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Exploiting group symmetry in truss topology optimization. (English) Zbl 1400.90242
Summary: We consider semidefinite programming (SDP) formulations of certain truss topology optimization problems, where a lower bound is imposed on the fundamental frequency of vibration of the truss structure. These SDP formulations were introduced in [M. Ohsaki et al., Comput. Methods Appl. Mech. Eng. 180, No. 1-2, 203–217 (1999; Zbl 0943.90060)]. 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.

MSC:
90C22 Semidefinite programming
74D10 Nonlinear constitutive equations for materials with memory
90C90 Applications of mathematical programming
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