- 學位論文
使用有限元素約束條件分析接觸問題
Finite Element Contact Analysis Using Constraint Equations
摘要
本論文利用約束條件從事有限元素接觸分析，並提出兩種分析程序，第一種是使用位移接觸條件以及應力接觸條件，且將應力接觸條件轉換為節點位移的多點約束條件以模擬接觸。第二種則是使用位移接觸條件以及節點力接觸條件，將節點力接觸條件轉換為節點位移的多點約束條件。第一種方法所求得之多點約束條件可輸入套裝軟體進行有限元素接觸分析，而第二種方法可使用子結構技巧進行分析。 本論文發現第一種方法分析時，在跨元素交界處節點會產生過多約束條件，必須刪除一部分接觸條件才能求解，如此造成一些接觸條件未能完全滿足。 以第二種方法分析時，由於使用了子結構消去了物體內部的節點及元素，因此求節點接觸應力過程中只能使用物體邊界上的節點力，無法使用物體內部節點力以估計節點應力。
並列摘要
In this thesis two methods for finite element contact analysis using constraint equationsare investigated. In the first method, displacement contact conditions and stress contact conditions are imposed on the model, and stress contact conditions are transformed into multiple point constraints of nodal displacements. In the second method, stress contact conditions are replaced by nodal force contact conditions, which are also transformed into multiple point constraints of nodal displacements. Multiple point constraints generated in the first method can be fed back to the commercial software in performing finite element analysis. The second method may utilizethe technique of substructuringto reduce degree of freedom in the system. The first method generally produces repeated constraint conditions for boundary nodes between two elements, leading to excessive constraints. Solutions can only be obtained after deletion of a certain constraint conditions,but some stress contact conditions are not imposed as a result of this deletion. Ifanalysis is performed with the second method, and if all internal degrees of freedom are removedfrom thesubstructure, then nodal stresses at contact nodes can only be estimated from nodal forces at contact nodes.
參考文獻
延伸閱讀
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