Efficient Methods for Flexibility-Based Meso-scale Dynamic Modeling

With the advent of additive manufacturing comes the opportunity to design novel components and systems, especially when one considers hierarchical structures. Our recent work Bielecki et al. (Struct Multidiscip Optim 64(6):3473–3487, 2021); Bielecki et al. (Multiscale compliant topology optimization for twistable wing design. In: AIAA AVIATION 2021 FORUM (2021), pp. 2429) has demonstrated a highly effective framework of multi-scale topology optimization for designing such structures. In this work, we focus on enhancing the efficiency of the analysis at the meso-scale by introducing a new complementary energy formulation. This enables the computationally attractive formulation of parametrically defined filament-based meso-structures of arbitrary path within each unit cell. We have implemented this framework for dynamical problems, specifically, for modal analysis. We considered mass lumping and static condensation within the unit meso-scale cells. Computational experiments are provided to test the robustness, accuracy, and computational efficiency of the approach.