時間不連續有限元素法薄殼振動分析之研究

A Study on Vibration Analysis of Thin Shell by the Time-Discontinuous Galerkin Finite Element Method

陳鉉文(Shiuan-Wen Chen)

指導教授 ： 簡秋記

中原大學/工學院/土木工程研究所/碩士(2003年)

https://doi.org/10.6840/cycu200300489

摘要

摘 要
本文主要利用時間不連續葛勒金有限元素法(簡稱TDG法)分析薄殼結構暫態問題。TDG法同時以位移及速度作為基本的未知數，而且速度函數與位移函數皆是一階線性函數作為內插近似，其在空間域中為連續函數而時間域內則為不連續函數。換句話說，即速度與位移在每個時階初的離散點上是不連續的。為增加TDG法在執行時的運算效率，本文使用Gauss-Seidel疊代法進行疊代運算。分析方法上，首先應用同參數八點曲面薄殼元素，於空間域內建立薄殼結構運動方程式。其次分別利用振態疊加法，HHT-α及TDG法分析薄殼結構暫態反應。本文共探討三個數值算例。由穩定性分析得知TDG法為無條件穩定且優於一般直接積分法。此外藉由算值算例的分析結果可以得知，將TDG法應用於薄殼結構暫態問題時，其精確度及穩定性皆優於一般直接積分法。

關鍵字：時間不連續葛勒金法有限元素法，薄殼結構，振態疊加法，HHT-α。

關鍵字

HHT-α ； 振態疊加法 ； 時間不連續葛勒金法有限元素法 ； 薄殼結構

並列摘要

ABSTRACT
This study presents a space and time-discontinuous Galerkin (TDG) finite element method for analyzing the transient elastodynamic problems of shell structure. This novel method uses both the displacements and velocities as basic unknowns and approximates them as piecewise linear functions which are continuous in space and discontinuous in time. Specifically, the variables of displacements and velocities are discontinuous at beginning of each time step. The improved algorithm employs the Gauss-Seidel method in the study to calculate iteratively the solutions that exist in the numerical implementation. An eight-node isoparametric quadrilateral shell element is applied to establish the equation of motion. Modal superposition, HHT-α and TDG method are used, respectively, to analyze the transient response of shell structures. Three numerical examples are discussed here. Stability analyses of TDG method reveal that such a method retains the unconditionally stable behavior with greater efficiency than other direct time integration algorithms such as HHT-α. In addition, numerical examples are presented, demonstrating that the proposed method is more accurate than several commonly used algorithms in structural dynamic applications.

KEY WORDS：time-discontinuous Galerkin finite element method,
shell structure, modal superposition, HHT-α.

並列關鍵字

time-discontinuous Galerkin finite element method

參考文獻

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