The nonlinear analysis of three dimensional buckled beam

• Main Author: 黃楚璋
• Other Authors: 蕭國模
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/93487796603806816497

碩士 === 國立交通大學 === 機械工程學系 === 99 === The buckling and postbuckling behavior of clamped spatial rods subjected to a prescribed end axial rotation first, and then under compressive axial displacements is investigated using the corotational finite element method. The consistent co-rotational finite element formulation for three-dimensional Euler beam presented by Hsiao and Lin [18] is employed here. Both the Green strain and engineering strain are used for the measure of strain here. All coupling among bending, twisting, and stretching deformations for beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. An incremental-iterative method based on the Newton-Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. Numerical examples are presented to investigate the effect of the prescribed end axial rotation and slenderness ratio on the initial, buckling, and postbuckling end axial reaction force of spatial rods under end compressive axial displacements. The results obtained using the Green strain and the engineering strain, are compared. The effect of self-weight and initial imperfection is investigated also.