向量式有限元素法於平面構架幾何非線性之應用

An Application of Vector Form Intrinsic Finite Element Method on Geometrically Nonlinear Problem for 2D-Frames

賴建豪(Chien-Hao Lai)

指導教授 ： 莊清鏘

中原大學/工學院/土木工程研究所/碩士(2003年)

https://doi.org/10.6840/cycu200300454

摘要

本文主旨在應用向量式有限元素法模擬平面構架的幾何非線性行為。有別於傳統有限元素法以變分法為基本理論的方式，向量式有限元素法是以構件和節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，因此向量有限元的計算變成一組簡單的向量方程式計算。模擬結構問題時利用共轉座標分解剛體位移和變形位移，因此能夠精確的計算多個連續體同時具有大的剛體運動和大的幾何變形行為，也使得非線性分析得以簡化，再配合顯式的時間積公式及對應的向量運動方程式，使向量有限元不論在計算速度或模擬精度上都有不錯的結果。

關鍵字

顯示時間積分 ； 向量式有限元素法 ； 共轉座標 ； 幾何非線性

並列摘要

In this study, the vector form intrinsic finite element (VFIFE) method is applied to simulate the geometrically nonlinear behaviors of plane frame structures. 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 co-rotational coordinate system is used to separate the rigid body motion and pure deformation of the system. After combining it with explicit time integration scheme, the VFIFE method can effectively simulate the dynamic behaviors of multi-bodies system having large deformation. Numerical examples demonstrate that this newly proposed method has quite good accuracy and efficiency on analyses of plane frame structures with large deformation.

並列關鍵字

co-rotational approach ； VFIFE ； geometrically nonlinear ； explicit time integration

參考文獻

[1] Minguet, P. and Dugundji, J., “Experiments and analysis for composite blades under large delfections Part I. static behavior”, AIAA J. 28, 1573-1597 (1990).

[2] Oden, J. T., “Finite Elements of Nonlinear Continua”, McGraw-Hill, New York (1972).

[3] Bathe, K. J., “Finite Elements Procedures in Engineering Analysis”, Prentice-Hall, Englewood Cliffs, NJ. (1982).

[4] Bauchau, O. A. and Hong, C. H. “Large displacement analysis of naturally curved and twisted composite beams”, AIAA J. 25, 1469 - 1475 (1987).

[5] Stemple, A. D. and Lee, S. W., “Finite-element model for composite beams with arbitrary cross-sectional warping”, AIAA J. 26, 1512-1520 (1988).