有限元素二維摩擦接觸分析

本論文使用有限元素分析軟體ANSYS進行接觸分析，首先探討接觸力學中的圓柱接觸問題，將其分析結果與Hertz、Mindlin的理論解進行比較，發現在不同材料的圓柱平面接觸問題上，接觸壓力與切向應力會互相影響，導致切向應力與理論解有所差異。在不同材料中的圓柱圓柱接觸問題上，由於上下圓柱的材料性質不同會導致兩圓柱幾何變形不一致，在切向接觸時會發生阻擋，產生比理論解更大的切向應力。接著進行兩指抓取的穩定性分析，求出在手指急停時會使物件脫離的臨界加速度，分析結果顯示影響物件脫離手指之臨界加速度的因素包括摩擦係數、夾緊位移量、及物件的密度。

關鍵字

有限元素分析；摩擦接觸； Hertz-Mindlin接觸

並列摘要

In this thesis the finite element software ANSYS is used to analyze two dimensional frictional contact problems. Normal and tangential contacts of two parallel cylinders with difference material firstly are treated, results are compared to Hertz’s and Mindlin’s solutions. For a cylinder in contact with a plane made of different material, tangential stress and normal contact pressure are found to be mutually dependent, causing the results for tangential stress deviate from Mindlin’s solution. When two cylinders with different material constants are in contact, warping may occur which may block the tangential relative displacements, causing apparent difference with Mindlin’s solution. Also when two fingers grasping a circular object are subjected to a suddenly applied acceleration, the object may escape the fingers by sliding motion. In this study the critical acceleration for gross sliding to occur is also determined. Results show that the factors affecting the critical acceleration of the object to escape from the fingers include the coefficient of friction, the tightening displacement, and the density of the object.