Effect of crack location on buckling and dynamic stability in plate frame structures

It is well known that damages affect the dynamic characteristics of the structures in such a way that they may lead those structures to fail. Therefore, it is essential to construct a reliable mathematical model for estimating the effect of the damage in these structures. In this study, the effect of the straight, through-thickness crack and its location on the thin single-bay one-storey, two-bay-one-storey, and single-bay two-storey plate frames is investigated. For this purpose, a four-node quadrilateral plate bending and membrane elements are combined to perform finite element free vibration analysis of the healthy and cracked thin plate frame structures. The Classical Plate Theory is employed to satisfy the strain and stress conditions of these thin structures. A computer code is written using MATLAB to obtain the first three natural frequencies, critical buckling loads, and the first unstable regions of the healthy and cracked thin structures. To ensure the validity of the employed mathematical model, a convergence analysis is performed via ANSYS. The effect of crack location in plate frame structures is investigated by measuring the differences between the healthy and cracked structures' first three buckling modes and the first unstable region. It is seen that the bending regions of the buckling modes are more affected by the crack than the other zones. Besides, crack occurrence within these regions has more impact on the first unstable regions. Accordingly, it has been revealed that the bending regions are the weakest locations of the frame structures. Therefore, potential cracks occurred within these regions may affect the structural integrity more than those of emerged in other regions.