A symmetry reduction method for continuum structural topology optimization

It is considered that asymmetrical material layout design solutions are caused by numerical roundo€ and the convexity characteristics of alternative topology design formulations. Emphasis is placed here not on analyzing potential instabilities that lead to asymmetrical designs, but on a method to stabilize topology design formulations. A novel symmetry reduction method is proposed, implemented and studied. While enforcing symmetry and signi®cantly reducing the size of the optimization problem, the symmetry reduction method is shown to have the added bene®t of greatly simpli®ed design sensitivity analysis of non-simple repeated vibrational eigenvalues which occur in many symmetrical structures. # 1998 Elsevier Science Ltd. All rights reserved.