進階搜尋


   電子論文尚未授權公開,紙本請查館藏目錄
(※如查詢不到或館藏狀況顯示「閉架不公開」,表示該本論文不在書庫,無法取用。)
系統識別號 U0026-1307202015161600
論文名稱(中文) 異向黏彈性固體之接觸分析
論文名稱(英文) Contact Analysis of Anisotropic Viscoelastic Solids
校院名稱 成功大學
系所名稱(中) 航空太空工程學系
系所名稱(英) Department of Aeronautics & Astronautics
學年度 108
學期 2
出版年 109
研究生(中文) 阮文商
研究生(英文) Van Thuong Nguyen
學號 P48057044
學位類別 博士
語文別 英文
論文頁數 147頁
口試委員 指導教授-胡潛濱
口試委員-夏育群
口試委員-楊文彬
口試委員-吳光鐘
口試委員-馬劍清
口試委員-趙振綱
口試委員-陳正宗
中文關鍵字 邊界元素法  摩擦型接觸問題  剛體探頭  異向性彈性力學  異向黏彈性力學  時間步進法  彈性-黏彈性對應法則  壓痕問題  多探頭 
英文關鍵字 boundary element method  frictional contact  rigid punch  anisotropic elastic  anisotropic viscoelastic  time-stepping method  correspondence principle  indentation  contact problem  multiple punches 
學科別分類
中文摘要 本文探討二維異向性彈性/黏彈性材料的接觸問題,包括兩個彈性/黏彈性體之間的摩擦型接觸問題和同時多個剛體探頭壓在彈性/黏彈性體上的力學行為,並提供一個可以解決上述問題的邊界元素法。 在本文提出的邊界元素法中,針對不同問題可以選用包含或不包含孔洞/裂紋/異質的不同基本解。 如此一來,則不需要對孔洞/裂紋的表面或異質的界面進行網格分割。 透過對邊界積分式的離散化與配置法來建立系統方程式和接觸條件的約束關係式,同時利用疊代和增量加載法來獲得接觸問題的解,對多個剛體探頭的問題,我們將個別剛體探頭的剛體運動視為新的額外變數。 使用本文新發展的接觸型邊界元素法,在剛體探頭上不需要使用接觸元素。 目前這個方法已經被驗證在非完全或完全壓痕問題、在有摩擦或無摩擦的接觸面、且探頭處於平衡狀態或擬靜態滑動的條件下皆適用。
由於基本解的限制,在處理黏彈性問題時,常使用彈性-黏彈性對應法則。此方法將與時間相依的材料性質取拉式轉換,再將對應的彈性係數乘上自變數s,最後搭配數值拉式逆轉換即可獲得黏彈性問題的解。 然而,此方法受限於邊界條件必須與時間無關。 為了拋開對應法則的限制,本文提出一個時間步進法: 此法將異向性線黏彈力學問題分解為兩個部分,其一與初始時間相關,其二則與各步進時間相關,且各時段接可視為線彈性問題,最後把切割的時間段隨著時間的增加一步步的累加起來即可。 同理,邊界條件也可以因此可隨著時間段的不同而變化。
在本文中,兩種解黏彈性問題的方法皆有用以求解異向黏彈性材料的接觸問題。因受限於非依時性的邊界條件,若用彈性-黏彈性對應法則,只能處理探頭完全接觸基材的問題。然而,時間步進法則不受前者約束,由不同探頭狀態(完全或不完全接觸基材)或兩個異向黏彈性固體的接觸問題所產生的依時性的接觸面和接觸狀態皆可處理。
為了驗證前面所提的方法,使用本文的邊界元素法提供數個數值範例並分別與解析解或有限元素法軟體相比。其中包含了接觸面摩擦係數的影響、不同材料性值、不同加載條件、不同基材缺陷(孔洞/裂縫/異質)、等影響的討論。
英文摘要 The contact problems of anisotropic elastic/viscoelastic problems are studied, which include the frictional contact between two anisotropic elastic/viscoelastic solids and the indentation by multiple rigid punches on an anisotropic elastic/viscoelastic solid. To solve the frictional contact problems of two anisotropic elastic solids, a contact BEM extended from the conventional boundary element method solving for the problems of two-dimensional anisotropic elastic solids is first presented. In this contact BEM, the selected fundamental solutions are valid for the general anisotropic elastic solids with or without holes/cracks/inclusions. Hence, no meshes are needed along the hole/crack/inclusion boundaries. A complete system of linear equations is constructed by boundary integral equations and contact constraint relations. The contact solutions are obtained by using an efficient, iterative and fully incremental loading technique. Based upon on the proposed contact BEM, by taking the rigid body motions of rigid punches as additional variables, we further propose a brand-new contact BEM for the indentation problems by multiple rigid punches on an anisotropic elastic solid. By using this newly developed contact BEM, again, no meshed are required on the boundaries of rigid punches. This method is valid for both incomplete and complete indentation with the frictionless or frictional contact surface, and the punches can be in equilibrium status or in quasi-static sliding condition.
Due to the restriction of BEM on the availability of fundamental solutions of anisotropic viscoelasticity, the solutions of viscoelasticity are usually obtained through its associated elastic solutions. Following this concept, the most popular method to solve the anisotropic viscoelastic problems is the elastic-viscoelastic correspondence principle. This method is simple and easy to implement, however it is restricted on the time-independent boundaries. To get rid of restriction of the correspondence principle, in this dissertation, we propose a time-stepping method, in which the basic equations for linear anisotropic viscoelasticity can be separated into two parts: one is an elastic system of the initial state, and the other is an elastic-like system related to the follow-up time step. This method is processed step-by-step in time domain, and its boundary conditions may vary in each time step. And hence, it can be applied to the cases whose boundary conditions are time-dependent.
In this dissertation, both the correspondence principle and the time-stepping method are used to solve the contact problems with anisotropic viscoelasticity. Among them, if the correspondence principle is used, only complete indentation with time-independent contact status is considered. Whereas, by using time-stepping method, both incomplete and complete indentation as well as contact between two anisotropic viscoelastic solids whose contact region and contact status may vary with time are considered.
The validation of the proposed methods is demonstrated through several numerical examples, and their results are compared with each other and/or those obtained from analytical method or finite element method. Through these examples, we also study the effects of friction coefficient, material properties, applied forces/moments, holes, cracks and inclusions as well as the iteration between punches on contact solutions.
論文目次 CONTENTS
摘要 i
ABSTRACT iii
ACKNOWLEDGMENTS i
CONTENTS ii
LIST OF TABLES v
LIST OF FIGURES vi
NOMENCLATURE ix
CHAPTER I INTRODUCTION 1
1.1 Background of research 1
1.2 Scope of dissertation 6
CHAPTER II ANSIOTROPIC ELASTICITY AND VISCOELASTICITY 10
2.1 Anisotropic elasticity 10
2.1.1 Stroh formalism 11
2.1.2 Boundary element method for anisotropic elastic solids 12
2.2 Anisotropic viscoelasticity 16
2.2.1. Elastic-viscoelastic corresponding principle 16
2.2.2 Time-stepping method 18
CHAPTER III CONTACT OF TWO ANISOTROPIC ELASTIC SOLIDS 22
3.1 Boundary element method for contact problems of two elastic solids 22
3.2. Contact constraint relations 24
3.3. Incremental loading technique 28
3.3.1. Determination of slip direction and incremental load 30
3.3.2. Criteria for contact status 33
3.3.3. Fast solver for iteration 34
3.3.4. Iteration procedure 35
3.4 Numerical examples and discussions 38
3.4.1. Numerical examples 39
3.4.2 Discussions 45
CHAPTER IV INDENTATION BY MULTIPLE RIGID PUNCHES ON AN ANISOTROPIC ELASTIC SOLID 46
4.1. Complete or incomplete indentation by multiple rigid punches 46
4.2. Contact constraint relations 47
4.3. Criteria for contact status 52
4.4. Iteration procedure 52
4.5 Numerical examples and discussions 56
4.5.1 Numerical examples 57
4.5.2 Discussions 61
CHAPTER V CONTACT OF TWO ANISOTROPIC VISCOELASTIC SOLIDS 62
5.1 BEM for contact of two anisotropic viscoelastic solids 62
5.2 Contact constraint relations 65
5.3 Iteration procedure 70
5.4 Numerical examples and discussions 74
5.4.1 Numerical examples 75
5.4.2 Discussions 81
CHAPTER VI INDENTATION BY MULTIPLE RIGID PUNCHES ON AN ANISOTROPIC VISCOELASTIC SOLID 82
6.1 Complete indentation solved by correspondence principle 82
6.2 Incomplete and complete indentation solved by time-stepping method 86
6.3 Numerical examples and discussions 92
6.3.1 Numerical examples 93
6.3.2 Discussions 98
CHAPTER VII CONCLUSIONS AND RECOMMENDATIONS 99
7.1 Conclusions 99
7.2 Recommendations 101
REFERENCES 103
APPENDICES 110
TABLES 113
FIGURES 115
PUBLICATION LIST 146


參考文獻 Abouhamzeh M, Sinke J, Jansen KMB, Benedictus R. Thermo-viscoelastic analysis of GLARE. Compos Part B 2016; 99(15): 1-8.
Aliabadi MH, Martín D. Boundary element analysis of two-dimensional elastoplastic contact problems. Eng Anal Bound Elem 1998; 21(4): 349-360.
Aliabadi MH. The boundary element method: applications in solids and structures. Chichester: Wiley; 2002.
Almasi A, Kim T, Laursen TA, Song JH. A strong form meshfree collocation method for frictional contact on a rigid obstacle. Comput Methods Appl Mech Eng 2019; 357: 112597.
Amendola G, Fabrizio M, Golden JM. Thermodynamics of materials with memory. Boston: Springer; 2012.
Andersson T. Boundary elements in two-dimensional contact and friction. PhD Dissertation No.85, Linkoping University; 1982.
Armendáriz I, Millán JS, Encinas JM, Olarrea J. Strategies for dynamic failure analysis on aerospace structures. In Makhlouf ASH, Aliofkhazraei M (eds.) Handbook of Materials Failure Analysis with Case Studies from the Aerospace and Automotive Industries; 2016.
Bagault C, Nélias D, Baietto MC, Ovaert TC. Contact analyses for anisotropic half space coated with an anisotropic layer: Effect of the anisotropy on the pressure distribution and contact area. Int J Solid Struct 2013; 50(5):743-754.
Blázquez A, Mantic V, París F. Application of BEM to generalized plane problems for anisotropic elastic materials in presence of contact. Eng Anal Bound Elem 2006; 30(6):489–502.
Brebbia CA, Telles JCF, Wrobel LC. Boundary element techniques: theory and applications in engineering. Berlin: Springer; 1984.
Brinson HF, Brinson LC. Polymer engineering science and viscoelasticity. Boston: Springer; 2008.
Browne DJ, Battikha E. Optimisation of aluminium sheet forming using a flexible die. J Mater Process Technol 1995; 55(3-5): 218-223.
Bugnicourt R, Sainsot P, Lesaffre N, Lubrecht AA. Transient frictionless contact of a rough rigid. Tribol Int 2017; 113:279-285.
Carbone G, Scaraggi M, Tartaglino U. Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories. Eur Phys J E 2009; 30(65).
Cesbron J, Lédée FA, Yin HP, Duhamel D, Houédec DL. Influence of road texture on tyre/road contact in static conditions. Road Mater Pavement 2008; 9(4): 689-710.
Chen T. Determining a Prony series for a viscoelastic material from time varying data. Nasa 2000.
Chen WH, Chen TC. Boundary element analysis for contact problems with friction. Comput Struct 1992; 45(3): 431-438.
Chen WH, Chang CM, Yeh JT. An incremental relaxation finite element analysis of viscoelastic problems with contact and friction. Comput Methods Appl Mech Eng 1993; 109(3-4): 315-329.
Chen YC, Hwu C. Boundary element analysis for viscoelastic solids containing interfaces/holes/cracks/inclusions. Eng Anal Bound Elem 2011; 35(8): 1010-1018.
Chen YP, Zhang XQ, He YM, Pan E. Elastic field by a dislocation loop in an anisotropic elastic half-space with general boundary conditions and its application in nanoindentation of single crystals. Int J Mech Sci 2019; 160: 26-37.
Cheng L, Xia X, Scriven LE, Gerberich WW. Spherical-tip indentation of viscoelastic material. Mech Mater 2005; 37(1): 213-226.
Choi ST, Lee SR, Earmme YY. Flat indentation of a viscoelastic polymer film on a rigid substrate. Acta Mater 2008; 56(19): 5377-5387.
Chernov A, Maischak M, Stephan EP. A priori error estimates for hp penalty BEM for contact problems in elasticity. Comput Methods Appl Mech Eng 2007; 196(37-40): 3871-3880.
Christensen RM. Theory of Viscoelasticity. New York: Academic Press; 1982.
Clements DL, Ang WT. On some contact problems for inhomogeneous anisotropic elastic materials. Int J Eng Sci 2009; 47(11-12): 1149-1162.
Dubois G, Cesbron J. Yin HP, Lédée FA. Macro-scale approach for rough frictionless multi-indentation on a viscoelastic half-space. Wear 2011; 272(1): 69-78.
Dubois G, Cesbron J, Yin HP, Lédée FA. Numerical evaluation of tyre/road contact pressures using a multi-asperity approach. Int J Mech Sci 2012; 54(1): 83-94.
Eck C, Jarušek J, Krbec M. Unilateral Contact Problems, Variational Methods and Existence Theorems. Boca Raton: Chapman & Hall CRC, 2005.
Fan CW, Hwu C. Punch problems for an anisotropic elastic half-plane. ASME J Appl Mech 1996; 63(1):69-76.
Fu G, Chandra A. Normal indentation of elastic half-space with a rigid frictionless axisymmetric punch. J Appl Mech 2002; 69(2):142-147.
Galin LA. Contact problems of the theory of elasticity, Gostehizdat, Moscow. Translated from Russian edition by H. Moss, In: Sneddon, I.N. (Ed.), North Carolina State University at Raleigh; 1953.
Giannakopoulos AE. Elastic and viscoelastic indentation of flat surfaces by pyramid indentors. J Mech Phys Solids 2006; 54(7): 1305-1332.
Goryacheva IG. The periodic contact problem for an elastic half-space. J Appl Maths Mechs 1998; 62(6): 959-966.
Goryacheva IG. Mechanics of discrete contact. Tribol Int 2006; 39:381–386.
Goryacheva IG, Torskaya EV. Modeling of fatigue wear of a two-layered elastic half-space in contact with periodic system of indenters. Wear 2010; 268: 1417–1422.
Graham GAC. The contact problem in the linear theory of viscoelasticity when the time dependent contact area has any number of maxima and minima. Int J Eng Sci 1967; 5(6): 495-514.
Graham GAC. Viscoelastic contact problems with friction. Int J Eng Sci 1980; 18: 191-196.
Greenwood JA. Contact between an axisymmetric indenter and a viscoelastic half-space. Int J Mech Sci 2010; 52(6): 829-835.
Gun H. Elasto-plastic static stress analysis of 3D contact problems with friction by using the boundary element method. Eng Anal Bound Elem 2004; 28:779-790.
Guyot N, Kosior F, Maurice G. Coupling of finite elements and boundary elements methods for study of the frictional contact problem. Comput Methods Appl Mech Eng 2000; 181(1-3): 147-159.
Haddad YM. Viscoelasticity of engineering materials. London: Chapman & Hall; 1995.
Hilton HH, Yi S. Anisotropic viscoelastic finite element analysis of mechanically and hygrothermally loaded composites. Compos Eng 1993; 3(2): 123-135.
Huesmann A, Kuhn G. Automatic load incrementation technique for plane elastoplastic frictional contact problems using boundary element method. Comp Struct 1995; 56(5):733-744.
Hunter S. The Hertz problem for a rigid spherical indenter and viscoelastic half-plane. J Mech Phys Solids 1960; 8(4): 219-234.
Hwu C. Anisotropic elastic plates. New York: Springer; 2010.
Hwu C, Fan CW. Contact problems of two dissimilar anisotropic elastic bodies. J Appl Mech 1998a; 65(3): 580-587.
Hwu C, Fan CW. Sliding punches with or without friction along the surface of an anisotropic elastic half-plane. Q J Mech Appl Math 1998b; 51(1): 159-177.
Igumnov LA, Amenitskii AV, Belov AA, Litvinchuk SY, Petrov AN. Numerical-analytic investigation of the dynamics of viscoelastic and porous elastic bodies. J Appl Mech Tech Phy 2014; 55:89–94.
Igumnov L, Маrkov IP, Amenitsky AV. A three-dimensional boundary element approach for transient anisotropic viscoelastic problems. Key Eng Mater 2016; 685:267–271.
Jaffar MJ. Axi-symmetric contact of a punch on an elastic half-space in the presence of tangential tractions. Int J Mech Sci 2004; 46: 1233–1244.
Kozhevnikov IF, Cesbron J, Duhamel D, Yin HP, Lédée FA. A new algorithm for computing the indentation of a rigid body of arbitrary shape on a viscoelastic half-space. Int J Mech Sci 2008; 50(7):1194-1202.
Kuo TL, Hwu C. Interface corners in linear anisotropic viscoelastic materials. Int J Solid Struct 2013; 50(5):710-724.
Lapin RL, Kuzkin VA, Kachanov M. Rough contacting surfaces with elevated contact areas. Int J Eng Sci 2019; 145: 103171.
Lee EH, Radok JRM. The contact problem for viscoelastic bodies. J Appl Mech 1960; 27: 438-444.
Liu X, Tang T, Yu W, Pipes RB. Multiscale modeling of viscoelastic behaviors of textile composites. Int J Eng Sci 2018; 130: 175-186.
Man KW, Aliabadi MH, Rooke DP. BEM frictional contact analysis: load increment technique. Comp Struct 1993; 47(6):893-905
Menga N, Afferrante L, Demelio GP, Carbone G. Rough contact of sliding viscoelastic layers: numerical calculations and theoretical predictions. Tribol Int 2018; 122: 67-75.
Menga N, Putignano C, Carbone G, Demelio GP. The sliding contact of a rigid wavy surface with a viscoelastic half-space. Proc R Soc A 2014; 470: 20140392.
Munteanu L, Chiroiu V, Brişan C, Dumitriu D, Sireteanu T, Petre S. On the 3D normal tire/off-road vibro-contact problem with friction. Mech Syst Signal Process 2015; 54-55: 377-393.
Nečas J, Jarušek J, Haslinger J: On the solution of the variational inequality to the Signorini problem with small friction. Boll Un Mat Ital 1980; 17: 796–811.
Nedjar B. An anisotropic viscoelastic fibre–matrix model at finite strains: Continuum formulation and computational aspects. Comput Methods Appl Mech Eng 2007; 196(9-12): 1745-1756.
Nguyen VT, Hwu C. Holes, cracks, or inclusions in two-dimensional linear anisotropic viscoelastic solids. Compos Part B 2017; 117: 111-123.
Nguyen VT, Hwu C. Multiple holes, cracks, and inclusions in anisotropic viscoelastic solids. Mech Time-Depend Mate 2018a. 22: 187–205.
Nguyen VT, Hwu C. A boundary element approach for indentation by rigid punches on two-dimensional anisotropic elastic or viscoelastic Solids. In Proceedings of the 6th Asian Conference on Mechanics of Functional Materials and Structures (ACMFMS) 2018b; Tainan, Taiwan.
Panagiotopoulos CG, Mantič V, Roubíček T. A simple and efficient BEM implementation of quasistatic linear visco-elasticity. Int J Solids Struct 2014; 51(13): 2261-2271.
Panzeca T, Salerno M, Terravecchia S, Zito L. The symmetric boundary element method for unilateral contact problems. Comput Methods Appl Mech Eng 2008; 197(33-40): 2667-2679.
Paris F, Garrido JA. An incremental procedure for friction contact problems with the boundary element method. Eng Anal Bound Elem 1989: 6(4): 202-213.
Putignano C, Afferrante L, Carbone G, Demelio G. A new efficient numerical method for contact mechanics of rough surfaces. Int J Solids Struct 2012a; 49(2):338-343.
Putignano C, Afferrante L, Carbone G, Demelio G. The influence of the statistical properties of self-affine surfaces in elastic contacts: a numerical investigation. J Mech Phys Solids 2012b; 60(5): 973-982.
Putignano C, Carbone G, Dini D. Mechanics of rough contacts in elastic and viscoelastic thin layers. Int J Solids Struct 2015; 69-70: 507-517.
Putignano C, Carbone G. Viscoelastic reciprocating contacts in presence of finite rough interfaces: a numerical investigation. J Mech Phys Solids 2018; 114: 185-193.
Putignano C, Menga N, Afferrante L, Carbone G. Viscoelasticity induces anisotropy in contacts of rough solids. J Mech Phys Solids 2019; 129: 147-159.
Ramezani M, Ripin Z, Ahmad R. Computer aided modelling of friction in rubber-pad forming process. J Mater Process Technol 2009; 209(10): 4925-4934.
Raous M. Quasistatic signorini problem with coulomb friction and coupling to adhesion. In Wriggers P, Panagiotopoulos P (Eds.), New Developments in Contact Problems. Verlag Wien: Springer, 1999.
Renaud C, Feng ZQ. BEM and FEM analysis of Signorini contact problems with friction. Comput Mech 2003; 31(5):390-399.
Rodriguez NV, Masen MA, Schipper DJ. A model for the contact behaviour of weakly orthotropic viscoelastic materials. Int J Mech Sci 2013a; 72: 75-79.
Rodriguez NV, Masen MA, Schipper DJ. A contact model for orthotropic-viscoelastic materials. Int J Mech Sci 2013b; 74: 91-98.
Schapery RA. Approximate methods of transform inversion for viscoelastic stress analysis. Proceeding of the 4th US National Congress on Applied Mechanic, ASME 1962; 1075-1084.
Sfantos GK, Aliabadi MH. A boundary element sensitivity formulation for contact problems using the implicit differentiation method. Eng Anal Bound Elem 2006; 30(1): 22-30.
Shen JJ, Wu YY, Lin JX, Xu FY, Li CG. Partial slip problem in frictional contact of orthotropic elastic half-plane and rigid punch. Int J Mech Sci 2018; 135: 168-175.
Sherman J, Morrison WJ. Adjustment of an inverse matrix corresponding to changes in the elements of a given column or a given row of the original matrix. Ann Math Stat 1949; 20:621.
Stehfest H. Algorithm 368: numerical inversion of Laplace transforms. Commu ACM 1970; 13(1):47–49.
Tembleque LR, Buroni FC, Abascal R, Sáez A. 3D frictional contact of anisotropic solids using BEM. Eur J Mech A/Solids 2011. 30(2): 95-104.
Thatte A, Salant RF. Effects of multi-scale viscoelasticity of polymers on high-pressure, high-frequency sealing dynamics. Tribol Int 2012; 52: 75-86.
Ting T. The contact stresses between a rigid indenter and a viscoelastic half-space. J Appl Mech 1966; 33(4): 845-854.
Timoshenko SP, Goodier JN. Theory of Elasticity - Third Edition. London: McGraw-Hill; 1982.
Vandamme M, Ulm FJ. Viscoelastic solutions for conical indentation. Int J Solids Struct 2006; 43(10): 3142–3165.
Vodička R, Mantič V, Roubíček T. Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM. J Comput Appl Math 2017; 315: 249-272.
Willis JR. Hertzian contact of anisotropic bodies. J Mech Phys Solids 1966; 14(3):163-176.
Wriggers P, Reinelt J. Multi-scale approach for frictional contact of elastomers on rough rigid surfaces. Comput Methods Appl Mech Eng 2009; 198(21-26): 1996-2008.
Yastrebov VA, Durand J, Proudhon H, Cailletaud G. Rough surface contact analysis by means of the Finite Element Method and of a new reduced model. CR Mecanique 2011; 339:473-490.
Yastrebov VA, Anciaux G, Molinari JF. Contact between representative rough surfaces. Phys Rev E 2012; 86: 035601.
Yastrebov VA, Anciaux G, Molinari JF. The role of the roughness spectral breadth in elastic contact of rough surfaces. J Mech Phys Solids 2017; 107:469-493.
Zhou Y, Xiao Y, He Y, Zhang Z. A detailed finite element analysis of composite bolted joint dynamics with multiscale modeling of contacts between rough surfaces. Compos Struct 2020; 236: 111874.
Zhou YT, Kim TW. Closed-form solutions for the contact problem of anisotropic materials indented by two collinear punches. Int J Mech Sci 2014; 89: 332-343.
Zhupanska OI, Ulitko AF. Contact with friction of a rigid cylinder with an elastic half-space. J Mech Phys Solids 2005; 53(5): 975-999.
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2021-08-01起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2021-08-01起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw