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LEONEL, E.D. Nonlinear Boundary Element Models to Analyse Fracture Problems and Reliability / Optimization Models applied to Structures submitted to Fatigue. 406p. Tese (Doutorado em Engenharia de Estruturas) Escola de Engenharia de São Carlos, São Carlos, 2009. This work deals with the development of Boundary Element Method (BEM) formulations to be used in engineering problems. Particular attention is given to using these formulations in development of reliability and optimization models applied to fatigue problems. Contributions to BEM formulations are developed, particularly, models that deal with crack growth in plane domains composed by brittle, quasi-brittle and ductile materials. Taking into account these different types of materials, the proposed formulation properly represents the nonlinear structural behaviour induced by crack growth and the resulting structural damage. The dual BEM formulation is adopted here for the proposed crack model and to analyse random crack propagation. In this thesis tangent operators are used in the non-linear BEM formulations, in order to deal with cohesive crack, contact problems and debonding problems in reinforced domains. Regarding structural reliability analysis, the fatigue mechanical model was coupled with appropriate reliability algorithms to compute the reliability index and other important random values. Several reliability algorithms were tested for this coupled model, in order to find the most efficient in the analysis of fatigue problems. An optimization model was also coupled with the fatigue reliability model, in order to evaluate the optimal structural element dimensions and also to schedule the intervals for maintenance and inspection procedures, taking into account the minimum cost and problem uncertainties. Many examples are presented in order to show the efficiency and accuracy of the proposed formulations in dealing with crack propagation, fatigue reliability analysis and optimization problems.

Modelos não lineares do método dos elementos de contorno para análise de problemas de fratura e aplicação de modelos de confiabilidade e otimização em estruturas submetidas à fadiga