Detection of contact failures employing combination of integral transforms with single-domain formulation, finite differences, and Bayesian inference

摘要

This work addresses the hybrid numerical–analytical solution of heat conduction in multilayered media by means of a single-domain formulation, integral transforms, and the finite difference method. The basic concept is to incorporate different materials into spatially variable coefficients with abrupt transitions, representing different subdomains of the original problem. The classical integral transform technique is employed, and the problem solution is written as an expansion in terms of eigenfunctions obtained from an eigenvalue problem with spatially variable coefficients. To solve this eigenvalue problem, the finite difference method with a second-order accuracy scheme was employed. In order to illustrate the application of the methodology, the problem of heat conduction within a multilayered pipe was considered, including the identification of a defect in the junction region of a laminated composite, in which the adhesion of two different materials is imperfect. The failure identification was carried out by estimating the thermal conductivity throughout the region containing adhesive using the formulation and the solution of an inverse problem within the Bayesian framework.