Fundamentos para o projeto de vigas de concreto reforçado com fibras de aço com suporte de técnicas de otimização topológica

Abstract

In recent years, the use of steel fiber-reinforced concrete (SRFC) structural elements has been driven by technical developments and research that have enhanced our understanding of the mechanical behavior of this material. Aimed at improving the ductility and toughness of concrete, randomly incorporating steel fibers into the mix presents an alternative for reinforcing concrete in a post-cracking stage. However, despite various advancements in applications, there is still an open research field regarding the application of structural optimization techniques for this material. In terms of constitutive models, SRFC is considered a heterogeneous material. Using homogenization theory, based on micromechanics of mean fields, effective elastic properties can be defined for the homogenized material, given the properties of the constituents and mix proportions. To predict post-cracking behavior, a strength criterion can be adopted for composite characterization. In this context, the Drucker-Prager model is used as a criterion for evaluating the strength parameters of the homogenized material. This study contributes to the fundamentals of structural design assisted by topology optimization techniques, through numerical analysis in finite element software ABAQUS®, employing homogenization models in conjunction with the SIMP method. In the presented examples, topology optimization is validated for elastoplastic materials, specifically for beam analysis. Results demonstrate the influence of optimization parameters, mix proportions, and design requirements in accordance with normative references. With the goal of establishing a methodology of analysis that facilitates the use of lighter and stronger elements, without the traditional incorporation of steel bars into concrete, the case study indicates that, for the elements of SFRC, reinforcements are necessary to ensure ductile failure.