Buckling and modal analysis of rotationally restrained orthotropic plates

This paper describes a theoretical approach for the static buckling, eigenfrequency and vibration buckling analysis of typical orthotropic plates used in aeronautical constructions. The plates are constrained with any combination of simply-supported and rotationally restrained edges, and are subjected to biaxial compressive loads. The derivation of closed-form solutions is discussed, and the results are presented in the form of design charts, where the effect of the restraint stiffness is highlighted. The proposed design charts allow a more accurate initial sizing of typical aerospace structural components, like stiffened panels, where both static and dynamic buckling loads are fundamental for the final design. As compared to classical solutions based on simply-supported and clamped edges, the modeling of the edge constraint as an elastic restraint provides a more refined description of the real stringer-stiffened panel. The results demonstrate that, in contrast to the commonly adopted simply-supported boundary condition, a reduction of the design conservativeness can be achieved if the stiffness of the restraint is accounted for. A novel set of results relative to the vibration buckling is derived, illustrating that the dynamic buckling tends to increase for load frequencies higher than the first natural frequency.