Plates and shells are well used in structures. In order to study the nonlinear stability of plate, the total potential energy expression was deduced after analyzing the geometrical conditions of four ends simply supported rectangular plate on large deflection, the cusp catastrophic model of the rectangular plate was established based on catastrophe theory, and the bifurcation set that makes the system unstable was obtained to analyze the instability conditions of rectangular plate. The instability conditions of rectangular plate were analyzed based on this set, the critical inner stress is at the cusp point, the necessary condition of instability is σ>σcr, but the plate is stable when the movement path of control variables composed by inner stress and landscape load not across the bifurcation curves in the control space. Structures in some projects can be predigested to such a rectangular plate and this cusp catastrophic model can be used for analyzing its instability conditions for taking preventive measures.
This work investigated the fatigue crack propagation behavior of the 2195-T8 Al-Li alloy with precorroded holes. The microstructure, crack growth path, and the fracture surfaces of the samples with the precorroded holes have been examined with scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and computed tomography (CT). The characteristics of the crack growth have been analyzed via fracture mechanics by employing the finite element method (FEM). The results showed that the bulk of the fatigue cracks had been initiated from the corrosion pits and corroded discontinuously and precipitated further to become intergranular. Owing to the superposed stress concentration caused by the corrosion pits, the porous region at the bottom of the precorroded hole had affected the crack propagation performance. Crack growth rates were different in multiple positions owing to the difference of
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at crack fronts.
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