Identificação de falhas de contato em meios compostos via inferência Bayesiana e modelos reduzidos

Abstract

This work presents a heat conduction problem in a laminated composite with heating through the application of a heat flux on the lower surface and exchanging heat with the environment by convection on the upper surface and aims to evaluate and detect the possible existence of contact failures in the region of an adhesive that joins the layers. The problem equations were written following a single domain formulation, which makes it possible to write the same system of equations for the different problem domains, just writing the material properties as functions with spatial variation. Due to the high computational cost observed to solve the associated direct problem, in this work two different reduced models are proposed that represent an approximation of the complete model, but with lower computational cost. The first involves modeling the adhesive region using an Improved Lumped formulation. In turn, the second involves modeling the top layer of material. The direct problem was solved using the NDSolve function of the software Mathematica and to verify the convergence of the solution both the Classical Integral Transform Technique and the software COMSOL were used. The failures detection, for both proposed models, involves the estimation of functions with spatial variation. The inverse problem was solved using the Markov Chain Monte Carlo (MCMC) method within a Bayesian approach, which was implemented with the Metropolis Hastings algorithm with Total Variation priori. Failure detection methodologies were analyzed through simulated temperature measurements. It was observed that the proposed reduced models were able to estimate the contact failure region in all cases considered with reduced computational cost .