Stability analysis of curved panels

Abstract

Aerospace, mechanical and civil engineering systems extensively use curved panels as structural components. The curved panels exhibit high risk of loss of stability especially with modern requirements for increasingly lighter designs. Correct identification of the load-carrying capabilities and thorough understanding of the stability behavior under transient excitations provide necessary information to safely design such structural components. In this work we use the arclength and branch-switching methods to correctly identify the buckling load and all equilibria. Compared to other methods, prior knowledge of the bifurcation modes is not required and the same mesh is used for tracing all secondary equilibrium paths. This method can identify secondary branches that other procedures failed to retrieve. Finally, the transient behavior of curved panels is also examined; in particular we seek to identify the dynamic snap-through boundary that separates small amplitude non-snap from large amplitude post-snap vibrations. Typically, analytical solutions for such highly nonlinear behavior are not available, and extensive parametric studies are usually required leading to very high computational cost.We examine the connections between different dynamic snap-through boundaries and seek to correlate them with features of the equilibrium manifold to identify computationally more efficient ways for their estimation.