Postbuckling analysis of elastic structures is used to identify the imperfection sensitivity of structures. In real structures, as opposed to academic examples, imperfections are unavoidable.
Imperfection-sensitive structures may fail at much lower loads than the buckling load of the corresponding perfect structures. To prevent such failure, the designer should consider converting imperfection-sensitive structures into imperfection insensitive ones by changing suitable design parameters. Sensitivity analysis of the initial postbuckling behavior provides information about the influence of parametric changes of a structure on its imperfection sensitivity. Koiter's initial postbuckling analysis, in the framework of the Finite Element Method (FEM), was applied to mathematically describe postbuckling paths and quantify the degree of imperfection sensitivity of a structure. The consistently linearized eigenvalue problem, representing a generalized eigenvalue problem, was thoroughly analyzed with regard to its usefulness for classification of structures on the basis of their state of stress at buckling. It was also used for derivation of a mathematical condition for buckling from a membrane stress state. Another topic that was investigated in this work is hilltop buckling, which is characterized by the coincidence of a bifurcation and a snap-through point. It was shown that a structure exhibiting hilltop buckling is inherently imperfection sensitive. This was the reason for considering hilltop buckling as the starting point of sensitivity analysis of the initial postbuckling behavior of structures, aimed at the aforementioned conversion from imperfection sensitivity to insensitivity.
Another special case is zero-stiffness postbuckling, representing a desirable mode if transition from imperfection sensitivity to imperfection insensitivity. Theoretical investigations of the possibility and predictability of its occurrence were made. In order to support the theoretical results, a considerable part of this dissertation was the implementation of theoretical results into a computer program based on the FEM. Using finite element routines from FEAP, an arc-length method for nonlinear problems, Koiter's postbuckling analysis and the consistently linearized eigenvalue problem were implemented in MATLAB. Because of limitations of the interface between the two programs, the practical applicability of the program is limited to a few thousand degrees of freedom. This was good enough for treating problems that were solved in order to verify theoretical results. The structures investigated in the numerical part of the thesis cover the whole range of the theoretical work: A pin-jointed two-bar system with two degrees of freedom, exhibiting zero-stiffness postbuckling, was treated analytically, as opposed to the other examples, for which the FEM was used. The second example, a von Mises truss, is characterized by buckling from a membrane stress state. Conversion from imperfection sensitivity into imperfection insensitivity occurs without zero-stiffness postbuckling. A shallow cylindrical shell serves as an example of a structure that buckles from a general stress state. A parametrized family of two-hinges arches, subjected to a uniformly distributed load, containing a parabolic arch as a special case, allows numerical verification of special features related to this special case.