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題 名 | 平面構架幾何勁度矩陣之簡易推導法=Simplified Procedure for Derivation of Geometric Stiffness Matrix for Planar Frame Element |
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作 者 | 楊永斌; 楊順欽; 姚忠達; | 書刊名 | 中國土木水利工程學刊 |
卷 期 | 9:2 1997.06[民86.06] |
頁 次 | 頁249-261 |
分類號 | 440.15 |
關鍵詞 | 剛體運動法則; 幾何勁度矩陣; 元素檢測; 線性化挫屆; Rigid body rule; Geometric stiffness matrix; Element quality test; Linearized buckling analysis; |
語 文 | 中文(Chinese) |
中文摘要 | 本文旨在說明如何以剛體運動法則,推求平面構架元素之幾何勁度矩陣。對於傳 統有限元素法以形狀函數推導元素矩陣的作法,很可能因為元素本身幾何條件的限制,而無 法求得良好的幾何功度矩陣,改用本文之方法後,此一問題將平再出現。此法係以元素於平 衡力系作用下,受到剛體運動所產生之幾何效應為基礎,僅須進行簡單的代數運算,即可求 得元素之幾何勁度矩陣,不僅可以免除元素本身所受幾何條件的限制,亦可通過剛體運動法 則的檢測。此法由於忽略了元素自然變形的幾何效應,因此可以說是一種近似方法,但只要 在分析時,使用夠多的元素,即可得到非常良好的結果,而對於越複雜的結構,其計算效率 亦越高。採用本法的最大特色為簡單和合理,並且具有推廣至其他複雜元素之潛能。 |
英文摘要 | In this paper, it is demonstrated how the rigid body rule can be appli ed to deriving the geometric stiffness matrix for a planar frame ele-ment. Conventionally, the derivation of stiffness matrices for an element begins with the selection of shape functions. Such a method may fail be-cause of the inability to meet the various constraints imposed by the ge-ometry of the element. With the peresent method, the constraint problem can be easily circumvented. The present emthod starts by considering an element that is in equilibrium under the action of a set of initial nodal forces. By subjecting the element to rigid body displacements, one can determine from the rigid body forces the geometric stiffness matrix for the element, which requires only very simple algebraic operation. using this method, the geometric constraints of each element need not be con-sidered, while the derived stiffness matrix is guaranteed to pass the rigid body test. As the member deformation has been neglected in the formu-lation, the stiffness matrix derived herein is only neglected in the formu-lation, the stiffness matrix derived herein is only approximate. However, it works generally well if the mesh used is fine enough. of most im-portance is the fact that the more complicated the structure, the higher efficiency can be achieved in the computation. One basic characteristic of the pressent method is its simplicity and rationality, which has the potentia l of application to other complex complex elements. |
本系統中英文摘要資訊取自各篇刊載內容。