Discussion on symmetry of optimum topology design

Authors:
Gengdong Cheng;Xiaofeng Liu
Affiliations:
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, China;State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, China
Venue:
Structural and Multidisciplinary Optimization
Year:
2011

Citing 1
Cited 3

On symmetry and non-uniqueness in exact topology optimization

Structural and Multidisciplinary Optimization

Author's reply to a discussion by Gengdong Cheng and Xiaofeng Liu of the review article "On symmetry and non-uniqueness in exact topology optimization" by George I. N. Rozvany (2011, Struct Multidisc Optim 43: 297---317)

Structural and Multidisciplinary Optimization
Symmetry and asymmetry of solutions in discrete variable structural optimization

Structural and Multidisciplinary Optimization
Symmetry properties in structural optimization: some extensions

Structural and Multidisciplinary Optimization

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Abstract

Recent study by Rozvany discussed an important topic in structural topology optimization: non-uniqueness and symmetry. This paper demonstrates that for the frame topology optimization with frequency objective or frequency constraints, the topology optimum is not symmetric even when the geometry, material distribution and ground structure are symmetric. Two benchmark examples with fundamental frequency constraints support our view. Nonlinear and non-convex constraints are contributors to non-symmetric optimum solution for the class of topology optimization problems considered here.