利用有限元素分析受拘束拱梁在集中力矩作用下之穩定性

Abstract

拱梁在工程上有許多實際應用，然而對受拘束面約束拱梁受力後的行為尚未有完整的研究。本文利用有限元素法分析受拘束拱梁在集中力矩作用下的平衡解，接著由系統在平衡位置上的特徵值判別平衡解的穩定性。拱梁因其特有的挫屈行為，加上拘束面的限制，使得負載-軸力曲線有複雜的分歧現象。為了確認有限元素法結果的正確性，另以模態展開法分析並相比較。我們發覺，模態展開法所得的資料對於有限元素分析結果的完整性極有助益。我們討論了拱梁初始高度、力矩作用點、力矩大小對拱梁行為的影響。最後架設實驗驗證所得結果的正確。

Arches have many applications in different engineering fields and have been studied thoroughly complete. However, the behavior of an arch with a constraint plane is not well understood. This thesis employs the finite element method (FEM) to study the behavior of a pinned half-sine arch together with a constraint plane under a concentrated moment. Equilibrium positions and the associated stability of the arch under different conditions are investigated thoroughly. Due to the snap-through property and the appearance of the constraint plane, the load-axial force curve of the arch is quite complex and exhibits bifurcation phenomena. To confirm the results, the results of the FEM are compared with those of the modal analysis. We found that the results of the modal analysis provide useful information for determining the equilibrium positions of the arch using the FEM. The variation of the equilibrium positions with the applied load and values of system parameters are examined in detail. Finally, experimental apparatus is set up to validate the theoretical results.