite series while the method of characteristics using the diamond rule can exactly derive the dead zone. Besides, it is found that discontinuities always occur at the location on the characteristic lines. Discussions of direct and inverse problems are also addressed.
Fri, 22 Apr 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/215542022-04-22T00:00:00ZStudy on the double-degeneracy mechanism of BEM/BIEM for a plane elasticity problem with line segmentshttp://scholars.ntou.edu.tw/handle/123456789/21055Title: Study on the double-degeneracy mechanism of BEM/BIEM for a plane elasticity problem with line segments
Authors: Chen, Jeng-Tzong; Kao, Jeng-Hong; Kao, Shing-Kai; Lee, Ying-Te; Kuo, Shyh-Rong
Abstract: There are four degenerate problems by using the BEM/BIEM. Only the degenerate scale and degenerate boundary may appear at the same time. This is called double degeneracy. A double-degeneracy mechanism of BEM/BIEM for the plane elasticity problem with line segments is studied, and the degenerate scale is analytically examined and numerically performed. Different from the past result with complex variables, we propose a new idea to deal with the problem, and obtain the analytical solution of the degenerate scale. This analytical derivation can clearly show why the BEM/BIEM suffer the degenerate scale in the plane elasticity problem with the line segment. Only rigid inclusion faces this problem instead of the crack due to the use of single-layer kernel. Double degeneracy of degenerate boundary and degenerate scale in the BEM are numerically examined. The double degeneracy mechanism is clearly displayed through numerical results by showing the number of zero singular values in the influence matrix. Following the result of single line segment, we can extend to multiple line segments. Finally, the analytical and numerical results show consistency.
Tue, 01 Mar 2022 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/210552022-03-01T00:00:00ZA study on the degenerate scale by using the fundamental solution with dimensionless argument for 2D elasticity problemshttp://scholars.ntou.edu.tw/handle/123456789/1059Title: A study on the degenerate scale by using the fundamental solution with dimensionless argument for 2D elasticity problems
Authors: Jeng-Tzong Chen; Ying-Te Lee; Jia-Wei Lee; Sheng-Kuang Chen
Abstract: The influence matrix may be of deficient rank in the specified scale when we have solved the 2D elasticity problem by using the boundary element method (BEM). This problem stems from lnr in the 2D Kelvin solution. On the other hand, the single-layer integral operator can not represent the constant term for the degenerate scale in the boundary integral equation method (BIEM). To overcome this problem, we have proposed the enriched fundamental solution containing an adaptive characteristic length to ensure that the argument in the logarithmic function is dimensionless. The adaptive characteristic length, depending on the domain, differs from the constant base by adding a rigid body mode. In the analytical study, the degenerate kernel for the fundamental solution in polar coordinates is revisited. An adaptive characteristic length analytically provides the deficient constant term of the ordinary 2D Kelvin solution. In numerical implementation, adaptive characteristic lengths of the circular boundary, the regular triangular boundary and the elliptical boundary demonstrate the feasibility of the method. By employing the enriched fundamental solution in the BEM/BIEM, the results show the degenerate scale free.
Fri, 01 May 2020 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10592020-05-01T00:00:00ZSemi-analytical approach for torsion problems of a circular bar containing multiple holes and/or crackshttp://scholars.ntou.edu.tw/handle/123456789/1080Title: Semi-analytical approach for torsion problems of a circular bar containing multiple holes and/or cracks
Authors: Ying-Te Lee; Jeng-Tzong Chen; Shyh-Rong Kuo
Abstract: A semi-analytical approach of the null-field integral equation in conjunction containing the degenerate kernels is used to deal with the torsion problems of a circular bar with circular or elliptic holes and/or line cracks. In order to fully capture the elliptic geometry, the use of the addition theorem in terms of the elliptic coordinates plays an important role to expand the fundamental solution into the degenerate form. The boundary densities are expressed by using the eigenfunction expansion for the elliptic boundary. It is worthy of noting that the model of elliptic hole in companion with the limiting process of approaching the length of the semi-minor axis to zero is adopted to simulate the line crack. Besides, we also make the length of the semi-major axis close to the length of the semi-minor axis to approximate the circular boundary. By collocating the observation point exactly on the real boundary and matching the boundary conditions, a linear algebraic system is easily constructed to determine the unknown eigenfucntion coefficients. This approach can be seen as a semi-analytical manner since error purely attributes to the truncation of eigenfunction expansions and the convergence rate of exponential order is better than the linear order of the conventional boundary element method. Finally, several numerical examples of a circular bar with circular or elliptic holes and/or line cracks are employed to show the validity of the proposed approach. Not only the torsional rigidity but also the stress intensity factors are calculated to compare with the available results in the literature.
Tue, 01 Oct 2019 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10802019-10-01T00:00:00ZA self-regularized approach for rank-deficient systems in the BEM of 2D Laplace problemshttp://scholars.ntou.edu.tw/handle/123456789/1053Title: A self-regularized approach for rank-deficient systems in the BEM of 2D Laplace problems
Authors: Jeng-Tzong Chen; Ying-Te Lee; Yu-Lung Chang; Jie Jian
Abstract: The Laplace problem subject to the Dirichlet or Neumann boundary condition in the direct and indirect boundary element methods (BEM) sometimes both may result in a singular or ill-conditioned system (some special situations) for the interior problem. In this paper, the direct and indirect BEMs are revisited to examine the uniqueness of the solution by introducing the Fichera’s idea and the self-regularized technique. In order to construct the complete range of the integral operator in the BEM lacking a constant term in the case of a degenerate scale, the Fichera’s method is provided by adding the constraint and a slack variable to circumvent the problem of degenerate scale. We also revisit the Fredholm alternative theorem by using the singular value decomposition (SVD) in the discrete system and explain why the direct BEM and the indirect BEM are not indeed equivalent in the solution space. According to the relation between the SVD structure and Fichera’s technique, a self-regularized method is proposed in the matrix level to deal with non-unique solutions of the Neumann and Dirichlet problems which contain rigid body mode and degenerate scale, respectively, at the same time. The singularity and proportional influence matrices of 3 by 3 are studied by using the property of the symmetric circulant matrix. Finally, several examples are demonstrated to illustrate the validity and the effectiveness of the self-regularized method.
Sun, 01 Jan 2017 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10532017-01-01T00:00:00ZRevisit of degenerate scales in the BIEM/BEM for 2D elasticity problemshttp://scholars.ntou.edu.tw/handle/123456789/1047Title: Revisit of degenerate scales in the BIEM/BEM for 2D elasticity problems
Authors: Jeng-Tzong Chen; Wen-Sheng Huang; Ying-Te Lee; Shyh-Rong Kuo; Shing-Kai Kao
Abstract: The boundary integral equation method in conjunction with the degenerate kernel, the direct searching technique (singular value decomposition), and the only two-trials technique (2 × 2 matrix eigenvalue problem) are analytically and numerically used to find the degenerate scales, respectively. In the continuous system of boundary integral equation, the degenerate kernel for the 2D Kelvin solution in the polar coordinates is reviewed and the degenerate kernel in the elliptical coordinates is derived. Using the degenerate kernel, an analytical solution of the degenerate scales for the elasticity problem of circular and elliptical cases is obtained and compared with the numerical result. Further, the triangular case and square case were also numerically demonstrated.
Sun, 01 Jan 2017 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10472017-01-01T00:00:00ZA necessary and sufficient BEM/BIEM for two-dimensional elasticity problemshttp://scholars.ntou.edu.tw/handle/123456789/1046Title: A necessary and sufficient BEM/BIEM for two-dimensional elasticity problems
Authors: Jeng-Tzong Chen; Wen-Sheng Huang; Ying-Te Lee; Shing-Kai Kao
Abstract: It is well known that the patch test is required for the finite element method (FEM). We may wonder whether we need any special test for the boundary element method (BEM). A sufficient and necessary boundary integral equation method (BIEM) to ensure a unique solution is our concern. In this paper, we revisit this issue for the interior two-dimensional (2-D) elasticity problem and investigate the equivalence of the solution space between the integral equation and the partial differential equation. Based on the degenerate kernel and the eigenfunction expansion, the range deficiency of the integral operator for the solution space in the degenerate-scale problem for the 2-D elasticity in the BIEM is analytically studied. According to the Fichera׳s idea, we enrich the conventional BIEM by adding constants and corresponding constraints. In addition, we introduce the concept of modal participation factor (MPF) to examine whether the adding term of rotation is required for interior simply-connected problems. Finally, two simple examples of degenerate-scale problems containing circular and elliptical boundaries subjected to various boundary conditions of the rigid body translation and rotation for 2-D elasticity problems are demonstrated by using the necessary and sufficient BIEM.
Description: BEM/MRM 38 英國布羅肯赫斯特
Wed, 01 Jun 2016 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10462016-06-01T00:00:00ZGreen's Function Problem of Laplace Equation with Spherical and Prolate Spheroidal Boundaries by Using the Null-Field Boundary Integral Equationhttp://scholars.ntou.edu.tw/handle/123456789/1038Title: Green's Function Problem of Laplace Equation with Spherical and Prolate Spheroidal Boundaries by Using the Null-Field Boundary Integral Equation
Authors: Yu-Lung Chang; Ying-Te Lee; Li-Jie Jiang; Jeng-Tzong Chen
Abstract: A systematic approach of using the null-field integral equation in conjunction with the degenerate kernel and eigenfunction expansion is employed to solve three-dimensional (3D) Green’s functions of Laplace equation. The purpose of using degenerate kernels for interior and exterior expansions is to avoid calculating the principal values. The adaptive observer system is addressed to employ the property of degenerate kernels in the spherical coordinates and in the prolate spheroidal coordinates. After introducing the collocation points on each boundary and matching boundary conditions, a linear algebraic system is obtained without boundary discretization. Unknown coefficients can be easily determined. Finally, several examples are given to demonstrate the validity of the present approach.
Mon, 07 Mar 2016 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10382016-03-07T00:00:00ZA nonsingular boundary collocation method for the inverse problems in elasticityhttp://scholars.ntou.edu.tw/handle/123456789/18370Title: A nonsingular boundary collocation method for the inverse problems in elasticity
Authors: Ying-Te Lee; Chia-Ming Fan; Shyh-Rong Kuo
Thu, 01 Oct 2015 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/183702015-10-01T00:00:00ZNumerical Solutions of Two-dimensional Stokes Flows by the Boundary Knot Methodhttp://scholars.ntou.edu.tw/handle/123456789/1076Title: Numerical Solutions of Two-dimensional Stokes Flows by the Boundary Knot Method
Authors: Fan, CM; Huang, YK; Li, PW; Lee, YT
Abstract: In this paper, the boundary knot method (BKM) is adopted for accurately analyzing two-dimensional Stokes flows, dominated by viscous force and pressure gradient force. The Stokes flows, which denoted the flow fields with extremely viscous fluid or with very small velocity, appear in various engineering applications, such that it is very important to develop an efficient and accurate numerical method to solve the Stokes equations. The BKM, which can avoid the controversial fictitious boundary for sources, is an integral-free boundary-type meshless method and its solutions are expressed as linear combinations of non-singular general solutions for Stokes equations. The weighting coefficients in the solution expressions can be acquired by enforcing the satisfactions. of boundary conditions at every boundary node, since the non-singular general solutions are derived in this paper and already satisfied the Stokes equations. Three examples of two-dimensional Stokes flows. were adopted to validate the accuracy and the simplicity of the BKM. Besides, the optimal shape parameter in the non-singular general solutions was determined by examining the minimum average residual of the linear system from the BKM.
Wed, 01 Apr 2015 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10762015-04-01T00:00:00Z一種第一類Fredholm積分方程組解的存在唯一性充分必要條件http://scholars.ntou.edu.tw/handle/123456789/16694Title: 一種第一類Fredholm積分方程組解的存在唯一性充分必要條件
Authors: 韓厚德; 李應德; 殷東生; 陳正宗
Abstract: 本文研究由二維多連通區域上Laplace方程Dirichlet問題產生的第一類Fredholm積分方程組解的存在唯一性;引進了一個判別指標,它是可計算的;證明了第一類Fredholm積分方程組解的存在唯一性的充分必要條件為γN≠0;並通過數值例子驗證了本文的理論結果。
Thu, 01 Jan 2015 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/166942015-01-01T00:00:00ZFormulation of the MFS for the two-dimensional Laplace equation with an added constant and constrainthttp://scholars.ntou.edu.tw/handle/123456789/1073Title: Formulation of the MFS for the two-dimensional Laplace equation with an added constant and constraint
Authors: Jeng-Tzong Chen; Jheng-Lin Yang; Ying-Te Lee; Yu-Lung Chang
Abstract: Motivated by the incompleteness of single-layer potential approach for the interior problem with a degenerate-scale domain and the exterior problem with bounded potential at infinity, we revisit the method of fundamental solutions (MFS). Although the MFS is an easy method to implement, it is not complete for solving not only the interior 2D problem in case of a degenerate scale but also the exterior problem with bounded potential at infinity for any scale. Following Fichera׳s idea for the boundary integral equation, we add a free constant and an extra constraint to the traditional MFS. The reason why the free constant and extra constraints are both required is clearly explained by using the degenerate kernel for the closed-form fundamental solution. Since the range of the single-layer integral operator lacks the constant term in the case of a degenerate scale for a two dimensional problem, we add a constant to provide a complete base. Due to the rank deficiency of the influence matrix in the case of a degenerate scale, we can promote the rank by simultaneously introducing a constant term and adding an extra constraint to enrich the MFS. For an exterior problem, the fundamental solution does not contain a constant field in the degenerate kernel expression. To satisfy the bounded potential at infinity, the sum of all source strengths must be zero. The formulation of the enriched MFS can solve not only the degenerate-scale problem for the interior problem but also the exterior problem with bounded potential at infinity. Finally, three examples, a circular domain, an infinite domain with two circular holes and an eccentric annulus were demonstrated to see the validity of the enriched MFS.
Mon, 01 Sep 2014 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10732014-09-01T00:00:00ZTrue and Spurious Eigensolutions of an Elliptical Membrane by Using the Nondimensional Dynamic Influence Function Methodhttp://scholars.ntou.edu.tw/handle/123456789/1050Title: True and Spurious Eigensolutions of an Elliptical Membrane by Using the Nondimensional Dynamic Influence Function Method
Authors: Jeng-Tzong Chen; Jia-Wei Lee; Ying-Te Lee; Wen-Che Lee
Abstract: In this paper, we employ the nondimensional dynamic influence function (NDIF) method to solve the free vibration problem of an elliptical membrane. It is found that the spurious eigensolutions appear in the Dirichlet problem by using the double-layer potential approach. Besides, the spurious eigensolutions also occur in the Neumann problem if the single-layer potential approach is utilized. Owing to the appearance of spurious eigensolutions accompanied with true eigensolutions, singular value decomposition (SVD) updating techniques are employed to extract out true and spurious eigenvalues. Since the circulant property in the discrete system is broken, the analytical prediction for the spurious solution is achieved by using the indirect boundary integral formulation. To analytically study the eigenproblems containing the elliptical boundaries, the fundamental solution is expanded into a degenerate kernel by using the elliptical coordinates and the unknown coefficients are expanded by using the eigenfunction expansion. True and spurious eigenvalues are simultaneously found to be the zeros of the modified Mathieu functions of the first kind for the Dirichlet problem when using the single-layer potential formulation, while both true and spurious eigenvalues appear to be the zeros of the derivative of modified Mathieu function for the Neumann problem by using the double-layer potential formulation. By choosing only the imaginary-part kernel in the indirect boundary integral equation method (BIEM) to solve the eigenproblem of an elliptical membrane, spurious eigensolutions also appear at the same position with those of NDIF since boundary distribution can be lumped. The NDIF method can be seen as a special case of the indirect BIEM by lumping the boundary distribution. Both the analytical study and the numerical experiments match well with the same true and spurious solutions.
Tue, 01 Apr 2014 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10502014-04-01T00:00:00ZNull-field integral approach for the piezoelectricity problems with multiple elliptical inhomogeneitieshttp://scholars.ntou.edu.tw/handle/123456789/1079Title: Null-field integral approach for the piezoelectricity problems with multiple elliptical inhomogeneities
Authors: Ying-Te Lee; Jeng-Tzong Chen; Shyh-Rong Kuo
Abstract: Based on the successful experience of solving anti-plane problems containing multiple elliptical inclusions, we extend to deal with the piezoelectricity problems containing arbitrary elliptical inhomogeneities. In order to fully capture the elliptical geometry, the keypoint of the addition theorem in terms of the elliptical coordinates is utilized to expand the fundamental solution to the degenerate kernel and boundary densities are simulated by the eigenfunction expansion. Only boundary nodes are required instead of boundary elements. Therefore, the proposed approach belongs to one kind of meshless and semi-analytical methods. Besides, the error stems from the number of truncation terms of the eigenfunction expansion and the convergence rate of exponential order is better than the linear order of the conventional boundary element method. It is worth noting that there are Jacobian terms in the degenerate kernel, boundary density and contour integral. However, they would cancel each other out in the process of the boundary contour integral. As the result, the orthogonal property of eigenfunction is preserved and the boundary integral can be easily calculated. For verifying the validity of the present method, the problem of an elliptical inhomogeneity in an infinite piezoelectric material subject to anti-plane shear and in-plane electric field is considered to compare with the analytical solution in the literature. Besides, two circular inhomogenieties can be seen as a special case to compare with the available data by approximating the major and minor axes. Finally, the problem of two elliptical inhomogeneities in an infinite piezoelectric material is also provided in this paper.
Sat, 01 Feb 2014 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10792014-02-01T00:00:00ZStudy on harbor resonance and focusing by using the null-field BIEMhttp://scholars.ntou.edu.tw/handle/123456789/1051Title: Study on harbor resonance and focusing by using the null-field BIEM
Authors: Jeng-Tzong Chen; Jia-Wei Lee; Chine-Feng Wu; Ying-Te Lee
Abstract: In this paper, the resonance of a circular harbor is studied by using the semi-analytical approach. The method is based on the null-field boundary integral equation method in conjunction with degenerate kernels and the Fourier series. The problem is decomposed into two regions by employing the concept of taking free body. One is a circular harbor, and the other is a problem of half-open sea with a coastline subject to the impermeable (Neumann) boundary condition. It is interesting to find that the SH wave impinging on the hill can be formulated by the same mathematical model. After finding the analogy between the harbor resonance and hill scattering, focusing of the water wave inside the harbor as well as focusing in the hill scattering are also examined. Finally, two numerical examples, circular harbor problems of 60° and 180° opening entrance, are both used to verify the validity of the present formulation.
Mon, 01 Jul 2013 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10512013-07-01T00:00:00ZNull-field integral approach for the piezoelectricity problems with arbitrary elliptical inhomogeneitieshttp://scholars.ntou.edu.tw/handle/123456789/16750Title: Null-field integral approach for the piezoelectricity problems with arbitrary elliptical inhomogeneities
Authors: Ying-Te Lee; Jeng-Tzong Chen; Shyh-Rong Kuo
Abstract: Based on the successful experience of solving anti-plane problems containing arbitrary elliptical inclusions, we extend to deal with the piezoelectricity problems containing arbitrary elliptical inhomogeneities. In order to fully capture the elliptical geometry, the keypoint of the addition theorem in terms of the elliptical coordinates is utilized to expand the fundamental solution to the degenerate kernel and boundary densities are simulated by the eigenfunction expansion. Only boundary nodes are required instead of boundary elements. Therefore, the proposed approach belongs to one kind of meshless and semi-analytical methods. Besides, the error stems from the number of truncation terms of the eigenfuntion expansion and the convergence rate of exponential
order is better than the linear order of the conventional boundary element method. It is worth noting that there are Jacobian terms in the degenerate kernel, boundary density and contour integral. However, they would cancel each other out in the process of the boundary contour integral. As the result, the orthogonal property of eigenfunction is preserved and the boundary integral can be easily calculated. Finally, the problem of two elliptical inhomogeneities in an infinite piezoelectric material subject to anti-plane remote shear and in-plane electric field is considered to demonstrate the validity of the present method. Besides, two circular inhomegenieties can be seen as a special case to compare with the available data by approximating the major and minor axes.
Description: 13th International Conference on Fracture, June 16–21, 2013, Beijing, China
Sun, 16 Jun 2013 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/167502013-06-16T00:00:00ZON THE TRUE AND SPURIOUS EIGENVALUES BY USINGTHE REAL OR THE IMAGINARY-PART OF THE METHODOF FUNDAMENTAL SOLUTIONShttp://scholars.ntou.edu.tw/handle/123456789/1039Title: ON THE TRUE AND SPURIOUS EIGENVALUES BY USINGTHE REAL OR THE IMAGINARY-PART OF THE METHODOF FUNDAMENTAL SOLUTIONS
Authors: Chen, I. L.; Ying-Te Lee; Kuo, P. S.; Jeng-Tzong Chen
Abstract: In this paper, the method of fundamental solutions (MFS) of real-part or imaginary-part kernels is employed to solve two-dimensional eigenproblems. The occurring mechanism of spurious eigenvalues for circular and elliptical membranes is examined. It is found that the spurious eigensolution using the MFS depends on the location of the fictitious boundary where the sources are distributed. By employing the singular value decomposition technique, the common left unitary vectors of the true eigenvalue for the single- and double-layer potential approaches are found while the common right unitary vectors of the spurious eigenvalue are obtained. Dirichlet and Neumann eigenproblems are both considered. True eigenvalues are dependent on the boundary condition while spurious eigenvalues are different in the different approach, single-layer or double-layer potential MFS. Two examples of circular and elliptical membranes are numerically demonstrated to see the validity of the present method and the results are compared well with the theoretical prediction.
Tue, 08 Jan 2013 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10392013-01-08T00:00:00ZNull-field approach for the antiplane problem with elliptical holes and/or inclusionshttp://scholars.ntou.edu.tw/handle/123456789/1078Title: Null-field approach for the antiplane problem with elliptical holes and/or inclusions
Authors: Ying-Te Lee; Jeng-Tzong Chen
Abstract: In this paper, we extend the successful experience of solving an infinite medium containing circular holes and/or inclusions subject to remote shears to deal with the problem containing elliptical holes and/or inclusions. Arbitrary location, different orientation, various size and any number of elliptical holes and/or inclusions can be considered. By fully employing the elliptical geometry, fundamental solutions were expanded into the degenerate kernel by using an addition theorem in terms of the elliptic coordinates and boundary densities are described by using the eigenfunction expansion. The difference between the proposed method and the conventional boundary integral equation method is that the location point can be exactly distributed on the real boundary without facing the singular integral and calculating principal value. Besides, the boundary stress can be easily calculated free of the Hadamard principal values. It is worthy of noting that the Jacobian terms exist in the degenerate kernel, boundary density and contour integral; however, these Jacobian terms would cancel each other out and the orthogonal property is preserved in the process of contour integral. This method belongs to one kind of meshless methods since only collocation points on the real boundary are required. In addition, the solution is regarded as semi-analytical form because error purely attributes to the number of truncation term of eigenfunction. An exact solution for a single elliptical inclusion is also derived by using the proposed approach and the results agree well with Smith’s solutions by using the method of complex variables. Several examples are revisited to demonstrate the validity of our method.
Tue, 01 Jan 2013 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10782013-01-01T00:00:00ZOn null fields in the BIEM/BEMhttp://scholars.ntou.edu.tw/handle/123456789/16736Title: On null fields in the BIEM/BEM
Authors: Jeng-Tzong Chen; Ying-Te Lee; Jia-Wei Lee; I-Lin Chen
Abstract: eview of the BEM and BIEM development in Taiwan in the past thirty years is introduced in the beginning (by the personal point of view). Besides, the current status of EABE journal is reported (on behalf of an associate editor). Then, the recent advances by NTOU/MSV group for null fields in the BIEM/BEM are addressed (as a head of this group). Solvability of integral equations as well as
nonuniqueness occurs in the BIEM/BEM for boundary value problems containing degenerate scale, degenerate boundary, spurious eigenvalue and
fictitious frequency. By employing the SVD technique with respect to the four influence matrices in the dual BEM, the degenerate mechanism can be studied in a unified manner. True information in physics due to rigid body mode and true eigensolution are found in the right unitary vector with respect to the corresponding zero singular value while the spurious information in mathematics due to degenerate boundary, degenerate scale, spurious eigenvalue and fictitious frequency is imbedded in the left unitary vector. The SVD updating term is employed to extract the true information while the SVD updating document is utilized to filter out the spurious information. Null field and nonzero field in the complementary domain for the ordinary case and
irregular case, respectively, are emphasized. Treatment to ensure the unique solution is also examined. Several examples including degenerate scale, spurious
eigenvalue and fictitious frequency are demonstrated to examine null fields.
Description: ICOME2012/JASCOME2012, 12-14 December, Kyoto, Japan
Wed, 12 Dec 2012 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/167362012-12-12T00:00:00ZAnalytical derivation and numerical experiments of degenerate scale for an ellipse in BEMhttp://scholars.ntou.edu.tw/handle/123456789/1057Title: Analytical derivation and numerical experiments of degenerate scale for an ellipse in BEM
Authors: Jeng-Tzong Chen; Ying-Te Lee; Shyh-Rong Kuo; Yi-Wei Chen
Abstract: Degenerate scale of an ellipse is studied by using the dual boundary element method (BEM), degenerate kernel and unit logarithmic capacity. Degenerate scale stems from either the nonuniqueness of logarithmic kernel in the BIE or the conformal radius of unit logarithmic capacity in the complex variable. Numerical evidence of degenerate scale in BEM is given. Analytical formula for the degenerate scale can be derived not only from the conformal mapping in conjunction with unit logarithmic capacity, but also can be derived by using the degenerate kernel. Eigenvalues and eigenfunctions for the weakly singular integral operator in the elliptical domain are both derived by using the degenerate kernel. It is found that zero eigenvalue results in the degenerate scale. Based on the dual BEM, the rank-deficiency (mathematical) mode due to the degenerate scale is imbedded in the left unitary vector for weakly singular and strongly singular integral operators. On the other hand, we obtain the common right unitary vector of a rigid body (physical) mode in the influence matrices of strongly singular and hypersingular operators after using the singular value decomposition. Null field for the exterior domain and interior nonzero fields are analytically derived and numerically verified in case of the normal scale while the interior null field and nonzero exterior field are obtained for the homogeneous Dirichlet problem in case of the degenerate scale. No failure CHEEF point is confirmed in the nonzero exterior field to overcome the degenerate-scale problem. To deal with the nonuniqueness-solution problem, the constraint of boundary flux equilibrium instead of rigid body term, CHEEF and hypersingular BIE, is added to promote the rank of influence matrices to be full rank. Both analytical and numerical results agree well in the demonstrative example of an ellipse.
Sat, 01 Sep 2012 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10572012-09-01T00:00:00ZStudy on connections of the MFS, Trefftz method, indirect BIEM and invariant MFS in the three-dimensional Laplace problems containing spherical boundarieshttp://scholars.ntou.edu.tw/handle/123456789/1070Title: Study on connections of the MFS, Trefftz method, indirect BIEM and invariant MFS in the three-dimensional Laplace problems containing spherical boundaries
Authors: Jeng-Tzong Chen; Jhen-Jyun Tsai; Ying-Te Lee; Jia-Wei Lee
Abstract: Following the success of a study on the method of fundamental solutions using an image concept [13], we extend to solve the three-dimensional Laplace problems containing spherical boundaries by using the three approaches. The case of eccentric sphere for the Laplace problem is considered. The optimal locations for the source distribution to include the foci in the MFS are also examined by using the image concept in the 3D problems. Whether a free constant is required or not in the MFS is also studied. The error distribution is discussed after comparing with the analytical solution derived by using the bispherical coordinates. Besides, the relationship between the Trefftz bases and the singularity in the MFS for the three-dimensional Laplace problems is also addressed. It is found that one source of the MFS contains several interior and exterior Trefftz sets through a degenerate kernel. On the contrary, one single Trefftz base can be superimposed by some lumped sources in the MFS through an indirect BIEM. Based on this finding, the relationship between the fictitious boundary densities of the indirect BIEM and the singularity strength in the MFS can be constructed due to the fact that the MFS is a lumped version of an indirect BIEM.
Thu, 01 Dec 2011 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10702011-12-01T00:00:00ZScattering of Sound from Point Sources by Multiple Circular Cylinders Using Addition Theorem and Superposition Techniquehttp://scholars.ntou.edu.tw/handle/123456789/1062Title: Scattering of Sound from Point Sources by Multiple Circular Cylinders Using Addition Theorem and Superposition Technique
Authors: Jeng-Tzong Chen; Ying-Te Lee; Yi‐Jhou Lin; I‐Lin Chen; Jia‐Wei Lee
Abstract: In this study, we use the addition theorem and superposition technique to solve the scattering problem with multiple circular cylinders arising from point sound sources. Using the superposition technique, the problem can be decomposed into two individual parts. One is the free‐space fundamental solution. The other is a typical boundary value problem (BVP) with specified boundary conditions derived from the addition theorem by translating the fundamental solution. Following the success of null‐field boundary integral formulation to solve the typical BVP of the Helmholtz equation with Fourier densities, the second‐part solution is easily obtained after collocating the observation point exactly on the real boundary and matching the boundary condition. The total solution is obtained by superimposing the two parts which are the fundamental solution and the semianalytical solution of the Helmholtz problem. An example was demonstrated to validate the present approach. The parameter study of size and spacing between cylinders are addressed. The results are well compared with the available theoretical solutions and experimental data.
Tue, 01 Nov 2011 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10622011-11-01T00:00:00ZA novel method for solving the displacement and stress fields of an infinite domain with circular holes and/or inclusions subject to a screw dislocationhttp://scholars.ntou.edu.tw/handle/123456789/1044Title: A novel method for solving the displacement and stress fields of an infinite domain with circular holes and/or inclusions subject to a screw dislocation
Authors: Jeng-Tzong Chen; K. H. Chou; Ying-Te Lee
Abstract: In this paper, the degenerate kernel and superposition technique are employed to solve the screw dislocation problems with circular holes or inclusions. The problem is decomposed into the screw dislocation problem with several holes and the interior Laplace problems for several circular inclusions. Following the success of the null-field integral equation approach, the typical boundary value problems can be solved easily. The kernel functions and unknown boundary densities are expanded by using the degenerate kernel and Fourier series, respectively. To the authors’ best knowledge, the angle-type fundamental solution is first derived in terms of degenerate kernel in this paper. Finally, four examples are demonstrated to verify the validity of the present approach.
Fri, 01 Apr 2011 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10442011-04-01T00:00:00ZBipolar coordinates, image method and the method of fundamental solutions for Green's functions of Laplace problems containing circular boundarieshttp://scholars.ntou.edu.tw/handle/123456789/1069Title: Bipolar coordinates, image method and the method of fundamental solutions for Green's functions of Laplace problems containing circular boundaries
Authors: Jeng-Tzong Chen; Shieh, H. C.; Ying-Te Lee; Lee, J. W.
Abstract: Green’s functions of Laplace problems containing circular boundaries are solved by using analytical and semi-analytical approaches. For the analytical solution, we derive the Green’s function using the bipolar coordinates. Based on the semi-analytical approach of image method, it is interesting to find that the two frozen images for the eccentric annulus using the image method are located on the two foci in the bipolar coordinates. This finding also occurs for the cases of a half plane with a circular hole and an infinite plane containing two circular holes. The image method can be seen as a special case of the method of fundamental solutions, which only at most four unknown strengths are required to be determined. The optimal locations of sources in the method of fundamental solutions can be captured using the image method and they are dependent on the source location and the geometry of problems. Three illustrative examples were demonstrated to verify this point. Results are satisfactory.
Tue, 01 Feb 2011 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10692011-02-01T00:00:00ZWater wave interaction with surface-piercing porous cylinders using the null-field integral equationshttp://scholars.ntou.edu.tw/handle/123456789/1067Title: Water wave interaction with surface-piercing porous cylinders using the null-field integral equations
Authors: Jeng-Tzong Chen; Lin, Y. J.; Ying-Te Lee; Wu, C. F.
Abstract: Following the successful experiences of solving water wave scattering problems for multiple impermeable cylinders by the authors' group, we extend the null-field integral formulation in conjunction with the addition theorem and the Fourier series to deal with the problems of surface-piercing porous cylinders in this paper. In the implementation, the null-field point can be exactly located on the real boundary free of calculating the Cauchy and Hadamard principal values, thanks to the introduction of degenerate kernels (or separable kernels) for fundamental solutions. This method is a semi-analytical approach, since errors attribute from the truncation of the Fourier series. Not only a systematic approach is proposed but also the effect on the near-trapped modes due to porous cylinders and disorder of layout is examined. Several advantages such as mesh-free generation, well-posed model, principal value free, elimination of boundary-layer effect and exponential convergence, over the conventional boundary element method (BEM) are achieved. It is found that the disorder has more influence to suppress the occurrence of near-trapped modes than the porosity. The free-surface elevation is consistent with the results of William and Li and those using the conventional BEM. Besides, the numerical results of the force on the surface of cylinders agree well with those of William and Li. Besides, the present method is a semi-analytical approach for problems containing circular and elliptical shapes at the same time.
Tue, 01 Feb 2011 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10672011-02-01T00:00:00ZFree vibration analysis of a finite bar with an external springhttp://scholars.ntou.edu.tw/handle/123456789/16815Title: Free vibration analysis of a finite bar with an external spring
Authors: Yin-Hsiang Hsu; Jia-Wei Lee; Ying-Te Lee; Jeng-Tzong Chen
Abstract: In this paper, we study the free vibration of a finite bar with an external spring. Several methods, including the method of separation variables, the finite element method (FEM) and the approach of diamond rule, are employed to solve this problem. Two analytical solutions are derived by using the approach of diamond rule and the method of separation variables. A numerical solution by
using the FEM is also provided for comparison. Advantages and disadvantages of each method are addressed. It is found that the approach of diamond rule
can satisfy the causality condition, while the other two disobey. Besides, the Gibbs phenomenon occurs in the two series-based solutions obtained by the method of separation variables and mode superposition using the FEM. 本文使用分離變數法、有限元素法與鑽石法則來求解有限桿加邊彈簧的自由振動經典問題。文中分別以鑽石法則以及分離變數法推導出解析解，其結果與有限元素法的數值結果做比較，並討論各方法間的優劣性。我們發現鑽石法則滿足因果律，其它兩方法會違背此規律；此外，由於使用有限元素法中的模態疊加與分離變數法，可以從結果觀察到吉布斯現象。
Description: 國立雲林科技大學, November 19-20, 2010
Fri, 19 Nov 2010 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/168152010-11-19T00:00:00ZAnalysis of mutiple-shepers radiation and scattering problems by using a null-field integral equation approachhttp://scholars.ntou.edu.tw/handle/123456789/1061Title: Analysis of mutiple-shepers radiation and scattering problems by using a null-field integral equation approach
Authors: Jeng-Tzong Chen; Ying-Te Lee; Yi-Jhou Lin
Abstract: A systematic approach using the null-field integral equation in conjunction with the degenerate kernel is employed to solve the multiple radiation and scattering problems. Our approach can avoid calculating the principal values of singular and hypersingular integrals. Although we use the idea of null-field integral equation, we can locate the point on the real boundary thanks to the degenerate kernel. The proposed approach is seen as one kind of semi-analytical methods, since the error is attributed from the truncation of spherical harmonics. Finally, the numerical examples including one and two spheres are given to verify the validity of proposed approach.
Sun, 01 Aug 2010 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10612010-08-01T00:00:00ZImage solutions for boundary value problems without sourceshttp://scholars.ntou.edu.tw/handle/123456789/1068Title: Image solutions for boundary value problems without sources
Authors: Jeng-Tzong Chen; Hung-Chih Shieh; Ying-Te Lee; Jia-Wei Lee
Abstract: In this paper, we employ the image method to solve boundary value problems in domains containing circular or spherical shaped boundaries free of sources. two and threeD problems as well as symmetric and anti-symmetric cases are considered. By treating the image method as a special case of method of fundamental solutions, only at most four unknown strengths, distributed at the center, two locations of frozen images and one free constant, need to be determined. Besides, the optimal locations of sources are determined. For the symmetric and anti-symmetric cases, only two coefficients are required to match the two boundary conditions. The convergence rate versus number of image group is numerically performed. The differences of the image solutions between 2D and 3D problems are addressed. It is found that the 2D solution in terms of the bipolar coordinates is mathematically equivalent to that of the simplest MFS with only two sources and one free constant. Finally, several examples are demonstrated to see the validity of the image method for boundary value problems.
Sat, 01 May 2010 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10682010-05-01T00:00:00ZEigensolutions of the Helmholtz equation for a multiply connected domain with circular boundaries using the multipole Trefftz methodhttp://scholars.ntou.edu.tw/handle/123456789/1048Title: Eigensolutions of the Helmholtz equation for a multiply connected domain with circular boundaries using the multipole Trefftz method
Authors: Jeng-Tzong Chen; Kao, S. K.; Lee, W. M.; Ying-Te Lee
Abstract: In this paper, 2D eigenproblems with the multiply connected domain are studied by using the multipole Trefftz method. We extend the conventional Trefftz method to the multipole Trefftz method by introducing the multipole expansion. The addition theorem is employed to expand the Trefftz bases to the same polar coordinates centered at one circle, where boundary conditions are specified. Owing to the introduction of the addition theorem, collocation techniques are not required to construct the linear algebraic system. Eigenvalues and eigenvectors can be found at the same time by employing the singular value decomposition (SVD). To deal with the eigenproblems, the present method is free of pollution of spurious eigenvalues. Both the eigenvalues and eigenmodes compare well with those obtained by analytical methods and the BEM as shown in illustrative examples.
Sat, 01 May 2010 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10482010-05-01T00:00:00ZTorsional rigidity of an elliptic bar with multiple elliptic inclusions using a null-field integral approachhttp://scholars.ntou.edu.tw/handle/123456789/1058Title: Torsional rigidity of an elliptic bar with multiple elliptic inclusions using a null-field integral approach
Authors: Jeng-Tzong Chen; Ying-Te Lee; Jia-Wei Lee
Abstract: Following the success of using the null-field integral approach to determine the torsional rigidity of a circular bar with circular inhomogeneities (Chen and Lee in Comput Mech 44(2):221–232, 2009), an extension work to an elliptic bar containing elliptic inhomogeneities is done in this paper. For fully utilizing the elliptic geometry, the fundamental solutions are expanded into the degenerate form by using the elliptic coordinates. The boundary densities are also expanded by using the Fourier series. It is found that a Jacobian term may exist in the degenerate kernel, boundary density or boundary contour integral and cancel out to each other. Null-field points can be exactly collocated on the real boundary free of facing the principal values using the bump contour approach. After matching the boundary condition, a linear algebraic system is constructed to determine the unknown coefficients. An example of an elliptic bar with two inhomogeneities under the torsion is given to demonstrate the validity of the present approach after comparing with available results.
Sun, 11 Apr 2010 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10582010-04-11T00:00:00ZOn the spurious eigenvalues for a concentric sphere in BIEMhttp://scholars.ntou.edu.tw/handle/123456789/1049Title: On the spurious eigenvalues for a concentric sphere in BIEM
Authors: Jeng-Tzong Chen; Shing-Kai Kao; Ying-Te Lee; Yi-Jhou Lin
Abstract: In this paper, the null-field integral equation method is employed to study the occurring mechanism of spurious eigenvalues for a concentric sphere. By expanding the fundamental solution into degenerate kernels and expressing the boundary density in terms of spherical harmonics, all boundary integrals can be analytically determined. It is noted that our null-field integral formulation can locate the collocation point on the real boundary thanks to the degenerate kernel. In addition, the spurious eigenvalues are parasitized in the formulations while true eigensolutions are dependent on the boundary condition such as the Dirichlet or Neumann problem. By using the updating term and updating document of singular value decomposition (SVD) technique, true and spurious eigenvalues can be extracted out, respectively. Besides, true and spurious boundary eigenvectors are obtained in the right and left unitary vectors in the SVD structure of the influence matrices. This finding agrees with that of 2D cases.
Mon, 01 Mar 2010 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10492010-03-01T00:00:00ZImage Location for Screw Dislocation-A New Point of Viewhttp://scholars.ntou.edu.tw/handle/123456789/1056Title: Image Location for Screw Dislocation-A New Point of View
Authors: Jeng-Tzong Chen; Ying-Te Lee; Ke-Hsun Chou; Jia-Wei Lee
Abstract: An infinite plane problem with a circular boundary under the screw dislocation is solved by using a new method. The angle-based fundamental solution for screw dislocation is expanded into degenerate kernel. Our method can explain why the image screw dislocation is required. Besides, the location of the image point can be obtained easily by using degenerate kernel after satisfying boundary conditions. Even though the image concept is required, the location of image point can be determined straightforwardly through the degenerate kernel instead of the method of reciprocal radii. Finally, two examples are demonstrated to verify the validity of the present method.
Fri, 01 Jan 2010 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10562010-01-01T00:00:00ZTrapping and near-trapping by arrays of cylinders in water waves using the addition theorem and superposition techniquehttp://scholars.ntou.edu.tw/handle/123456789/16726Title: Trapping and near-trapping by arrays of cylinders in water waves using the addition theorem and superposition technique
Authors: Yi-Jhou Lin; Ying-Te Lee; Jeng-Tzong Chen
Abstract: In this paper, we employ the addition theorem and superposition technique to examine the trapped mode of water wave problems. The scattering of water waves by arrays of vertical circular cylinders is solved by using the null-field integral equations in conjunction with degenerate kernels and Fourier series to avoid calculating the Cauchy and Hadamard principal values. In the implementation, the null-field point can be exactly located on the real boundary free of principalvalue calculation using bump contour owing to the introduction of degenerate kernels for fundamental solutions. This method can be seen as a semi-analytical approach since errors attribute from the truncation of Fourier series. The physical-resonance phenomena of near-trapped modes are our concern. Several examples are given to demonstrate the validity of the proposed approach.
Description: 第二屆兩岸船舶、海洋工程及環境工程水動力學研討會(CSHydro2009)
October 12-17, 2009 台灣海洋大學(NTOU), 基隆
Mon, 12 Oct 2009 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/167262009-10-12T00:00:00ZTrapping and near-trapping by arrays of porous cylinders in water waves using the addition theorem and superposition techniquehttp://scholars.ntou.edu.tw/handle/123456789/16871Title: Trapping and near-trapping by arrays of porous cylinders in water waves using the addition theorem and superposition technique
Authors: Yi-Jhou Lin; Ying-Te Lee; Jia-Wei Lee; Jeng-Tzong Chen
Abstract: Following the successful experiences of solving water-wave scattering problems for multiple impermeable cylinders, we extend the null-field integral formulation to deal with the problems of surface-piercing porous cylinders in this paper. The null-field integral equations in conjunction with the addition theorem and Fourier series are employed to solve the water-wave problem. In the implementation, the null-field point can be exactly located on the real boundary free of calculating the Cauchy and Hadamard principal values thanks to the introduction of degenerate kernels for fundamental solutions. This method can be seen as a semi-analytical approach since errors attribute from the truncation of Fourier series. Not only a systematic approach is proposed but also the effect on the near-trapped modes due to porous cylinders and disorder of layout is examined. It is found that the disorder is more sensitive to suppress the occurrence of near-trapped modes than the porosity. The free-surface elevation is consistent with the results of William and Li and those by using the conventional BEM. Besides, the numerical results of the force on the surface of cylinders agree well with those in the literature.
Description: 礁溪, Yilan, July, 2009
Fri, 31 Jul 2009 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/168712009-07-31T00:00:00ZRevisit of two classical elasticity problems by using the Trefftz methodhttp://scholars.ntou.edu.tw/handle/123456789/1063Title: Revisit of two classical elasticity problems by using the Trefftz method
Authors: Jeng-Tzong Chen; Ying-Te Lee; Shieh, S. C.
Abstract: In this paper, the two classical elasticity cases, Lamé problem and stress concentration factor (SCF), are revisited by using the Trefftz method instead of the inverse or semi-inverse approach in the previous study. First, the Timoshenko and Goodier's approach is reviewed. Based on the superposition principle and the concept of taking free body, the problem of stress concentration factor as well as Lamé problem can be solved without any difficulty in a direct way using the Trefftz method.
Mon, 01 Jun 2009 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10632009-06-01T00:00:00ZEquivalence between the Trefftz method and the method of fundamental solution for the annular Green's function using the addition theorem and image concepthttp://scholars.ntou.edu.tw/handle/123456789/1064Title: Equivalence between the Trefftz method and the method of fundamental solution for the annular Green's function using the addition theorem and image concept
Authors: Jeng-Tzong Chen; Ying-Te Lee; Shang-Ru Yu; Shiang-Chih Shieh
Abstract: In this paper, the Green's function for the annular Laplace problem is first derived by using the image method which can be seen as a special case of method of fundamental solutions. Three cases, fixed–fixed, fixed–free and free–fixed boundary conditions are considered. Also, the Trefftz method is employed to derive the analytical solution by using T-complete sets. By employing the addition theorem, both solutions are found to be mathematically equivalent when the number of Trefftz base and the number of image points are both infinite. On the basis of the same number of degrees of freedom, the convergence rate of both methods is compared with each other. In the successive image process, the final two images freeze at the origin and infinity, where their singularity strengths can be analytically and numerically determined in a consistent manner.
Fri, 01 May 2009 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10642009-05-01T00:00:00ZInteraction of water waves with vertical cylinders using null-field integral equationshttp://scholars.ntou.edu.tw/handle/123456789/1060Title: Interaction of water waves with vertical cylinders using null-field integral equations
Authors: Jeng-Tzong Chen; Ying-Te Lee; Yi-Jhou Lin
Abstract: The scattering of water waves by bottom-mounted vertical circular cylinders is solved by using the null-field integral equations in conjunction with degenerate kernels and Fourier series to avoid calculating the Cauchy and Hadamard principal values. In the implementation, the null-field point can be exactly located on the real boundary owing to the introduction of degenerate kernels for fundamental solutions. An adaptive observer system of polar coordinates is considered to fully employ the properties of degenerate kernels. For the hypersingular equation, vector decomposition for the radial and tangential gradients is carefully considered. This method can be seen as a semi-analytical approach since errors attribute from the truncation of Fourier series. Neither hypersingularity in the Burton and Miller approach nor the CHIEF concept was required to deal with the problem of irregular frequencies. Five advantages of free of calculating principal value, well-posed algebraic system, convergence rate of exponential order, meshfree and elimination of boundary-layer effect, are achieved by using the present approach. Numerical results are given for the forces and free-surface elevation around the circular boundaries. Also, the near-trapped behavior arisen from the physical resonance is detected. A general-purpose program for water wave impinging several circular cylinders with arbitrary number, radii, and positions was developed. Several examples of water wave structure interaction by vertical circular cylinders were demonstrated to see the validity of the present formulation.
Wed, 01 Apr 2009 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10602009-04-01T00:00:00ZTorsional rigidity of a circular bar with multiple circular inclusions using the null-field integral approachhttp://scholars.ntou.edu.tw/handle/123456789/1052Title: Torsional rigidity of a circular bar with multiple circular inclusions using the null-field integral approach
Authors: Jeng-Tzong Chen; Ying-Te Lee
Abstract: In this article, a systematic approach is proposed to calculate the torsional rigidity and stress of a circular bar containing multiple circular inclusions. To fully capture the circular geometries, the kernel function is expanded to the degenerate form and the boundary density is expressed into Fourier series. The approach is seen as a semi-analytical manner since error purely attributes to the truncation of Fourier series. By collocating the null-field point exactly on the real boundary and matching the boundary condition, a linear algebraic system is obtained. Convergence study shows that only a few number of Fourier series terms can yield acceptable results. Finally, torsion problems are revisited to check the validity of our method. Not only the torsional rigidities but also the stresses of multiple inclusions are also obtained by using the present approach.
Tue, 10 Feb 2009 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10522009-02-10T00:00:00ZA Semi-Analytical Approach for Boundary Value Problems with Circular Boundarieshttp://scholars.ntou.edu.tw/handle/123456789/16485Title: A Semi-Analytical Approach for Boundary Value Problems with Circular Boundaries
Authors: Jeng-Tzong Chen; Ying-Te Lee; Wei-Ming Lee
Abstract: In this paper, a semi-analytical approach is developed to deal with problems including multiple circular boundaries. The boundary integral approach is utilized in conjunction with degenerate kernel and Fourier series. To fully utilize the circular geometry, the fundamental solutions and the boundary densities are expanded by using degenerate kernels and Fourier series, respectively. Both direct and indirect formulations are proposed. This approach is a semi-analytical approach, since the error stems from the truncation of Fourier series in the implementation. The unknown Fourier coefficients are easily determined by solving a linear algebraic system after using the collocation method and matching the boundary conditions. Five goals: (1) free of calculating principal value, (2) exponential convergence, (3) well-posed algebraic system, (4) elimination of boundary-layer effect and (5) meshless, of the formulation are achieved. The proposed approach is extended to deal with the problems containing multiple circular inclusions. Finally, the general-purpose program in a unified manner is developed for BVPs with circular boundaries. Several examples including the torsion bar, water wave and plate vibration problems are given to demonstrate the validity of the present approach.
Thu, 01 Jan 2009 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/164852009-01-01T00:00:00ZScattering of sound from point sources by multiple circular cylinders using addition theorem and superposition techniquehttp://scholars.ntou.edu.tw/handle/123456789/16801Title: Scattering of sound from point sources by multiple circular cylinders using addition theorem and superposition technique
Authors: Yi-Jhou Lin; Ying-Te Lee; I-Lin Chen; Jeng-Tzong Chen
Abstract: In this paper, we employ the addition theorem and superposition technique to solve the scattering problem with multiple circular cylinders arising from a point
sound source. Using the superposition technique, the problem can be decomposed into two individual parts. One is the free-space fundamental solution. The other is a typical boundary value problem (BVP) with boundary
conditions derived from the addition theorem by translating the fundamental solution. Following the success of null-field boundary integral formulation to
solve the typical BVP of the Helmholtz equation with Fourier boundary densities, the second-part solution can be easily obtained after collocating the observation point exactly on the real boundary and matching the boundary
condition. The total solution is obtained by superimposing the two parts which are the fundamental solution and the semi-analytical solution of the Helmholtz problem. An example was demonstrated to validate of the present approach. The parameters of size and spacing between cylinders are considered. The
results are well compared with the available theoretical solutions and experimental data.
Description: 國立中正大學機械工程學系, November 28-29, 2008
Fri, 28 Nov 2008 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/168012008-11-28T00:00:00ZOn the spurious eigenvalues for a concentric sphere in BIEMhttp://scholars.ntou.edu.tw/handle/123456789/16802Title: On the spurious eigenvalues for a concentric sphere in BIEM
Authors: Shang-Kai Kao; Ying-Te Lee; Jia-Wei Lee; Jeng-Tzong Chen
Abstract: Researchers have paid attention on spurious eigenvalues for multiply-connected domain (2D) eigenproblems by using BEM/BIEM. This paper employs the null-field integral equation method to study the occurring mechanism of spurious eigenvalues for 3D problems with an inner hole. By expanding the fundamental solution into degenerate kernels and expressing the boundary density in terms of spherical harmonics, all boundary integrals can be analytically determined. It is noted that our null-field integral formulation can locate the collocation point on the real boundary thanks to the degenerate kernel. In addition, the spurious eigenvalues are parasitized in the formulations, e.g. singular and hypersingular formulations in the dual BIEM while true eigensolutions are dependent on the
boundary condition such as the Dirichlet or Neumann problem. By using the updating terms and updating document of singular value decomposition (SVD)
technique, true and spurious eigenvalues can be extracted out, respectively. Besides, true and spurious boundary eigenvectors are obtained in the right and left unitary vectors in the SVD structure of the influence matrices. This finding agrees with that of 2D cases.
Description: 國立中正大學機械工程學系, November 28-29, 2008
Fri, 28 Nov 2008 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/168022008-11-28T00:00:00ZA linkage of Trefftz method and method of fundamental solutions for annular Green's functions using addition theoremhttp://scholars.ntou.edu.tw/handle/123456789/16803Title: A linkage of Trefftz method and method of fundamental solutions for annular Green's functions using addition theorem
Authors: Shiang-Chih Shieh; Ying-Te Lee; Shang-Ru Yu; Jeng-Tzong Chen
Abstract: In this paper, the Green's function for the annular Laplace problem is first derived by using the image method which can be seen as a special case of method of fundamental solutions. Three cases, fixed-fixed, fixed-free and free-fixed boundary conditions are considered. Also, the Trefftz method is employed to derive the Green’s function by using T-complete sets. By employing the addition theorem, both solutions are found to be mathematically equivalent when the number of Trefftz bases and the number of image points are both
infinite. On the basis of the finite number of degrees of freedom, the convergence rates of both methods are demonstrated and compared with each other. In the successive image process, the final two images freeze at the origin and infinity, where their singularity strengths can be analytically and numerically determined in a consistent manner.
Description: 國立中正大學機械工程學系, November 28-29, 2008
Fri, 28 Nov 2008 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/168032008-11-28T00:00:00ZAnalysis of two-spheres radiation problems by using the null-field integral equation approachhttp://scholars.ntou.edu.tw/handle/123456789/16804Title: Analysis of two-spheres radiation problems by using the null-field integral equation approach
Authors: Ying-Te Lee; Jeng-Tzong Chen
Abstract: In this paper, a system approach, null-field integral equation in conjunction with the degenerate kernel, is used to solve the radiation problem of two spheres. The null-field integral equation instead of the conventional boundary integral equation can avoid the singular and hypersingular integrals. To fully utilize the spherical geometry, the fundamental solutions and the boundary densities are expanded by using degenerate kernels and spherical harmonics in the spherical coordinate, respectively. The main difference between the present approach and the conventional boundary integral equation is that the collocation point can be exactly located on the real boundary owing to introducing the degenerate kernel. The proposed approach is seen as one kind of semi-analytical methods, since the error is attributed from the truncation of spherical harmonics in the implementation. For the single sphere, the present approach can obtain the analytical solution. Finally, a two-spheres radiation problem is given to verify the
validity of proposed approach.
Description: 國立中正大學機械工程學系, November 28-29, 2008
Fri, 28 Nov 2008 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/168042008-11-28T00:00:00ZImage method for the Green's functions of annulus and half-plane Laplace problemshttp://scholars.ntou.edu.tw/handle/123456789/16872Title: Image method for the Green's functions of annulus and half-plane Laplace problems
Authors: Shiang-Chih Shieh; Ying-Te Lee; Jeng-Tzong Chen
Abstract: In this paper, the image method is employed to solve the Green's function for the annular, eccentric and half-plane Laplace problems. For the annular case, not only the image method but also the Trefftz method is employed to derive the analytical solution. Their mathematical equivalence is also examined by using the bridge of addition theorem. For the half-plane problem with a circular hole and eccentric cases, a semi-analytical approach by using the image concept is used to solve the problems. After determining the three constants which contain one constant term and two strengths of two frozen image points by matching
boundary conditions, we can obtain the semi-analytical solutions. The results are compared well with analytical solutions or other numerical results. In addition, it is interesting to find that the image locations can be seen as the optimum location for the source in the method of fundamental solution.
Description: October 22, 2008, 宜蘭大學
Wed, 22 Oct 2008 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/168722008-10-22T00:00:00ZNull-field integral equation approach for structure problems with circular boundarieshttp://scholars.ntou.edu.tw/handle/123456789/16836Title: Null-field integral equation approach for structure problems with circular boundaries
Authors: Jeng-Tzong Chen; Ying-Te Lee; Wei-Ming Lee; I-Lin Chen
Abstract: In this paper, null-field equation approach is developed to deal with the structural problems including multiple circular boundaries, e.g. holes or inclusions. The boundary integral approach is utilized in conjunction with degenerate kernel and Fourier series. To fully utilize the circular geometry, the fundamental solutions and the boundary densities are expanded by using degenerate kernels and Fourier series, respectively. Both direct and indirect formulations are proposed. This approach is a semi-analytical approach, since the error stems from the truncation of Fourier series in the implementation. The unknown Fourier coefficients are easily determined by solving a linear algebraic system after using the collocation method and matching the boundary conditions. Five goals: (1) free of calculating principal value, (2) exponential convergence, (3) well-posed algebraic system, (4) elimination of boundary-layer effect and (5) meshless model, of the formulation are achieved. Finally, the general-purpose program in a unified manner is developed for structure problems with circular boundaries including the torsion bar, plate vibration and elasticity problems. 本文使用零場積分方程配合退化核與傅立業級數來處理含多圓洞與夾雜結構問題。為了充分利用圓形的幾何特性，我們將基本解與邊界密度函數分別以退化核與傅立業級數展開。除了直接法外，我們也會使用間接法來求解。由於誤差來自於傅立業級數的項數擷取多寡，故此套方法可被視為是一套半解析法。我們藉由佈點法可建構出一線性代數系統並進而求得未知的傅立業係數。本法將達成五個預期目標: (1) 毋須計算主值問題，(2)指數收歛特性，(3)良態代數系統的建構，(4)邊界層效應的消除與(5)無網格模式。最後，我們將發展一套廣用程式來處理含圓型邊界的扭轉、薄板振動與彈力問題。
Description: Kaohsiung, Taiwan, R. O. C., 22-24 Aug. 2008
Fri, 22 Aug 2008 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/168362008-08-22T00:00:00ZApplications of the dual integral formulation in conjunction with fast multipole method to the oblique incident wave problemhttp://scholars.ntou.edu.tw/handle/123456789/1074Title: Applications of the dual integral formulation in conjunction with fast multipole method to the oblique incident wave problem
Authors: Chen, K. H.; Jeng-Tzong Chen; Kao, J. H.; Ying-Te Lee
Abstract: In this paper, the dual integral formulation is derived for the modified Helmholtz equation in the propagation of oblique incident wave passing a thin barrier (zero thickness) by employing the concept of fast multipole method (FMM) to accelerate the construction of an influence matrix. By adopting the addition theorem, the four kernels in the dual formulation are expanded into degenerate kernels that separate the field point and the source point. The source point matrices decomposed in the four influence matrices are similar to each other or only to some combinations. There are many zeros or the same influence coefficients in the field point matrices decomposed in the four influence matrices, which can avoid calculating the same terms repeatedly. The separable technique reduces the number of floating‐point operations from O((N)2) to O(N loga(N)), where N is the number of elements and a is a small constant independent of N. Finally, the FMM is shown to reduce the CPU time and memory requirement, thus enabling us to apply boundary element method (BEM) to solve water scattering problems efficiently. Two‐moment FMM formulation was found to be sufficient for convergence in the singular equation. The results are compared well with those of conventional BEM and analytical solutions and show the accuracy and efficiency of the FMM.
Wed, 20 Aug 2008 00:00:00 GMThttp://scholars.ntou.edu.tw/handle/123456789/10742008-08-20T00:00:00Z