Application of Straight-Beam Transfer Matrix to Buckling Theory of Curved-Beam with Variable Curvature

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簡歷

基本資料

Project title

Code/計畫編號

NSC99-2221-E019-016

Translated Name/計畫中文名

直梁傳接矩陣在變曲率梁挫屈理論的應用

Project Coordinator/計畫主持人

Shyh-Rong Kuo

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=2116673

Year

2010

Start date/計畫起

01-08-2010

Expected Completion/計畫迄

31-07-2011

Bugetid/研究經費

625千元

ResearchField/研究領域

土木水利工程

"本研究主要提出一個新的簡易方法，藉由直梁桿件的狀態傳接方程式，推導變曲率曲梁的挫屈理論。因為挫屈方程式是建立在變形後的力平衡狀態，文獻中主要是由連體力學的大變形理論出發，引進線性應變能及非線性應變能，應用變分法求得曲梁桿件的挫屈方程式。此推導過程須完整考慮六項非線性應變，及合理處理物理意義不明確的非線性應變能，並且正確的分析旋轉變形後彎矩引量所做的虛功，才能求得完整合理的曲梁挫屈方程式。由於推導過程較為複雜，文獻中有些曲梁桿件挫屈理論，無法通過剛體運動及增量力平衡的基本要求。本計畫主要可分成二個部分，其中第一部分是探討直梁元素勁度矩陣與元素傳接矩陣及其直梁挫屈方程式之間的關連性。首先說明直梁元素勁度矩陣與直梁元素傳接矩陣的關係，接著利用元素長度趨近於零之極限原理，求得直梁桿件的狀態方程式及其對應的挫屈理論。最後與文獻中的直梁挫屈方程式作比較，由此驗證本研究推導方法的正確性。本研究第二部分是探討直梁元素傳接矩陣與曲梁元素傳接矩陣及其變曲率曲梁挫屈理論之間的關係。由有限元素的理論可知，當曲梁桿件元素切得過多 (元素長度趨近於零)，則可採用直梁元素的勁度矩陣，模擬分析變曲率曲梁桿件的力學行為。因元素傳接矩陣是由元素勁度矩陣求得，由此可知當曲梁元素長度趨近於零，則直梁元素的傳接矩陣，藉由曲梁元素節點自由度在沿曲梁切線座標與直線座標的座標轉換運算後，可用來近似曲梁元素的傳接矩陣。本研究第二部分是應用上述的論點，推導變曲率曲梁的傳接矩陣，接著再利用極限原理，求得變曲率曲梁桿件的狀態方程式及挫屈理論。本計劃所提出的方法，僅需進行簡單的矩陣運算，物理意義明確，且可避免傳統繁雜且不易理解的推導過程，所求得的變曲率曲梁挫屈理論，能自動滿足剛體運動法則及力平衡此二項基本力學條件。" "When formulating the buckling equations of curved-beams with variable curvature, in addition to laborious derivations of conventional nonlinear strains, researchers usually need to deal with the induced moments caused by cross sectional stress results under rotations for satisfying the qualification of rigid body rule provided by Yang and Kuo (1994). To simplify the complicated procedure, this study attempts to introduce the concept of straight-beam transfer matrix into curved beam theory for a consistent derivation of governing equations of a curved beam element with variable curvature. The entire project is divided into two parts. The first part is to establish the relationship between straight-beam element stiffness matrix including geometric effect and beam element transfer matrix for deriving the governing equations of conventional straight beam theory. The purpose of this part is to verify the applicability of the present method to conventional buckled beam theory. Based on the state transfer matrix method developed previously, the second research work is focused on the theoretical development of transformation relationship between straight-beam transfer matrix and curved-beam transfer matrix. In this stage, the transformation matrix should take the second order effect induced by external forces due to buckling into account. Finally, the curved-beam equations with variable curvature at buckled state can be derived from the straight-beam equations in conjunction with the circular curved-beam transfer matrix through successive coordinate transformations. It is emphasized that since a curved beam can be treated in the limit as the composition of an infinite number of infinitesimal straight-beam segments, the equilibrium conditions at connected joints of the composition of straight-beam segments should be established in the buckled configuration. Concise physical meanings and fundamental matrix manipulation in deriving the governing equations of curved-beam with variable curvature considering buckling configurations are main features of this research project. Besides, both the qualification of rigid body test and the conditions of force equilibrium are always satisfied in the process of theoretical development."

Keyword(s)

變曲率曲梁
挫屈理論
狀態方程式
剛體運動法則
增量力平衡
傳接矩陣
beam theory
curved beam
variable curvature
rigid body motion rule
force equilibrium in the deformation state
transfer matrix

DSpace CRIS

Application of Straight-Beam Transfer Matrix to Buckling Theory of Curved-Beam with Variable Curvature

基本資料

Description