| 摘要: | 根據過去經驗，結構進入非線性時，由於計算複雜化，容易發生數值發散問題，導致無法順利完成分析，或分析時間過長，為解決傳統有限元素分析現有之困難點，本研究引入新隱式非線性動力有限元素法(New Implicit Nonlinear Dynamic Finite Element Method, NINDFEM)求解結構運動方程式，並開發一系列非線性元素。此有限元素法適用於處理大變形、大變位與剛體運動等問題，可以同時考量結構於極限狀況下，各構件進入非線性之動力行為，如大梁間的碰撞、橋面版掉落以及最終崩塌情形。
本研究將開發三維非線性元素於新隱式非線性動力有限元素法中，其一三維元素為非線性桁架元素，含有雙線性模型(Bilinear Model)和具可開孔塑性模型(Gap or Hook Plastic Model)，用以模擬橋梁之抗拉拔裝置或防落橋裝置等軸力構件於強震中之非線性行為。另一三維元素為非線性連結與支承元素，含有雙線性模型(Bilinear Model)、Takeda模型與具可開孔塑性模型(Gap or Hook Plastic Model)，用以模擬橋梁部分構件與裝置於地震中之非線性行為，如橋柱柱底塑鉸區、伸縮縫等。進行數值驗證時，將在同等模型及相同分析條件下與傳統有限元素法比較分析結果，證實所發展之三維元素之正確性，並比較新隱式非線性動力有限元素法與傳統有限元素法運算效率及準確性。;According to experience, when the structures go into the nonlinearity, the numerical divergence problem is prone to occur. Because the process of calculation becomes very complicated, the analysis cannot be completed successfully or the analysis time is too long. To solve the existing difficulties of traditional finite element analysis, this research introduces the New Implicit Nonlinear Dynamic Finite Element Method (hereinafter referred to as NINDFEM) to solve the structural motion equations and develop a series of nonlinear elements. This method is suitable for dealing with problems such as large deformation, large displacement, and rigid body motion. It can also consider the nonlinear dynamic behavior of each member under the limited condition of the structure, such as the collision between the beams, the falling of the bridge deck, and the situation of final collapse.
This research develops three-dimensional nonlinear truss elements, including the Bilinear Model and Gap or Hook Model, which are used to simulate the axial force components such as the tensile device of the bridge or the anti-dropping device of the bridge. The other three-dimensional element is a nonlinear connection and support element, including a bilinear model (Bilinear Model), a plastic model with a hole (Gap or Hook Model), and a Takeda model. It is used to simulate the nonlinear behavior of some bridge components and devices in earthquakes, such as the plastic hinge region at the bottom of the bridge column, expansion joints, etc.To verify the correctness of the developed three-dimensional elements, the analysis results will be compared under the same model and the same analysis conditions. Additionally, we compared the computational efficiency and accuracy of NINDFEM and the traditional finite element method. |
