A STUDY ON THE GEOMETRICALLY NONLINEAR BUCKLING AND POST-BUCKLING BEHAVIOR OF THIN-WALLED OPEN-SECTION BEAMS
蕭 國 模
|關鍵字:||薄壁開口梁;幾何非線性;翹曲自由度;非線性挫屈;共旋轉全拉格蘭日法;Thin-walled open-section beam;Geometrical nonlineaity;Warping degrees of freedom;Nonlinear buckling;Corotational total Lagrangian formulation|
Studies on the geometrically nonlinear behavior and nonlinear buckling analysis of thin-walled open-section beams have been relatively rare. A two-node displacement-based thin-walled open-section beam element with seven degrees of freedom per node is developed by using corotational total Lagrangian formulation for the geometrically nonlinear, nonlinear buckling and postbuckling analysis of thin-walled open-section beams. In this thesis, element nodes are chosen to be the shear centers of end sections of the element. The shear center axis is employed as the reference axis of the beam element. The element deformations are referred to the initial undeformed geometry of the beam element and described in element coordinates which are constructed at the current configuration of the beam element. The internal nodal forces are systematically derived by using virtual work principal and a consistent second-order linearization of the fully geometrically nonlinear beam theory based on the exact kinematics of Euler beam to consider the coupling among bending, twisting and stretching deformations for the beam element. The third-order term of twist rate is the dominant term for the third-order terms and may be a very important term to reflect the nonlinear behavior of the beam subjected to a pure torque. Hence, the third-order term of twist rate is also considered in the element nodal forces. 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. For the buckling and postbuckling analysis of the structural system, only the nongyroscopic conservative system is considered in this thesis. A parabolic interpolation method of the arc length is proposed to find the nonlinear buckling load. An inverse power method for the solution of the generalized eigenvalue problem is used to find the corresponding buckling mode. In order to gain access to the secondary path from the primary path, at the bifurcation point a perturbation displacement proportional to the first buckling mode is added. To verify the accuracy of the present finite element formulation, numerical examples are studied and compared with published experimental results and numerical results obtained by nonlinear shell elements available in the literature. Comparisons between the present numerical results and those obtained by other beam elements or other methods available in the literature are also given in this thesis. Case studies are performed to investigate the effects of section geometry, slenderness ratio, warping boundary conditions, and location of loading point on the elastic buckling load and postbuckling behavior of the thin-walled beam structures.
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