A topology optimization algorithm based on topological derivative and level set function to design phononic crystals

ROLANDO YERA; ALFREDO EDMUNDO HUESPE; CARLOS GUSTAVO MENDEZ; LUISINA FORZANI

ENGINEERING COMPUTATIONS

EMERALD GROUP PUBLISHING LIMITED

Año: 2021

0264-4401

Purpose: This work presents a topology optimization method for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as aconsequence of wave propagation phenomena in these media, bandgaps between two specifiedbands. An additional target is to enlarge the range of frequencies of these bandgaps.Design/methodology/approach: The resulting optimization problem is solved employingan augmented Lagrangian technique based on the proximal point methods. The main primalvariable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. Thischaracteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtainedthrough the dispersion relation of the phononic crystal.Findings: The description of the optimization algorithm is emphasized and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examplesfor several cases are presented, and the numerical performance of the optimization algorithmfor attaining the corresponding solutions is discussed.Originality: the original contribution results in the description and numerical assessment of atopology optimization algorithm using the joint concepts of the level-set function and topologicalderivative to design phononic crystals.