標題: 一非均勻樑的隨機動態分析Stochastic Dynamic analysis of a nonuniform beam 作者: 張曉欽Chang, Hsiao-Chin 關鍵字: Monte Carlo Simulation蒙地卡羅模擬法Perturbation techniqueStochastic finite element微擾法隨機有限元素法 出版社: 應用數學研究所 摘要: 本篇論文主要以微擾法及有限元素法, 討論一具有隨機楊氏彈性係數的非 均勻樑之動態反應分析。因為, 一樑元件之楊氏彈性係數在製造過程中, 極可能產生差異而變成非確定。為了工程應用之需要, 我們討論了下列幾 種非常有用的統計分析 : 撓度, 應變, 應力之期望值, 標準差,及自相關 函數。然後這些由微擾法所計算出之統計分析, 我們則利用蒙地卡羅模擬 法來加以檢驗。最後, 本文對此一樑結構之可靠度分析, 一有所討論。In this paper, the statistical dynamic responses of a nonuniform beam with stochastic Young's modulus of elasticity are obtained by using the perturbation technique in conjunction with the finite element method. The Young's modulus of elasticity is considered as random in position because of the unevenness due to the process of manufacture or construction. The proposed method produces the expectation, variance and autocorrelation functions of the deflection, strain and stress that are quite useful in estimating the structural safety and reliability. Some statistical responses obtained by the perturbation method are checked by the Monte Carlo simulation, also, the reliability analysis of the structure is performed based on certain failure criteria of the structure. URI: http://hdl.handle.net/11455/18625 顯示於類別： 應用數學系所