臺灣博碩士論文加值系統

摘要
複合材料(composite materials)具有質量輕及高抗壓強度等特性，已廣泛的使用在各個領域且逐漸取代傳統材料，例如：在航空業、造船業、汽車業……等方面，現今以航太結構為複合材料最主要的用途，其中複合材料又以三明治平板(sandwich plate)結構為最常使用的材料。三明治平板由於力量傳遞、支承、幾何及材質不連續所造成的影響，且受到壓力負載時，容易造成挫屈變形，使結構破壞產生不穩定的行為。
由文獻中得知三明治結構中，並沒有學者探討膠黏層對結構的挫屈造成的影響，所以本文研究的目的是五層三明治平板的挫屈分析，本研究考慮的三明治結構為上下兩個面板和中間心材之間分別加入一層膠黏層，為了將膠黏層的因素考慮進去，使用三明治平板理論分析其變形的理論值結果，並利用Rayleigh-Ritz能量法求解，而得到挫屈強度。
再針對三明治板之負荷情況、尺寸大小、材料性質、疊層方式等因素的影響，研究其挫屈強度的差異性以及比較加入膠黏層後的變化，由計算結果得知，加入膠黏層後複合板的挫屈強度約增加0.1% ~ 4%，其影響因素為膠黏層的厚度，隨著膠黏層厚度的增加其挫屈強度會增加，所以在分析上有需將膠黏層考慮進去的必要性。

關鍵詞：三明治平板、膠黏層、Rayleigh-Ritz能量法

Abstract
Composite materials are used extensively for lightweight spacecraft, aircraft structures, owing to the advantage of the characteristics of low weight and high compressive strength. Nowadays the structure of composite sandwich plates is one kind of the most common composite material. Sandwich structures are very susceptible to failure due to local stress concentrations induced in areas of load introduction, supports, geometrical and material discontinuities. And while receiving pressure load, it is apt to cause buckle, it produces the unstable behavior to make the structure destroy.
From the references, it is known that most of the researches do not consider the existence of adhesive layers in sandwich plates in the structural analysis. This paper studies the buckling analysis of five layers sandwich plates, between the faces and the core adding the adhesive layer. In order to consider the factor of the adhesive layers , we use the theory of sandwich plate to analyse its theoretical value , utilizing Rayleigh-Ritz energy law to get the buckling strength.
Based on the ability of sandwich plate to withstand pressure, its dimension, material properties, and the layup of laminated composite plates, this paper studies the varying buckling strength of sandwich plate for without accounting the adhesive layer and with it. Upon the introduction of an adhesive layer, buckling strength could increase from 0.1% to 4%, depending on the thickness of the adhesive layer. The thicker the adhesive layer, the stronger the sandwich plate becomes. Hence taking adhesive layer into consideration is important when analyzing the buckling strength of the sandwich plate.

Keywords: sandwich plates, adhesive layers, Rayleigh-Ritz energy law.

目錄
摘要 I
ABSTRACT III
圖目錄 VII
表目錄 X
符號說明 XI
第一章 緒論 1
1-1 前言 1
1-2 研究動機與目的 2
1-3 文獻回顧 3
1-3-1 三明治結構的挫屈分析 3
1-3-2 含膠黏層之三明治結構理論分析 6
1-3-3 文獻整理心得 7
1-4 研究方法 8
1-5 研究流程 10
第二章 三明治結構與理論分析 11
2-1 蜂巢結構概念 11
2-2 膠黏行為簡介 15
2-2-1 膠黏界面分析 16
2-2-2 矽烷膠黏劑的弁遄B優點與應用 17
2-3 三明治結構複合板彈性基礎理論 18
2-4 線性挫屈分析 19
2-5 RAYLEIGH-RITZ 能量法 21
2-6 複材層板的等效彈性常數 22
第三章 含膠黏層之三明治平板挫屈強度解析解之分析 24
3-1 問題描述 24
3-2 方程式推導概述 25
3-3 方程式推導之基本假設 26
3-4 位移表示函數 27
3-5 方程式推導 29
3-6 解析解方程式 32
3-6-1 系統全勢能 32
3-6-2 系統方程式 36
第四章 實例探討 40
4-1 無膠黏層之三明治板 40
4-2 含膠黏層之三明治板 44
4-3 影響因素之探討 47
4-3-1 層板尺寸大小之影響 47
4-3-2 層板受負荷情形之影響 51
4-3-3 疊層方式不同之影響 52
4-3-4 膠黏層之影響 53
4-4 有限元素分析 58
第五章 結論與未來研究方向 65
5-1 結論 65
5-2 未來研究方向 68
參考文獻 70
附錄一 73
附錄二 93

參考文獻
[1]C. M. Wang, J. N. Reddy, “Buckling load relationship between Reddy and Kirchhoff plates of polygonal shape with simply supported edges”, Mechanics Research Communications, Vol. 24, No. 1, pp. 103-108, 1997.
[2]A. Muc, P. Zuchara, “Buckling and failure analysis of FRP faced sandwich plates”, Composite Structures, Vol. 48, pp. 145-150, 2000.
[3]D. J. Dawe, W. X. Yuan, “Overall and local buckling of sandwich plates with laminated faceplates, Part I: Analysis”, Comput. Methods Appl. Mech. Engrg. Vol. 190, pp. 5197-5213, 2001.
[4]Zdenek P. Bazant, Alessandro Beghini, “Sandwich buckling formulas and applicability of standard computational algorithm for finite strain”, Composites: Part B 35, pp. 573-581, 2004.
[5]Radoslaw Mania, “Buckling analysis of trapezoidal composite sandwich plate subjected to in-plane compression”, Composite Structures, Vol. 69, pp. 482-490, 2005
[6]Tomas Nordstrand, “On buckling loads for edge-loaded orthotropic plates including transverse shear”, Composite Structures, Vol. 65, pp. 1-6, 2004.
[7]Liangjin Gui, Zhengneng Li, “Delamination buckling of stitched laminates”, Composite Structures, Vol. 61, pp. 629-636, 2001.
[8]B. K. Hadi, “Wrinkling of sandwich column: comparison between finite element analysis and analytical solutions”, Composite Structures, Vol. 53, pp. 477-482, 2001.
[9]B. K. Hadi, F. L. Matthews, “Predicting the buckling load of anisotropic sandwich panels: an approach including shear deformation of the faces”, Composite Structures, Vol. 42, pp. 245-255,1998.
[10]H. Matsunaga, “Buckling instabilities of thick elastic plates subjected to in-plane stress”, Composite Structures, Vol. 62, No. 1, pp. 205-214, 1997.
[11]D. W. Sleight, J. T. Wang, “Buckling Analysis of Debonded Sandwich Panel Under Compression”, NASA Technical Memorandum 4701, 1995.
[12]Lajos Pomazi, Jozesef UJ, “Stability of asymmetrically built and loaded multi-layered rectangular sandwich-type plates (FEM solutions)”, Periodica Polytechnica Ser. MECH. ENG. Vol. 44, No. 1, pp. 127-138, 2000.
[13]H. C. Wu, B. Mu, K. Warnemuende, "Failure analysis of FRP sandwich bus panels by finite element method", Composites Part B:engineering, Vol. 34, pp. 51-58, 2003.
[14]C. G. Kim, C. S. Hong, "Buckling of Unbalanced Anisotropic Sandwich plates with Finite Bonding Stiffness”, AIAA Journal, Vol. 26, pp. 982-988, 1988.
[15]J. Hohe, W. Becker, "Assessment of the delamination hazard of the core face sheet bond in structural sandwich panels", International Journal of Fracture, Vol. 109, n 4, pp. 413-432, June, 2001.
[16]Song-Jeng Huang, “An analytical method for calculating the stress and strain in adhesive layers in sandwich beams”, Composite Structures, Vol. 60, pp. 105-114, 2003.
[17]S. J. Huang, W. Y. Wang, “Viscoelastic analysis for adhesive layer of composite sandwich structure”, Transactions of the Aeronautical and Astronautical Society of ROC, Vol. 35, No. 2, pp. 135-151, 2002.
[18]S. J. Huang, H. W. Liu, “Viscoelastic analysis for adhesive layer of composite sandwich plates”, The Chinese Journal of Mechanics, Vol. 19, No. 2, pp. 57-68, 2003.
[19]S. Zhang, K. J. Hsia, “Modeling the fracture of a sandwich structure due to cavition in a ductile adhesive layer”, Journal of Applied Mechanics, Vol.68, pp. 93-100, 2001.
[20]Robert M. Jones, “Mechanics of composite materials”, 1980.
[21]Stephen R. Swanson, “Introduction to Design and Analysis with Advanced Composite Materials”, Prentice-Hall International, Inc. , 1997.
[22]“Maple 7 Learning Guide”, Waterloo Maple Inc. , 2001.
[23]Bulson, P. S. , “The Stability of Flat plates, Elsevier, New York, 1969”, Timoshenko, Woinowski-krieger, “Theory of plates and Shells”, 2nd Ed., McGraw-Hill, New York 1959.
[24]莫兆松, “複合夾心板挫屈強度最佳化之探討”,碩士論文，國立成奶j學航空太空工程研究所, 1994.
[25]邱林威, “含扣件三明治板的結構力學分析—五層理論法”,碩士論文，國立中正大學機械工程研究所, 2004.
[26]張志民,“複合材料結構力學”, 北京航空航天大學出版社, 1993.
[27] 陳泰良,“含蜂巢心材層板的潛變行為”, 碩士論文，國立成奶j學土木工程研究所, 2005.
[28] P.K. Mallick, “Fiber-reinforced composites : materials, manufacturing, and design” , 1993.
[29] V.F. Panin, Y.A. Gladkov, “Structures with Core Handbook”, Moscow Mashinostroenie, 1991.
[30] 愛發股份有限公司, ”ABAQUS實務入門引導”, 全華科技圖書股份有限公司.