有限元素法多點拘束條件分析彈性材質圓柱接觸之再思

Revisiting the Multiple Point Constraints in Finite Element Analysis of Contact between Cylinders of Elastic Materials

魏克輝(Ke-Huei Wei)

指導教授 ： 劉昭華

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00980

摘要

本論文是針對兩圓柱之二維彈性接觸，分為正向接觸與側向局部滑動接觸，接觸條件可轉換為有限元素之多點拘束條件。本論文修正滑動接觸切線方向之接觸條件，使滑動時切線力可以由所輸入之側向位移量產生，改變以往外加切線力的方式。本論文可求出接觸區域大小(contact length)，接觸區域內附著區(stick region)和滑動區(slip region)寬度，正向應力及側向節點力分佈。

關鍵字

圓柱之彈性接觸 ； 多點拘束條件 ； 有限元素法 ； 局部滑動 ； 接觸應力

並列摘要

In this thesis we use the finite element method to analyze normal and partial slip contact between two elastic cylinders. Contact conditions are transformed into multiple point constraints for nodal displacements. In a previous study the tangential contact force can only be produced by imposing tangential nodal forces upon the contact region. In this study tangential contact conditions are modified so that tangential contact forces may be produced by the specified tangential displacements. The method developed in this study may be used to obtain the contact length, lengths of the stick and the slip regions, the normal and the tangential contact stresses.

並列關鍵字

elastic contact of cylinders ； multiple point constraints ； finite element methods ； partial slip ； contact stresses

參考文獻

[1] Duvaut, G., and Lions J.L., Inequalities in Mechanics and Physics, Springer, Berlin, 1976

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[5] Bathe, K. J., and Chaudhary, A., “A Solution Method for Planar and Axisymmetric Contact Problems”, International Journal for Numerical Methods in Engineering, 21, pp. 65~88, 1985.

[6] Kalker, J. J., Three-Dimensional Elastic Bodies in Rolling Contact, Kluwer Academic Publishers, Delft, The Netherlands, 1990.

[7] Carter, F. W., “On the Action of a Locomotive Driving Wheel”, Royal Society, A112, p. 151, 1926.