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CATEGORIES:Optimisation and Numerical Analysis Seminars
SUMMARY:Topology optimization of discrete structures by se
midefinite programming - Marek Tyburec (Czech Tech
nical University\, Prague)
DTSTART:20191016T110000Z
DTEND:20191016T120000Z
UID:TALK3891AT
URL:/talk/index/3891
DESCRIPTION:This contribution investigates applications of sem
idefinite programming (SDP) techniques to two prob
lems of structural topology optimization. We consi
der first the problem of designing optimum truss r
einforcement of a thin-walled composite laminate t
o withstand manufacturing and operational loads an
d to suppress elastic wall instabilities. For this
problem\, the instabilities can be described usin
g free-vibration eigenmodes\, allowing thus for a
convex SDP representation. To accelerate the solut
ion of these types of problems\, we utilize the st
atic condensation/(generalized) Schur complement l
emma\, which additionally provides us with an uppe
r bound on the maximum admissible fundamental eige
nfrequency\, and a lower bound on the minimum admi
ssible compliance of the manufacturing load case.
Finally\, we manufacture the composite beam protot
ype with a 3D-printed internal structure\, perform
experimental validation\, and conclude that the s
tructural response agrees well with the model pred
ictions. As the second problem\, we consider the t
opology optimization of frame structures. In this
case\, the SDP formulation is no longer convex in
general. However\, because the SDP constraints are
polynomial matrix inequalities\, we adopt the mom
ent-sums-of-squares hierarchy for their solution.
It turns out that each relaxation of this hierarch
y generates both lower and upper bounds on the opt
imal design\, which provides us not only with a me
asure of the solution quality but also an inexpens
ive sufficient condition of global optimality. For
all the tested problems\, finite convergence was
observed.\n
LOCATION:Strathcona\, SR5
CONTACT:Sergey Sergeev
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