運動阻尼於向量式有限元素法靜力分析之研究

On the Static Analysis Using Vector Form Intrinsic Finite Element Method with Kinetic Damping

莊清鏘(Ching-Chiang Chuang)；陳璽予(Zi-Yu Chen)；吳俊霖(Chiun-lin Wu)

向量式有限元素法 ； 質量阻尼 ； 運動阻尼 ； 靜力分析 ； vector form intrinsic finite element method ； mass proportional damping ； kinetic damping ； static analysis

先進工程學刊

13卷2期（2018 / 07 / 01）

49 - 55

繁體中文

本研究主要利用運動阻尼概念進行向量式有限元素法的靜力分析，同時和原始向量式有限元素法的靜力模擬方式比較，說明其可行性。向量式有限元素法用點值描述、途徑單元、逆向運動、牛頓第二運動定律和顯式時間積分法分析結構反應，為動力分析方式，靜力分析要有消能或減速機制。原始的向量式有限元素法用正比質量的速度阻尼消散系統動態反應，但經常要多次的試誤和較多計算量，有時甚至不易獲得相應的靜力解。不同於傳統向量式有限元素法的靜力模擬方式，本研究改用運動阻尼，最後以簡單算例比較運動阻尼和質量阻尼靜力模擬的精確性、穩定性和有效性。

This paper presents an improved approach to conducting structural static analysis using the Vector Form Intrinsic Finite Element (also known as VFIFE) method with incorporation of kinetic damping. VFIFE is a powerful tool for conducting structural dynamic analysis, which integrates the ideas of mass particles, path of motion, fictitious reversed rigid body motion, Newton's second law of motion, and explicit time integration scheme. VFIFE needs to employ artificial energy dissipation and/or deceleration mechanisms in order to carry out static analysis. The original version of VFIFE introduces fictitious mass-velocity proportional damping to perform static analysis, which requires trial-and-error for selection of damping level and extra computational efforts to obtain accurate solutions. In contrast to the original VFIFE, this study suggests the usage of kinetic damping and illustrative examples are given to compare the proposed approach with the original VFIFE in terms of accuracy, numerical stability, and effectiveness.

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1. 莊清鏘,孫東磊,吳俊霖(2021)。向量式有限元素法於馬鞍型索網結構的找形研究。先進工程學刊，16(2)，43-49。
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