An extensive comparative analysis on multi-cracked beams with uncertain damage

Abstract

The present paper is devoted to the structural response analysis of multi-damaged beams with open cracks characterized by uncertain parameters. The generic crack is modeled as a linearly-elastic rotational spring whose stiffness (in turn related to the crack depth) and position are treated as uncertain variables. Following both probabilistic and non-probabilistic approaches, the uncertain parameters are described by random variables with assigned probability density functions (PDFs) as well as by uncertain-but-bounded variables defined in terms of lower and upper bounds. Taking full advantage of the closed analytical forms for all the beam response functions with an explicit dependence on the uncertain parameters the Probability Transformation Method (PTM) applied in the stochastic setting returns the PDFs of the response functions; within a non-probabilistic framework, a sensitivity-based (SB) method or a global optimization (GO) technique allow to evaluate their bounds. Through a broad numerical investigation, the response intervals are directly compared with the response PDFs, overcoming the common comparison in terms of the so-called confidence intervals related to a second-order stochastic analysis and providing a new perspective on the interpretation of the results.