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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27998完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 楊德良(Der-Liang Young) | |
| dc.contributor.author | Je-Jium Chu | en |
| dc.contributor.author | 朱哲均 | zh_TW |
| dc.date.accessioned | 2021-06-12T18:32:33Z | - |
| dc.date.available | 2007-08-03 | |
| dc.date.copyright | 2007-08-03 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-31 | |
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Eng., Vol. 193, pp. 4511-4539, 2004 [3.8] Sutradhar A. and Paulino G. H., Gary L. J., Transient Heat Conduction in Homogeneous and Non-Homogeneous Materials by the Laplace Transform Galerkin Boundary Element Method, Eng. Anal. Bound. Elem., Vol. 26, pp. 119-132, 2002. [3.9] Ochiai Y., Two-Dimensional Steady Heat Conduction in Functionally Gradient Materials by Triple-Reciprocity Boundary Element Method, Eng. Anal. Bound. Elem., Vol. 28, pp. 1445-1453, 2004. [3.10] Sladek J., Sladek V., Zhang C., A Local BIEM for Analysis of Transient Heat Conduction with Nonlinear Source Terms in FGMs, Eng. Anal. Bound. Elem., Vol. 28, pp. 1-11, 2004. [3.11] Sladek J., Sladek V., Krivacek J., Zhang C., Local BIEM for Transient Heat Conduction Analysis in 3D Axisymmetric Functionally Graded Solids, Comput. Mech., Vol. 32, pp. 169-176, 2003. [3.12] Chen C. S., Rashed Y. F., Golberg M. A., A mesh-free Method for Linear Diffusion Equations, Numer. Heat Trans., Part B, Vol.33, pp. 469-486, 1998. [3.13] Chen C. S., The Method of Fundamental Solution and the Quasi-Monte Carlo Method for Poisson’s Equation, in Lecture Notes in Statistics 106, eds. H. Niederreiter and P. Shuie, New York, USA, pp. 158-167, 1995. [3.14] Young D. L., Tasi C. C., Murugesan K., Fan C. M., Chen C. W., Time-dependent Fundamental Solutions for Homogeneous Diffusion Problems, Eng. Anal. Bound. Elem., Vol.29, pp. 1463-1473, 2004. [3.15] Young D. L., Tasi C. C., Fan C. M., Direct Approach to Solve Non-homogeneous Diffusion Problems Using Fundamental Solution and Dual Reciprocity Methods, J. Chin. Inst. Eng., Vol.27, pp. 597-609, 2004. [4.1] Brebbia C. A. and Walker S., Boundary Element Techniques in Engineering, Newnes-Butterworths, London, 1980. [4.2] Bialecki R. and Nowak A. J., Boundary Value Problems in Heat Conduction with Nonlinear Material and Nonlinear Boundary Conduction, Appl. Math. Modeling, Vol. 5, pp. 417-421, 1981. [4.3] Bialecki R. and Kuhn G., Boundary Element Solution of Heat Conduction Problems in Multizone Bodies of Non-Linear Materials, Int. J. Numer. Methods Eng., Vol. 36, pp. 799-809, 1993. [4.4] Bialecki R. and Nahlik R., Solving Nonlinear Steady-State Potential Problems in Homogeneous Bodies Using the Boundary Element Method, Numer. Heat Transf., Part B, Vol. 16, pp. 79-96, 1989. [4.5] Akkuratov Y. N. and Mikhailov V. N., The Method of Boundary Integral Equations for Solving Non-Linear Heat Transmission Problems, U.S.S.R. Comput. Maths. Math. Phys., Vol. 20, No. 3, pp. 117-125, 1980. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27998 | - |
| dc.description.abstract | 本論文主要在探討基本解法以及數值轉換的結合，去求解非均質材料的勢能和擴散問題。基本解法是屬於邊界類型的無網格方法。對於非均質的勢能或是擴散問題，無法直接使用基本解法去模擬。非均質材料在本篇論文中分為兩種類型，一為功能梯度材料，一是材料內部的熱傳導係數不為定值。功能梯度材料是指構成要素(組成、架構)沿濃度方向由一側向另一側呈現連續梯度變化。熱在功能梯度材料上的擴散問題能藉由指定數學轉換式轉換，在使用基本解法求解。而勢能問題在熱傳導係數不為定值的材料上，能使用柯西荷夫轉換法去轉換，再利用基本解法求解。經由轉換求得非均質材料的勢能以及擴散問題的答案，都能與解析解或者使用有限差分的方法所求得的答案一致，因此，基本解法也許能在非均質問題上做更廣泛的研究與應用。 | zh_TW |
| dc.description.abstract | This thesis mainly describes the combination of the method of fundamental solutions (MFS) and numerical transformation to solve potential and diffusion problems in non-homogeneous materials. The MFS is a meshless method which belongs to boundary-type method. For the potential and diffusion problems in non-homogeneous materials, the results can not be simulated by the MFS directly. Non-homogeneous materials can demarcate two types in this thesis, one is functionally graded materials (FGMs); one is the heat conductivity which is not constant inside the material. FGMs is a kind of material which is composed by the materials varying from one side to another in the direction of density continuously. The transient heat diffusion problems in FGMs can be solved by the MFS employing specific the transformation’s formulation. Potential problems in non-homogeneous materials can utilize the Kirchhoff’s transformation to transfer to be linear and the results also can be solved by the MFS. The results of potential and diffusion problems in non-homogeneous materials are simulated after transformation and the results are agreement with using finite difference method or analytical solutions. The MFS is successfully applied to solve potential and diffusion problems. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-12T18:32:33Z (GMT). No. of bitstreams: 1 ntu-96-R94521323-1.pdf: 1598328 bytes, checksum: 8e53c2f2ac1d8270d91d744f63a7aaaf (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | 口試委員會審定書i
誌謝ii 中文摘要iii Abstract iv List of Figures vii Symbols ix Chapter 1 Introduction 1.1 Motivations 1 1.2 Objective of the present thesis 4 1.3 Organization of the thesis 4 References 6 Chapter 2 Numerical scheme-The Method of Fundamental Solutions 2.1 Introduction 9 2.2 The theory of MFS 10 2.2.1 Laplace problems 12 2.2.2 Diffusion problems 13 References 16 Chapter 3 The MFS with Parameter Transformation for Functionally Graded Materials Heat Problems 3.1 Introduction 17 3.2 Governing equation 18 3.3 Result and discussions 21 3.4 Conclusions 26 References 34 Chapter 4 The MFS with Kirchhoff’s Transformation for Steady State Nonlinear Material Heat Problems 4.1 Introduction 36 4.2 Numerical scheme 37 4.3 Result and discussions 39 4.4 Conclusions 45 References 58 Chapter 5 Conclusions and Future Works 5.1 Conclusions 59 5.2 Future Works 60 | |
| dc.language.iso | en | |
| dc.subject | 解析解 | zh_TW |
| dc.subject | 有限差分 | zh_TW |
| dc.subject | 基本解法 | zh_TW |
| dc.subject | 非均質 | zh_TW |
| dc.subject | 勢能方程式 | zh_TW |
| dc.subject | 擴散方程式 | zh_TW |
| dc.subject | 無網格 | zh_TW |
| dc.subject | 功能梯度材料 | zh_TW |
| dc.subject | 熱傳導 | zh_TW |
| dc.subject | 柯西荷夫轉換法 | zh_TW |
| dc.subject | diffusion equation | en |
| dc.subject | potential equation | en |
| dc.subject | non-homogeneous | en |
| dc.subject | The method of fundamental solutions | en |
| dc.subject | functionally graded materials (FGMs) | en |
| dc.subject | meshless | en |
| dc.subject | analytical solution | en |
| dc.subject | finite difference method (FDM) | en |
| dc.subject | Kirchhoff’s transformation | en |
| dc.subject | nonlinear heat conductivity | en |
| dc.title | 以基本解法結合數值轉換求解非均質材料上之勢能和擴散導問題 | zh_TW |
| dc.title | The Method of Fundamental Solutions with Parameter Transformations for Potential and Diffusion in
Non-homogeneous Material Problems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 邱家麟,許泰文,廖清標,陳哲維 | |
| dc.subject.keyword | 基本解法,非均質,勢能方程式,擴散方程式,無網格,功能梯度材料,熱傳導,柯西荷夫轉換法,解析解,有限差分, | zh_TW |
| dc.subject.keyword | The method of fundamental solutions,non-homogeneous,potential equation,diffusion equation,meshless,functionally graded materials (FGMs),nonlinear heat conductivity,Kirchhoff’s transformation,finite difference method (FDM),analytical solution, | en |
| dc.relation.page | 60 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-08-01 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
| 顯示於系所單位： | 土木工程學系 | |
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