The Buckling and Post-Buckling and their Stability of a Circular Elastic Arc

• Main Authors: Wen-Sung Tan, 譚文松
• Other Authors: Chia-Ou Chang
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/61792764237903725715

碩士 === 國立臺灣大學 === 應用力學研究所 === 88 === When adoption of priciple of virtual work energy or the Hamilton''s principle, one thing should be noted is that one should construct virtual strain energy with linear strain Eij, not with nonlinear strain eij. According to this argument, this dissertation derived governing equations for circular arc under uniform pressure loading. Furthermore, this dissertation made linear analysis to obtain bulking loads of ring and circular arc with various angles under both fixed and pinned boundary conditions. Nonlinear terms are added into consideration to simulate the sub-equilibrium path after the occurrence of bulking correctly. At last, this dissertation made dynamic analysis for both primary equilibrium path and sub-equilibrium path to understand that if those paths are stable or not after the occurrence of bulking. We obtain the following conclusions: First, circular arc under uniform pressure loading will not buckle when direction of pressure remains constant after deformation of circular arc. Second, tendencies of sub-equilibrium paths are totally different for neutral axis extensible and inextensible circular arc under uniform pressure loading when direction of pressure remains orthogonal to the deformed surface (i.e. liquid pressure). For neutral axis extensible circular arc, the sub-equilibrium paths reveal stable phenomenon. On the other hand, the sub-equilibrium paths reveal unstable phenomenon for neutral axis inextensible circular arc. This shows that the assumption of neutral axis inextensible is unrealistic and unsuitable to adopt when trying to simplify the governing equations for circular arc.