盧中仁臺灣大學：機械工程學研究所蘇昱仁Su, Yu-JenYu-JenSu2007-11-282018-06-282007-11-282018-06-282004http://ntur.lib.ntu.edu.tw//handle/246246/61116當兩平面互相接觸時，接觸力與位移間的關係除了受到接觸平面本身的材料特性影響，接觸面間的表面型態（surface topography）也是一個重要的因素。本文利用Cantor集建立一個具有碎形特性的隨機表面模型，探討碎型參數的機率分佈對粗糙面間彈塑性接觸行為的影響。我們分析加載－卸載過程中施力的期望值和標準差與碎型參數的期望值和標準差間的關係。在純彈性變形的情形下，給定碎型參數的機率分佈函數，我們進一步推導得外力的機率分佈函數。最後用Monte-Carlo法驗證所得的結果。When two surfaces are in contact﹐the load-displacement relationship depends on the surface topography as well as the material properties of the surfaces.This thesis constructs a random fractal surface model based on the Cantor set.The effects of the random fractal parameters on the elastic-plastic contact behavior are investigated.Given the expectation and standard variation of the random fractal parameter﹐we can obtain the expectation and standard variation of the applied load.If the deformation is purely elastic﹐the probability distribution function of the applied load can also be determined.Finally﹐the Monte-Carlo simulation is employed to verify the analytical results.第一章 導論............................................1 1－1 研究動機............................................1 1－2 文獻回顧............................................1 1－3 研究方法............................................3 第二章 理論分析........................................4 2－1 碎形的起源..........................................4 2－2 Cantor表面模型......................................4 2－3 接觸模型............................................6 2－3－1 單一柱體彈塑性分析...............................7 2－3－2 Cantor表面模型彈性變形負載分析...................9 2－3－3 Cantor表面模型塑性變形負載分析..................14 2－3－4 Cantor表面模型塑性變形卸載分析..................19 2－3－5 Cantor模型彈性變形時的機率密度函數..............24 2－4 漸近分析...........................................30 第三章 結果分析.......................................33 3－1 Monte-Carol模擬....................................33 3－2 純彈性變形時的期望值與標準差.......................36 3－3 塑性變形時的期望值與標準差.........................48 3－4 純彈性變形時接觸力的機率密度函數...................53 第四章 結論...........................................58 參考文獻.................................................591116143 bytesapplication/pdfen-USCantor集隨機變數接觸力學碎型表面模型contact mechanicsrandom variableCantor setfractal surface modelthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/61116/1/ntu-93-R91522521-1.pdf