Inverse Bifurcation Problem as a Tool For Rapid Identification of Progressive Collapse for Thin-Walled Systems

Abstract

Notwithstanding recent advances in robust design, the problem of vulnerability of structures is still open. On the one hand, this leads to various structure collapses; on the other hand, this prompts researchers to develop models and methods to identify a state o f progressive collapse and estimate lifetime and residual functionality of perturbed structure. An inverse bifurcation problem implies that one identifies a pre-bifurcation state of a perturbed thin-walled system. The topological precursor (a tool to solve an inverse bifurcation problem) used is based on typical sequences o f deformed states extracted from clustered post-critical solutions o f non-linear boundary problem o f thin-walled systems theory. It implies that complete bifurcation structure o f the non-linear boundary problem (including primary, secondary and tertiary bifurcation paths) are constructed. The proposed approach was employed to identify a pre-bifurcation state of a cylindrical shell under uniform pressure (close to the critical) subjected to a pulse impact.