Numerical formulations based on the Isogeometric Boundary Element Method for the probabilistic analysis of crack propagation in nonhomogeneous media

• Grant number: 16/23649-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: July 01, 2017
• End date: March 31, 2021
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Edson Denner Leonel
• Grantee: Heider de Castro e Andrade
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 19/03340-3 - Extended isogeometric boundary element method formulation applied for multiple crack propagation modelling, BE.EP.DR

Abstract

This thesis project aims the development of numerical formulations based on the Boundary Element Method (BEM) for the mecano-probabilistic analyses of cracked materials into nonhomogeneous structural systems. The BEM is an accurate numerical method for such problems. Due to the non-requirement of a domain mesh with BEM, stresses concentrations at the crack tips are accurately determined. Moreover, the mesh dimensionality reduction provided by the BEM makes the remeshing procedures during the crack propagation a less complex task. Numerical formulations for crack propagation in brittle or quasi-brittle materials, isotropic or anisotropic materials, either viscous or not, subjected to fatigue or direct fracture, positioned in homogeneous or nonhomogeneous media will be developed. Initially, the BEM formulations will be based on the isoparametric approach. However, the extension of such a formulations for the isogeometric approach is intended, in order to improve the approximations over the geometry and the boundary conditions. Emphasis is dedicated to the coalescence and multiple crack propagation problems. The numerical analyses involving the Weibull's model and Fracking, particularly, will be addressed. The mechanical collapse mechanisms are subjected to large randomness. Thus, reliability algorithms will be coupled to the BEM formulations, in order to propose realistic approaches. Therefore, collapse configurations and mechanical resistance are analyzed in the probabilistic context. Finally, this thesis project aims the improvement on the field of application of BEM, especially in a domain in which it is acknowledged as more efficient than other numerical method. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DE CASTRO E ANDRADE, HEIDER; LEONEL, EDSON DENNER. The multiple fatigue crack propagation modelling in nonhomogeneous structures using the DBEM. Engineering Analysis with Boundary Elements, v. 98, p. 296-309, JAN 2019. (16/23649-0)

OLIVEIRA, HUGO LUIZ; DE CASTRO E ANDRADE, HEIDER; LEONEL, EDSON DENNER. An isogeometric boundary element approach for topology optimization using the level set method. Applied Mathematical Modelling, v. 84, p. 536-553, AUG 2020. (16/23649-0, 19/03340-3)

ANDRADE, H. C.; LEONEL, E. D.. An enriched dual boundary element method formulation for linear elastic crack propagation. Engineering Analysis with Boundary Elements, v. 121, p. 22-pg., 2020-12-01. (16/23649-0)