Application of state matrix to buckling theory of curved-beam with variable curvature

• Main Authors: Wei-Chao Wang, 王瑋詔
• Other Authors: Shyh-Rong Kuo
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/39180944247319907793

碩士 === 國立臺灣海洋大學 === 河海工程學系 === 100 === When formulating the buckling equations of curved-beams with variable curvature is laborious derivations of conventional nonlinear strains. This paper proposes a new method of a simplified formulating the buckling equations of curved-beams with variable curvature .The study is divided into two parts. The first part is to establish the relationship between a straight-beam with the element stiffness matrix including beam element transfer matrix and state matrix for deriving the governing equations of conventional straight beam theory. 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. The curved-beam equations with variable curvature can be derived from the straight-beam equations in conjunction with the transfer matrix through coordinate transformations. In this article, three derivation processes have been proposed to establish the relationship with the state matrix of straight beam and curved beam by using the transfer matrix through coordinate transformations. The second part is using the new method to the curved-beam equations with variable curvature at buckled state can be derived from the straight-beam equations with transfer matrix through coordinate transformations. 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 study.