A fully adaptive topology optimization algorithm with goal-oriented error control

2011 ◽  
Vol 89 (15-16) ◽  
pp. 1481-1493 ◽  
Author(s):  
Matteo Bruggi ◽  
Marco Verani
Keyword(s):  
Topology Optimization ◽  
Optimization Algorithm ◽  
Error Control ◽  
Fully Adaptive ◽  
Adaptive Topology

A topology optimization algorithm based on topological derivative and level-set function for designing phononic crystals

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Rolando Yera ◽  
Luisina Forzani ◽  
Carlos Gustavo Méndez ◽  
Alfredo E. Huespe
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Optimization Algorithm ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Lagrangian Function ◽  
Topological Derivative ◽  
Content Type ◽  
Level Set Function ◽  
Set Function

PurposeThis work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.Design/methodology/approachThe resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic 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 obtained through the dispersion relation of the phononic crystal.FindingsThe 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 examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.Originality/valueThe original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

Adaptive topology optimization

1995 ◽  
Vol 10 (2) ◽  
pp. 100-112 ◽  
Author(s):  
K. Maute ◽  
E. Ramm
Keyword(s):  
Topology Optimization ◽  
Adaptive Topology
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