Exploiting group symmetry in truss topology optimization

We consider semidefinite programming (SDP) formulations of certain truss topol-ogy optimization problems, where a lower bound is imposed on the fundamental fre-quency of vibration of the truss structure. These SDP formulations were introduced in: [M. Ohsaki, K. Fujisawa, N. Katoh and Y. Kanno, Semi-definite programming for topology optimization of trusses under multiple eigenvalue constraints, Comp. Meth. Appl. Mech. Engng., 180: 203–217, 1999]. We show how one may automatically ob-tain symmetric designs, by eliminating the ‘redundant ’ symmetry in the SDP problem formulation. This has the advantage that the original SDP problem is substantially reduced in size for trusses with large symmetry groups