向量式有限元素法於平面構架彈塑性及斷裂之應用

An Application of Vector Form Intrinsic Finite Element Method on Elastic-Plastic and Fragmentary Problem for 2D-Frames

陳建霖(Chien-Lin Chen)

指導教授 ： 莊清鏘

中原大學/工學院/土木工程研究所/碩士(2005年)

https://doi.org/10.6840/cycu200500396

摘要

本文主要嘗試利用向量式有限元素法來模擬平面構架同時具有幾何、材料非線性，及材料達到極限狀態後構架斷裂、坍塌等3種行為。有別於傳統有限元素法以變分法為基礎的方法，向量式有限元素法乃以構件和質點為模擬基礎的物理模式，它將連續體定義成一群質點的組合，利用牛頓運動定律描述質點的運動，因此向量有限元素法的計算變成一組簡單的向量方程式計算。
模擬問題時利用變形座標來分解剛體位移和變形位移且納入軸向力對彎矩勁度的影響，ㄧ般稱為弓形效應，因此能夠更真實地來模擬連續體同時具有大的剛體運動和大的幾何變形行為。從塑性理論建立平面構架由彈性進入塑性分析模形及流程，由材料力學彎矩-曲率的解析解來反應平面構架彈塑性行為，且以本文所建立簡易斷機制與向量式有限元易於節點再生的特性模擬平面構架由連續體到部份連續體之斷裂行為，最後配合顯式的時間積公式及對應的向量運動方程式使得非線性分析得以簡化，且從模擬的過程中可以看出每個時間增量不需要建立整體係統勁度矩陣及進行迭代運算，即可有效模擬與預測構架受力後因幾何及材料變化所產生的構件斷裂、構架坍塌等破壞現象。

關鍵字

斷裂 ； 彈塑性 ； 弓形效應 ； 變形座標 ； 向量式有限元

並列摘要

In this study, the vector form intrinsic finite element (VFIFE) method is applied to simulate plane frame structures having the following 3 behaviors at the same time ,the geometrically nonlinear,materially nonlinear,and frame ruptures. Different from the conventional finite element method which is based on the variational theory, the VFIFE method models the analyzed domain to be composed by finite particles and Newton’s second law is applied to describe each particle’s motion. Thus, the calculation of VFIFE method becomes solving a set of uncoupled vector form equations.
In the analysis of VFIFE method, the deformation coordinate system is used to separate the rigid body motion and pure deformation of the system，the moment-curvature relation is used to reflect the elastic-plastic behavior，and adding nodes is used to simulation fracture behavior of plane frame structure. After combining these with explicit time integration scheme, the VFIFE has the capability to simulate plane frame transformed form a continuous one and to study faiure and collapse without any matrix and iteration process.

並列關鍵字

elastic-plastic ； deformation coordinates ； fragmentary ； VFIFE

參考文獻

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