| In this study, finite element formulation and solution procedures for buckling and post-buckling analysis of regular and cracked structures under various loading conditions were studied. The study consists of two main parts. The first part focuses on the finite element formulation for buckling (eigen) analysis of regular and cracked structures and some eigen-analysis applications of cracked structures. The second part covers post-buckling analysis procedures with some applications. Buckling and post-buckling analysis of cracked structures requires special elements and additional procedures to trace fracture information during pre- and post-buckling stages. The "enriched crack tip element" is one of the special element types used to adopt crack the tip stress singularity into the finite element method. By using this type of element, post-buckling fracture information at crack tips or crack fronts in 3-dimensional structures can be properly traced with a high degree of precision.;In the first part of this study, basics of continuum mechanics, strain and stress definitions, and equilibrium equations are derived. Formulation of the finite element equations based on continuum mechanics was obtained. The subspace iteration method, as an eigen-solution technique, with effective sparse matrix storage format, was implemented into the FRAC3D finite element analysis software. Thin plates with cracks or cutouts under tensile loads exhibit local buckling. Although, this problem has been known for decades, it presents very difficult mathematical challenges even in cases with geometric simplicity. For example applications, buckling analysis of the cracked thin plates with inclined and straight central cracks under tensile loads were analyzed. Parametric studies were carried out to examine the effects of geometric and material properties on the critical buckling loads.;In the second part of this study, post-buckling analysis procedures are discussed and a perturbation method was applied to obtain postbuckling solution for cracked structures. It was observed that post-buckling fracture behaviour is fundamentally different than linear fracture analysis, in which buckling and large deformations are not considered. It can be concluded that fracture analysis of structures with cracks that exhibit localized buckling under tensile, thermal or other loading conditions, should be analyzed correctly by using coupled fracture/buckling and post-buckling analysis. |
