臺灣博碩士論文加值系統

摘要
在許多構造物中，由於施工過程之缺失，或使用非預期之因素造成構件產生瑕疵，瑕疵的產生通常會使整體勁度變弱，使得柱體柔度增加因而改變其勁度值。這種構件的穩定性問題，亦成為許多結構穩定研究之探討重點。本文以旋轉彈簧來描述瑕疵之情形，其瑕疵形式，依據位置而有不同程度之影響。為了研究結果的可用性，一般設計規範經常引用的支撐條件均將予以討論。結構物之安全性不僅取決於挫屈載重的大小，也與後挫屈的行為息息相關。基本上，現有論文對於瑕疵柱穩定行為的研究，大都僅止於推求挫屈載重及挫屈模態，甚少觸及後挫屈分析。為了對其結構安全性有更深入的了解，本文將以瑕疵柱之後挫屈為研究目標，探討不同抗彎勁度及不同鉸接位置對於瑕疵柱後挫屈行為的影響。

Abstract
Internally hinged columns are used in various engineering applications as real structures or as analysis model for columns containing a transverse open crack. Their buckling and postbuckling behaviors are investigated in this work to accurately predict the load capacity. On the basis of geometrically nonlinear finite element method and perturbation technique, the postbuckling equilibrium path is obtained as a number of asymptotic expansions of a gauge perimeter. Several column-end conditions are considered. Although the hinge location and the stiffness of the restraining spring significantly affect both buckling and postbuckling behavior, each studied column exhibits stable postbuckling characteristic.

目 錄
誌謝
摘要 I
Abstract II
目錄 III
圖目錄 V
表目錄 XI

第一章　緒論--------------------------------1
1.1 前言----------------------------------------------1
1.2 文獻回顧------------------------------------------2
1.3 研究內容------------------------------------------4

第二章　內鉸接或瑕疵柱之挫屈分析--------6
2.1 挫屈載重解析式之推導------------------------------6
2.2　內鉸接或瑕疵位置與挫屈載重之影響-------------14
2.3 挫屈模態-----------------------------------------20

第三章　數值分析方法之建構-----------------28
3.1 數值分析流程-------------------------------------29
3.2　挫屈行為數值分析---------------------------------30
3.3　後挫屈分析---------------------------------------34
第四章　柱有效長度之推求-------------------37
4.1 柱之有效長度-------------------------------------38
4.2 瑕疵柱之有效長度---------------------------------39

第五章　實例分析---------------------------44
5.1　柱兩端由鉸支端所組成之後挫屈分析-----------------45
5.2 柱由固定端及自由端組成之後挫屈分析---------------53
5.3 柱由固定端及固定滾接端組成之後挫屈分析-----------59
5.4 柱由固定端及鉸支端組成之後挫屈分析---------------66
5.5 柱兩端由固定端所組成之後挫屈分析-----------------72

第六章　結論與建議-------------------------80
6.1　結論與建議---------------------------------------80

附錄一-------------------------------------82
附錄二-------------------------------------85
附錄三-------------------------------------88
參考文獻-----------------------------------92

參考文獻
[1]Baluch, M. H., Al-Shayea, N., and Azad, A. K. “Mode shapes
and crack damage in subtangential buckling of columns”
Transacations of the Canadian Society for Mechanical Engineering, Vol.12,pp.183-189,（1988）.

[2]Cheng, G. F., Lee, Y. Y., and Mei, C. (2003). “Nonlinear
randomresponse of internally hinged beams.” Finite Elem. Anal. Design, 39(5–6),487–504.

[3]Dado, Mohammad. Samir Al-Sadder., Abuzeid, Osama.“Post -buckling behavior of two elastica columns linked with a rotational spring” International Journal of Non-Linear Mechanics 39 (2004) 1579 – 1587.

[4]Krawczuk, M., and Ostachowicz, W. (1995). “Modeling and vibration analysis of a cantilever composite beam with a transverse open crack.” J. Sound Vib., 183(1), 69–89.

[5]Krawczuk, M., Palacz, M., and Ostachowicz, W. (2003). “The dynamic analysis of a cracked Timoshenko beam by the spectral element method.” J. Sound Vib., 264(5), 1139–1153.

[6]Lee, Y. Y., Wang, C. M., and Kitipornchai, S. (2003). “Vibration of Timoshenko beams with internal hinge.” J. Eng.
Mech., 129(3), 293–301.

[7]Okamura, H.,Liu, H. W.,and Chu, C. S. “A Cracked Columns under
Compression”Engineering Fracture Mechanics,Vol.1,pp.547 -564,（1969）.

[8]Song O., Ha, T. W., and Librescu L. (2003). “Dynamics of anisotropic composite cantilevers weakened by multiple transverse open cracks.”Eng. Fract. Mech., 70(1), 105–123.

[9]Wang, C. Y. (1987). “Optimum location of an interior hinge on a column.”J. Struct. Eng., 113(1), 161–165.

[10]Wang, C. Y.“Buckling of an internally hinged column with an elastic support” Engineering Structures 24 (2002) 1357-1360.

[11]Wang, C. Y.,Wang, C. M., M.ASCE; and Tun Myint Aung” Buckling of a Weakened Column” JOURNAL OF ENGINEERING MECHANICS ASCE / NOVEMBER 2004 / 1373-1376

[12]Wang, Q., Quek, S. T., and Liew, K. M. (2002). “On the repair of a cracked beam with a piezoelectric patch.” Smart Mater. Struct., 11,404–410.

[13]W.T.Koiter,(1967)“On the stability of elastic equilibrium.
”, English translation,NASA,TT,F10,pp.883.

[14]Xiang, Y., Wang C. M., Wang C. Y., and Su G. H. (2003). “Ritz buckling analysis of rectangular plates with internal hinge.” J. Eng. Mech.,129(6), 683–688.