# Topology optimization approaches

@article{Sigmund2013TopologyOA, title={Topology optimization approaches}, author={Ole Sigmund and Kurt Maute}, journal={Structural and Multidisciplinary Optimization}, year={2013}, volume={48}, pages={1031-1055} }

Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsøe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future… Expand

#### 1,257 Citations

A direct approach to controlling the topology in structural optimization

- Computer Science
- 2020

A new approach is developed based on the graph theory and the set theory to control the number and size of interior holes of the optimization structures to enable the designer to have a direct control over the topology of the optimized structures. Expand

A Novel Heuristic Generator of Structural Topologies Based on Sorted Compliances

- Engineering
- 2017

Topology optimization, although well recognized and widely developed, remains still up-to-date challenge. It has gained recently more attention since large computational ability become available for… Expand

Topology and shape optimization methods using evolutionary algorithms: a review

- Mathematics
- 2015

Topology optimization has evolved rapidly since the late 1980s. The optimization of the geometry and topology of structures has a great impact on its performance, and the last two decades have seen… Expand

A Bi-directional Evolutionary Structural Optimisation algorithm with an added connectivity constraint

- Mathematics
- 2017

Abstract This paper proposes the introduction of a connectivity constraint in the Bi-directional Evolutionary Structural Optimisation (BESO) method, which avoids the possibility of arriving at highly… Expand

Progress on different topology optimization approaches and optimization for additive manufacturing: a review

- Physics
- 2021

The progress of topology optimizations for the last decade has been reviewed based on the five main methods mentioned in Sigmund’s article in 2013: density, level-set, topological derivative, phase… Expand

Topology optimization of multi-scale structures: a review

- 2021

Multi-scale structures, as found in nature (e.g., bone and bamboo), hold the promise of achieving superior performance while being intrinsically lightweight, robust, and multi-functional. Recent… Expand

Evolutionary computation for topology optimization of mechanical structures: An overview of representations

- Mathematics, Computer Science
- 2016 IEEE Congress on Evolutionary Computation (CEC)
- 2016

A contemporary overview on the various structural representations used in conjunction with evolutionary computation for topology optimization is provided and the important influence of the representation on the scalability of the approaches motivates the proposed classification in three groups: Grid, Geometric and Indirect Representations. Expand

An explicit length scale control approach in SIMP-based topology optimization

- Engineering
- 2014

Abstract The present paper aims to present a new approach for controlling both maximum and minimum length scales of structural members in the Solid Isotropic Material with Penalization (SIMP)-based… Expand

GHOST—Gate to Hybrid Optimization of Structural Topologies

- Materials Science, Medicine
- Materials
- 2019

It has been confirmed that the proposed hybrid technique based on switching between the considered rules allows the final structures having lower values of compliance as compared with the results of an application of basic algorithms running separately to be obtained. Expand

A short numerical study on the optimization methods influence on topology optimization

- 2017

Structural topology optimization problems are commonly defined using continuous design variables combined with material interpolation schemes. One of the challenges for density based topology… Expand

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