• 作者： 田堯彰; 楊仁和
• 作者服務機構： 台灣大學地震工程研究中心
• 中文摘要： 因不確定因素而作分析的結構可靠度乃結構設計時的重要參考依據。一個典型的系統隨機性問題即是材料性質具空問上的變異。是以本文旨在推導桁架與梁元素的隨機勁度矩陣，俾傳統的有限元素法得以計算因材料性質具空間隨機變異而引致之結構的反應變異性。 一個結構元素可依隨機場的變動度分為數個次元素。次元素的彈力特性以隨機場的局部“空問平均”表之。藉靜態濃縮將增加之自由度去除，使新導出的元素勁度矩陣自由度如傳統者。據此以建立系統勁度矩陣與方程式。利用一階擾動法吾人可求得節點位移，其由確定與隨機的兩部分組成。數值例顯示本研究提供一個較易處理的步驟，以求得複雜結構的反應變異性，同時有良好的精度與計算效率。
• 英文摘要： The reliability of structures in the presence of uncertainty has been a crucial factor in their analysisand design. A typical example of system stochasticity problems is the spatial variation of the materialproperty. Indeed, the primary focus of this study was to derive the stochastic stiffness matrices for atruss and a beam element, so that the conventional finite element method could be utilized to evaluatethe response variability of a structure whose material property exhibited spatial random variation. A structural element is divided into several sub-elements whose number depends on the scale offluctuation in a random field. In each sub-element, the elastic characteristics are represented by the local"spatial average" of the field. Upon application of static condensation, we eliminate the additional degrees-of-freedom stemming from the division of sub-elements to produce a new element stiffness matrix whosesize is equal to the conventional one. The global stiffness matrix and system equation are then established.With the aid of the first-order perturbation method, we obtain the nodal displacements, which consist notonly of the deterministic component, but also of the random component. Numerical examples show thatthis study provides a more tractable procedure for determining the response variability of a complexstructure, with good accuracy and computational efficiency.
• 中文關鍵字： material variationl finite element method; stochastic process
• 英文關鍵字： --