向量式有限元之剛架、薄膜、固體元、版殼、彈簧及索元素於PNS-PBC程式架構之研究

A study of Frame, Membrane, Solid, Shell, Spring and Cable elements using Vector Form Intrinsic Finite Element Method in PNS-PBC framework

尤信翰(Hsin-Han Yu)

指導教授 ： 王仁佐 ； 林炳昌

中原大學/工學院/土木工程研究所/碩士(2012年)

https://doi.org/10.6840/cycu201200637

摘要

摘要
本文研究內容主要在國家地震中心所開發點質計算數值模擬平台(Platform for Numerical Simulation-Point Based Computing, PNS-PBC )架構中增加向量式有限元(Vector Form Intrinsic Finite Element, VFIFE or V-5)方法中，版殻元素、纜索元素、薄膜元素、固體元素、彈簧元素、剛架元素等各類基本元素功能於PNS-PBC軟體中，讓軟體使用者將來能應用此新元素功能來模擬不同結構型式變形與破壞行為。除此之外，本研究中亦推導出VFIFE方法之Timoshenko梁(Timoshenko Beam Theory, TBT)與彈簧元素(Spring Element)及纜索元素(Cable Element)基本理論。為證明本文所撰寫C++程式之VFIFE各類元素正確性進行元素轉動測試分析，以及使用ANSYS中LS-DYNA功能與本文方法進行分析比較，由算例分析結果可證明VFIFE方法所建立各類元素能均能有效移除剛體位移所產生之內力。

關鍵字

彈簧元素 ； Timoshenko梁 ； 向量式有限元 ； 纜索元素

並列摘要

Abstract
The main purpose of this study is to add some functions for different types of the elements into the Platform for Numerical Simulation - Point Based Computing ( PNS-PBC ) framework. This framework is developed from the National Center for Research on Earthquake Engineering (NCREE) in 2011. The PNS-PBC is based on two methods which are vector form intrinsic finite element (VFIFE or V-5) method and discrete element method (DEM). In this study, the formulations of the shell, cable, spring, 4 point solid, Euler beam, Timoshenko beam in VFIFE method are implemented in PNS-PBC. Firstly, the internal forces of the Timoshenko beam, cable, and spring for VFIFE method are derived in this study. In order to prove the accuracy for deformation of the elements, the rotation tests and numerical simulations using ANSYS are compared with the numerical simulations using VFIFE method. It is confirmed the good accuracy of the VFIFE method.

並列關鍵字

Spring ； Cable ； Vector Form Intrinsic Finite Element ； Timoshenko Beam

參考文獻

陳子健，「向量式有限元於薄膜的應用」，中原大學土木工程學系，碩士論文(2011)。

王仁佐，「向量式結構運動分析」，中央大學土木工程學系，博士論文(2005)。

Belytschko, T. and Hseih, B. J., “Nonlinear finite element analysis with convected coordinates,” International Journal for Numerical Methods in Engineering Vol.7, pp.255-271,(1973).

Belytschko T. and Glaum L. W., “Appliciation of higher order co-rotational stretch theories to nonlinear finite element analysis,” Comput. Struct. 10, pp.175-182, (1979).

Hsiao, K. M. and Jang, J., “Dynamic analysis of planar flexible mechanisms byco-rotational formulation,” Comput. Mech. Appl. Mech. Engrg. 24, 359-381-161 (1991).