In this work, a parametric optimization framework is developed to deal with fiber-reinforced elastomeric matrices. The fiber orientations are in a continuous set to obtain the set of angles that minimizes a functional given by the designer. Although this topic has been extensively studied in recent years, the vast majority of works use either gradient-based or global-based methods to define the composite fiber orientation, with the first being very prone to reach poor local minima and the latter increasing the computational burden exponentially with the number of design variables. Besides that, considering finite strain hyperelasticity, the number of works is substantially reduced. The main goal of this research is to study the efficiency of a local-based derivative-free algorithm in the optimization of problems considering finite deformation and material nonlinearity assumptions in fiber composite design. In order to show the proposed methodology efficiency, two optimization problems are studied: strain energy density minimization and mechanical stress minimization, with the latter further divided into a global and a cluster approach. Therefore, the main novelty of this work is to deal with fiber-reinforced elastomers optimization by means of a direct search algorithm in a constrained nonlinear optimization. The methodology can easily be implemented in existing finite element codes and the results show the pros and cons of both types of optimization.
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