Abstract
We consider semidefinite programming (SDP) formulations of certain truss topology 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 obtain 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.
Highlights
In this paper we consider semidefinite programming (SDP) formulations of certain truss topology optimization problems
Kanno et al pointed out that, a symmetric truss design is desirable in practice, there may exist optimal solutions of the SDP formulation that do not exhibit this symmetry
In this paper we show how one may automatically obtain symmetric designs, by eliminating the ‘redundant’ symmetry in the SDP problem formulation
Summary
In this paper we consider semidefinite programming (SDP) formulations of certain truss topology optimization problems. Kanno et al pointed out that, a symmetric truss design is desirable in practice, there may exist optimal solutions of the SDP formulation that do not exhibit this symmetry. They proceed to show that certain search directions used in interior point algorithms for SDP preserve symmetry. We perform pre-processing to restrict the feasible set of the SDP problem to symmetric designs This is in the spirit of work by Schrijver [10], Gatermann and Parrilo [4], De Klerk et al [2], De Klerk, Pasechnik and Schrijver [3], and others, who have shown how ‘group symmetric’ SDP problems may be reduced in size using representation theory. Let Eij ∈ Rn×n denote the matrix with 1 in position ij and zero elsewhere
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