Finite element analysis of the plastic buckling of a cantilever beam

• Main Author: Yuan, Qizhong
• Other Authors: Memorial University of Newfoundland. Faculty of Engineering and Applied Science
• Format: Thesis
• Language: English
• Published: 1998
• Subjects: Buckling (Mechanics) > Mathematical models; Plasticity; Girders; Newfoundland studies; University of Newfoundland
• Online Access: http://collections.mun.ca/cdm/ref/collection/theses3/id/19872

Thesis (M.Eng.)--Memorial University of Newfoundland, 1999. Engineering and Applied Science Bibliography: leaves 86-88 Finite element analysis offers a general plastic buckling solution of structures by employing a nonlinear static plastic analysis with gradually increasing loads to seek the load level at which the structure becomes unstable. Nonlinear plastic finite element analysis requires inclusion of geometric nonlinearities and material nonlinearities in the model. Geometric nonlinearities refer to the nonlinearities in the structure due to changing geometry as it deflects. There are two kinds of geometric nonlinearities concerned in plastic buckling analysis, large strain and large deflection. On the present work, Newton-Raphson procedure, a process to solve the nonlinear equations by increasing load in several steps and iterative computation to reach the convergence criteria, is applied for the plastic buckling analysis. -- A general model for rectangular cross section cantilever beams is presented, which flexibly defines the material property and dimensions of a cantilever beam. Overall behavior of the beam is studied by combining analytical methods for elastic buckling analysis and finite element analysis for plastic buckling analysis. Two non-dimensional parameter ratios of thickness by length t/1 and ratio of height by thickness h/t are used to evaluate the overall behavior of a cantilever beam. The two boundaries of elastic buckling and yielding, and plastic buckling and collapse are also investigated.