本文主要以三維有限元素數值分析探討微柱結構與剛體間接觸滑動問題。在數值模型中分別以樑元素與實體元素模擬微柱結構之力學行為，並將數值模擬結果與尤拉撓曲理論、橡皮理論及尤拉挫曲理論相對照。探討微柱結構幾何參數如柱體傾斜角度φ0、柱頂形貌、及柱體深寬比λ等因素對柱體於接觸與滑移時之變形行為的影響。微柱結構在滑動之前所能承受之最大剪力不僅與微柱結構幾何參數有關，亦受剛體滑移方向和接觸摩擦係數μ影響。只有高深寬比且斷面小之柱體，其接觸滑動時受力與變形關係才可由橡皮理論預測。一般柱體接觸時端點旋轉角自由度隨接觸面積不同而有所限制，導致滑動時剪力值與理論預測值有出入。而微柱與圓球形剛體接觸滑移之情況則與接觸位置有關，其分析過程中之變異較為複雜。

This research uses three-dimensional finite element analysis to study the sliding contact between the micro-columns and the rigid indenter. In the numerical models, solid elements and beam elements were used for describing the mechanical behavior of micro-columns respectively. The numerical results were compared with the Euler bending theory, the Elastica theory, and the Euler buckling analysis. The influence of the geometric parameters of micro-columns, such as tilt angle φ0, tip shape, and the aspect ratio λ, on the deformed behavior of micro-columns during contact and sliding were investigated. The maximum shear force which micro-columns can sustained before sliding depends not only on the geometric parameters of micro-columns, but also on the sliding direction of the rigid indenter and the contact friction coefficient μ. Only for the micro-columns of high aspect ratio and small cross section, their behavior during contact and sliding can be predicted by Elastica theory. In general, the degree of freedom in rotation at tip depends on the shape and contact area of micro-columns. This results in the sliding shear force is not the same as theoretical prediction. The situation is much more complicated for the sliding contact between the rigid spherical indenter and micro-columns, since the behavior for each column depends on its location in contact.

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