可變形物體接觸之有限元素模擬研究

Abstract

當我們在利用有限元素法處理兩個可變形物體之間的接觸問題時，需要將兩物體分別建立網格系統以進行模擬，因此，這類型模擬經常會因為接觸面元素分割方式的改變而得到不同的結果。本研究的主旨即是在於為此類型接觸問題尋找一最適當的網格系統。首先，將具有解析解的二維圓柱赫茲接觸問題建成有限元素模型，分別以局部加密、節點對應、二次元素等不同網格進行模擬，將所得結果與理論解比較，測試各種網格的特性。接著再進一步以接觸面曲率較為複雜的齒輪為載具，將之前模擬的經驗代入進行測試與驗證。希望能經由這些模擬，找到一個適合用於接觸問題的網格系統，以期能達到提高準確度並降低程式計算時間的目標。

As the finite element method is used on surface contact problems of two deformable bodies, meshes should be built on both bodies. The solutions for these contact problems sometimes differ from each other only because of the variation of mesh system between contact interfaces. The purpose of this research is thus focused on finding suitable mesh systems for this kind of contact problem. In the beginning, a two-dimensional cylindrical Hertz bodies contact model was considered. The Hertzian analytical solution was used as a basis for the comparison of different mesh systems denoted as “localized element density”, “nodes touch on contact surfaces”, and “quadratic elements”. Through these comparisons, the characteristics of different meshes were obtained. Next, to validate universality of the above characteristics, similar simulations were tested on two-dimensional gear contact problem that has more complex surface features. Through these processes, mesh systems with higher numerical precision and suitable computing time were obtained for the contact simulation of deformable bodies.