A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects

Abstract

Topology Optimization (TO) is a powerful numerical technique to determine the optimal material layout in a design domain, which has accepted considerable developments in recent years. The classic Finite Element Method (FEM) is applied to compute the unknown structural responses in TO. However, several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO. In order to eliminate the negative influence of the FEM on TO, IsoGeometric Analysis (IGA) has become a promising alternative due to its unique feature that the Computer-Aided Design (CAD) model and Computer-Aided Engineering (CAE) model can be unified into a same mathematical model. In the paper, the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization (ITO) in methods and applications. Finally, some prospects for the developments of ITO in the future are also presented.

Topology Optimization with Aperiodic Load Fatigue Constraints Based on Bidirectional Evolutionary Structural Optimization

“…(3) If D (0) < 1, fatigue failure will not occur, so S (0) is increases and, vice versa, S (0) decreases; (4) S (0) takes a series of values S (1) , S (2) , . .…”

“…. , S (m) , the stress amplitudes change sequentially, and the corresponding damage D (1) , D (2) , . .…”

“…The field of topology optimization mainly focuses on minimizing structural compliance [1][2][3] to increase structural stiffness. At present, there are roughly three ways to solve topology optimization with fatigue constraints.…”

Evaluation of the Suitability of Draw Hook Used in Rail Systems for Topology Optimization

“…Bu alandaki çalışmalar yoğun bir şekilde devam etmekte ve bu yöntemlerin çoğunda yeni gelişmeler meydana gelmektedir. Bu yöntemler arasında en önde gelen ikisi evrimsel yapısal optimizasyondan türetilmiş olan çift yönlü evrimsel yapısal optimizasyon (Bi-directional Evolutionary Structural Optimization (BESO)) ve yoğunluk tabanlı yöntemden türetilmiş olan cezalandırmalı katı izotropik malzemedir (Solid Isotropic Material with Penalization (SIMP)) [29]. Simp metodu sonlu elemanlar tabanlı kullanıma en uygun yöntem olarak öne çıkmış ve pek çok sonlu elemanlar yazılımına entegre edilmiştir.…”

Bézier extraction based isogeometric approach to multi‐objective topology optimization of periodic microstructures

“…The other applications of the IGA related to the displacement, 26 eigenfrequencies, 27 and structural stress 43 were also integrated into TO making use of the NURBS‐based material interpolation model. Gao et al provided a comprehensive discussion about the isogeometric TO in methods and applications 44 . The main directions for the development of the isogeometric TO were discussed in detail.…”