Global optimality in minimum compliance topology optimization of frames and shells by moment-sum-of-squares hierarchy

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F21%3A00351153" target="_blank" >RIV/68407700:21110/21:00351153 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21230/21:00351153

Result on the web

<a href="https://doi.org/10.1007/s00158-021-02957-5" target="_blank" >https://doi.org/10.1007/s00158-021-02957-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00158-021-02957-5" target="_blank" >10.1007/s00158-021-02957-5</a>

Result language

angličtina

Original language name

Global optimality in minimum compliance topology optimization of frames and shells by moment-sum-of-squares hierarchy

Original language description

The design of minimum-compliance bending-resistant structures with continuous cross-section parameters is a challenging task because of its inherent non-convexity. Our contribution develops a strategy that facilitates computing all guaranteed globally optimal solutions for frame and shell structures under multiple-load cases and self-weight. To this purpose, we exploit the fact that the stiffness matrix is usually a polynomial function of design variables, allowing us to build an equivalent non-linear semidefinite programming formulation over a semi-algebraic feasible set. This formulation is subsequently solved using the Lasserre moment-sum-of-squares hierarchy, generating a sequence of outer convex approximations that monotonically converges from below to the optimum of the original problem. Globally optimal solutions can subsequently be extracted using the Curto-Fialkow flat extension theorem. Furthermore, we show that a simple correction to the solutions of the relaxed problems establishes a feasible upper bound, thereby deriving a simple sufficient condition of global ε-optimality. When the original problem possesses a unique minimum, we show that this solution is found with a zero optimality gap in the limit. These theoretical findings are illustrated on several examples of topology optimization of frames and shells, for which we observe that the hierarchy converges in a finite (rather small) number of steps.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/GX19-26143X" target="_blank" >GX19-26143X: Non-periodic pattern-forming metamaterials: Modular design and fabrication</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Structural and Multidisciplinary Optimization

ISSN

1615-147X

e-ISSN

1615-1488

Volume of the periodical

64

Issue of the periodical within the volume

4

Country of publishing house

DE - GERMANY

Number of pages

19

Pages from-to

1963-1981

UT code for WoS article

000664407300001

EID of the result in the Scopus database

2-s2.0-85108620101