Modelos de elementos finitos e técnica de homogeneização Aplicados à análise confiabilística de domínios bidimensionais reforçados

Abstract

The present work deals with reliability-based analysis of reinforced domains using finite element models and homogenization techniques. The search for solutions in problems of structural engineering have advanced significantly with the aid of numerical techniques developed in the last decades, such as the Finite Element Method (FEM), widely used in several applications. In the analysis of structures with heterogeneous materials, the coupling of different types of finite elements can be used to ensure a better approximation of the macroscopic or even mesoscopic constitution of some product, taking into account the contribution of the different phases. Thus, FEM stands out as a good choice for the study of stiffened domains, which refers to composite materials. The structural reliability theory contributes to the evaluation of the structural performance, quantifying the influence of the randomness of the design variables, allowing a more robust understanding of the safety levels. The methodology adopted considers the discretization of the matrix in 2-D quadratic quadrilateral finite elements and linear triangular finite elements, and the reinforcement incorporation is evaluated in two ways: by the discretization of the reinforcement in truss elements; and obtaining properties of the heterogeneous media by using the homogenization technique based on the Mori-Tanaka model. Plane stress state and linear elastic regime are considered. Material parameters, as Young Modulus and yielding limit stress, and load variables are described as random variables, according to the literature. The presented examples address the influence of reinforcement on the strength and rigidity of beams and plates, and the probability of occurrence of some serviceability limit states. Therefore, the applied methodology is validated, illustrating its application. The results illustrate the variability on the numerical response of the proposed examples, due to the consideration of the uncertainti es.