Topology optimization for energy dissipation design of lattice structures through snap-through behavior

摘要

Topology optimization for damping design of lattice structures is proposed in this work. Compared to metal lattice or viscoelastic materials, lattice structures made of soft materials composed of bi-stable elements show exceptional energy dissipation properties with fully recoverable capacity. Theoretical energy absorption capacity is a key concept to describe damping properties of architectured metamaterials, which reflects the maximum energy absorption per element if a bi-stable chain contains infinite buckling elements. To achieve extreme damping design, topology optimization algorithm is formulated to achieve extreme theoretical energy absorption capacity within a prescribed design domain. An approximate mathematical expression for the energy absorption capacity is formulated with rigorous derivation of sensitivities. Element strain energy in P-norm formulation is constrained at limit points to alleviate material softening failure under large strain. Four design cases are presented and discussed in detail. Results demonstrate that the optimal bi-stable elements achieved by topology optimization algorithm show programmable properties with desired energy dissipation capacity. (C) 2019 Elsevier B.V. All rights reserved.