隨機Cantor集表面模型下的彈塑性接觸分析

Elastic-perfectly Plastic Contact Analysis of Rough Surfaces Base on Random Cantor set Models

蘇昱仁(Yu-Jen Su)

指導教授 ： 盧中仁

國立臺灣大學/工學院/機械工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.01712

摘要

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。

關鍵字

Cantor集 ； 隨機變數 ； 接觸力學 ； 碎型表面模型

並列摘要

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.

並列關鍵字

contact mechanics ； random variable ； Cantor set ； fractal surface model

參考文獻

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