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題 名 | 混合型有限元素法用於二維接觸應力分析之研究 |
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作 者 | 蔡哲雄; 廖崇禮; | 書刊名 | 力學 |
卷 期 | 9:4 1993.12[民82.12] |
頁 次 | 頁319-330 |
分類號 | 440.133 |
關鍵詞 | 混合型有限元素法; 二維接觸問題; 彈塑性變形; Mixed finite element method; Two-dimensional contact problems; Elasto-plastic deformation; |
語 文 | 中文(Chinese) |
中文摘要 | 本文依據Hellinger-Reissner變分原理,配合updated Lagrangian formulation 以考慮變形體的幾何形狀改變,所建立的混合型有限元素模型之節點自由度除位移外還包括 應力,比較一般位移型的應力求解簡化許多,並直接獲得連續的應力域,因而適用於分析應 力變化大如接觸等問題。 由於接觸問題的邊界條件不斷變化, 利用 Lagrange multiplier method 修改混合型有限元素模型,使得已接觸的節點自由度,除了位移和應力外, 尚包含 了接觸力。利用本文所建立的有限元素模型,可以分析變形體的接觸問題,並容許接觸區域 有摩擦阻力, 及變形體產生塑性變形(假設材料為等向性並遵循 von Mises 降伏條件)。 經實際應用於二維接觸的實例探討,以顯示此一套方法的效用。 |
英文摘要 | Based on the incremental nonlinear theory and the Hellinger-Reissner principle, a mixed updated Lagrangian formulation for the large motion of solid bodies is derived. Using this mixed formulation a two-dimensional mixed finite element model is developed, which contains the displacements and stresses as the nodal degrees of freedom. In order to apply the present mixed finite element model for the analysis of contact problems, attention must be paid to the boundary conditions and the contact region. In the present study we use Lagrange multiplier method to incorporate the contact conditions in the above mixed finite element model. Therefore the degrees of freedom of contact nodes include contact forces, in addition to displacements and stresses. The present approach can be used for the contact analysis of deformable bodies. It takes account of the contact friction and elasto-plastic large deformation, in which the material is assumed isotropic and obeys von Mises yielding criterion. Numerical results are compared with the existing solutions to show the accuracy of the model. |
本系統中英文摘要資訊取自各篇刊載內容。