三維實體運動模擬與圖形化使用者介面之建立

A Study on Simulation of Motion of 3D Solids and Establishment of Graphical User Interface

吳政翰(Cheng-Han Wu)

指導教授 ： 何仲明 ； 吳東岳

中原大學/工學院/土木工程研究所/碩士(2005年)

https://doi.org/10.6840/cycu200500241

摘要

本文旨在以向量式有限元法為基礎推導四面體實體元，並應用於分析三維實體結構的運動。除了需要有一個效能良好的計算核心( Solver )外，一個完整的問題分析仍必須包含前處理以及後處理部分( Pre and post processor )。因此在前處理及後處理部分，應用了圖形化使用者介面模式( GUI )的視窗介面降低了計算結果判讀的困難度。計算核心方面是採用向量式有限元法理論發展而成的求解器。

向量式有限元基本的理論是將連續體視為一群質點的集合，質點與質點間的互制以及質點的運動皆遵守牛頓運動定律。不同於一般以變分法為基礎的有限元，應變的計算直接透過實體元的運動學得到。其中，剛體與變形位移的分離為強調的重點。為了滿足變形位移的連續條件，特別針對四面體實體元建立一組變形座標。數值算例結果顯示：本文所建議之實體元不但可通過大剛體轉動之補片測試，而且其數值結果與解析解或其它方法的解相當吻合。

前、後處理方面，本文建立圖形化使用者介面模式來展示有限元前後處理，發展平台為Microsoft Windows環境下使用Boland C++ Builder 6以C++語言為根基，並搭配SGI的OpenGL圖形程式庫。透過OpenGL圖形程式庫將使發展者更容易掌握圖形表現的能力。藉由圖形化使用者介面的發展，視覺化的反應將更容易讓使用者能快速判斷分析問題的結果。

關鍵字

OpenGL。 ； 四面體實體元 ； 向量式有限元(VFIFE) ； 變形座標 ； 圖形化使用面(GUI)

並列摘要

The main objective of this thesis is to formulate a 4-nodes tetrahedral solid element, in which the vector form intrinsic finite element method (VFIFE) is employed. The purpose of this element is to analyze the motion of 3D solids. In addition, a simple pre- and post-processor has also developed where the graphical user interface (GUI) is emphasized to alleviate the burden of modeling and numerical verification.

In contrast to commonly traditional finite element, the VFIFE approximates the continuum as the assembly of particles. In which the interactions and motions of particles obey the Newton’s law. Therefore the equation of motion is a vector. The key of VFIFE is on the dissection of deformation and rigid body motion. To satisfy the fundamental principles of continuum the deformation coordinate is designed. It is crucial in the formulation of kinematics of the element.

In the pre- and post-processor, the developed platform is designed by C++ language and OpenGL graphical library under Microsoft Windows environment. Through OpenGL graphical library, the developer can easily control the performance of figures. For the purpose of development with the graphical user interface, the vision responses enable users to verify numerical results.

Several numerical examples are presented in this thesis, which reveal that the presented element is able to pass the patch tests with large rigid body rotations and motion analysis of 3D solids is well established.

並列關鍵字

Four no ； Vector form intrinsic finite element ( VFIFE )

參考文獻

2. MATFOR, 2004, MATFOR in Fortran Reference Guide, AnCAD, Inc., Taiwan.

3. Belytschko, T. and Hsieh, B.J., “Nonlinear transient finite element analysis with converted coordinates”, International Journal for Numerical Method in Engineering, Vol. 7, pp.255-271 (1973).

4. Belytschko, T. and Bindeman L.P., “Assumed strain stabilization of the eight node hexahedral element”, Computer Methods in Applied Mechanics and Engineering, Vol. 105, pp.225-260 (1993).

6. Bonet, J., Marriott H. and Hassan O., “An average nodal deformation gradient linear tetrahedral element for large strain explicit dynamic applications”, Communications in Numerical Methods in Engineering, Vol. 17, pp.551-561 (2001).

7. Bonet, J., Marriott H. and Hassan O., “Stability and comparison of linear tetrahedral formulations for nearly incompressible explicit dynamic applications”, International Journal for Numerical Method in Engineering, Vol. 50, pp.119-133 (2001).