The probabilistic mechanical-material modeling of complex non-homogeneous structures using the coupling of isogeometric boundary element method and reliability approach

Describing mechanical fields with precision in engineering analyses can be a challenging task. Analytical solutions fall short for real complex problems. The widespread use of numerical methods to overcome this obstacle has increased along with the advances in computational capacity. For instance, in geotechnical and composite materials problems, the use of a numerical approach becomes indispensable in several situations. For large volume-to-boundary ratio problems or for non-uniform fields evaluation, the boundary element method is a suitable tool. The method is based on the boundary discretization and on solutions to boundary integral equations. Thus, this article introduces the isogeometric boundary element method formulation and explores techniques for enhancing its physical problem descriptions, specially focusing in geotechnical issues and description of body forces. Two numerical examples are presented. Firstly, a multi-material dam, inspired by the real Itaipu dam section, is analyzed and the results are compared to the well-known ANSYS (R) FEM software. Furthermore, the article presents a tunnel case study in which a reliability assessment is conducted to account for the inherent uncertainties in the problem. This assessment is accomplished using the improved Hasofer, Lind, Rackwitz e Fiessler-first-order reliability method algorithm, which provides insight into the structural failure risk.