Geometric parameterization of unit cell configurations for reduced basis approximation

Abstract

To facilitate rapid yet accurate multiscale homogenization, we formulate geometric mapping schemes that effectively handles the fiber radius changes of a unit cell to dispense with mesh regeneration. To further expedite unit cell analysis involving fiber radius variation, we integrate the formulated geometric transformations into reduced basis analysis using an empirical interpolation method. For demonstration, we examine the proposed geometric parameterization strategies with the linear elastic analyses of square and hexagonal unit cells under tension and shear loads, respectively. Overall, reduced basis analyses combined with the devised geometric mappings are found more efficient than the corresponding finite element analyses while producing insignificant errors.