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Concurrent topology and sizing optimisation for multifunctional structural design
KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Lättkonstruktioner, marina system, flyg- och rymdteknik, rörelsemekanik.
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The need for resource efficient transport is increasing as environmental concerns are growing ever more important. One of the most important vehicle properties when it comes to fuel consumption is the mass of the vehicle, with heavier vehicles requiring more energy and therefore more fuel to operate. A key strategy when designing more efficient vehicles for transport is thus to make the vehicles as light as possible.

During operation, different vehicles are have to fulfill a number of different requirements, such as protecting passengers and cargo from the elements, being safe in case of an accident and maintaining a comfortable sound level for the passengers. These requirements are often conflicting, especially in a lightweight context. It is well known that stiff and lightweight structures tend to vibrate more when exposed to dynamic loads, severely degrading the acoustic performance.

The aim of this doctoral thesis is to investigate design methodologies that can be used to design lightweight components with good structural and acoustic properties at an early stage of the design process, where the design freedom is large. Key is the fact that response to both static and dynamic loading is taken into account simultaneously instead of sequentially, this is to prevent the emergence of design solutions with very good structural performance, but whose poor dynamic behaviour requires mass-intensive sub-systems to be added at a later stage.

The investigated methodology is based on using topology optimization to minimize the mass of a structure subject to constraints on the response to static and dynamic loads. An initial study extends the use Topology Optimization of Binary Structures (TOBS) method to problems with vibration constraints. The TOBS method is later extended to allow for the concurrent optimization of the core topology and face sheet thickness of a sandwich structure. This new sandwich optimization method is then used to minimize the mass of a sandwich beam subjected to a static load. 

Finally, the concurrent sandwich optimization is used to minimize the mass of a sandwich beam subjected to simultaneous static and harmonic loads, at both single frequencies and in frequency bands.

The results show that the new concurrent sandwich optimization method offer significant improvements over optimizing the core topology with fixed face sheet thickness, resulting in a mass reduction of up to 22\%. The mass of the resulting structure is also shown to be very dependent on how strict the static constraint is, especially when compared to how sensitive it is to the dynamic constraint at single frequencies. For dynamic constraint imposed over frequency bands, the cost of lowering the response depends on the frequency band. If the band contains the fundamental resonance frequency, the mass is very sensitive to how strict the constraint is.

The multifunctional design methodology presented in this doctoral thesis offers design tools which can be used to design lightweight vehicle components early in the design process without locking the design into solutions that require the addition of heavy sub-systems later in the design process.

Abstract [sv]

Behovet av resurseffektiv transport ökar allt eftersom miljöfrågor blir allt viktigare. En av de viktigaste fordonsegenskaperna när det kommer till bränsleförbrukning är fordonets massa, där tyngre fordon kräver mer energi och därför mer bränsle för att använda. En nyckelstrategi vid design av mer effektiva transportfordon är således att göra fordonen så lätta som möjligt.

Fordon måste vid användning uppfylla en mängd olika krav, till exempel att skydda passagerare och last från väder och vind, vara säkra vid en olycka och hålla en bekväm ljudnivå för passagerarna. Dessa krav står ofta i konflikt med varandra, särskilt i en lättviktskontext. Det är välkänt att styva och lätta strukturer tenderar att vibrera mer när de utsätts för dynamisk last, vilket kraftigt försämrar den akustiska prestandan.

Målet med denna avhandling är att undersöka designmetodologier som kan användas för att designa lättviktskomponenter med goda strukturella och akustiska egenskaper i ett tidigt skede av designprocessen, när friheten att göra designförändringar är stor. Stor vikt läggs vid att hänsyn tas till statisk och dynamisk last samtidigt istället för sekventiellt, vilket förhindrar uppkomsten av designlösningar med god strukturell prestanda, men vars försämrade akustiska egenskaper kräver massintensiv efterbehandling i ett senare skede av designprocessen.

Den undersökta designmetodologin baseras på att använda topologioptimering för att minimera en strukturs massa, med bivillkor som begränsar responsen på statisk och dynamisk last. En första studie utökar optimeringsmetoden topologioptimering för binära strukturer (topology optimization of binary structures, TOBS) till problem med vibrationsbivillkor. TOBS-metoden utökas sedan till att tillåta samtidig optimering av kärntopologin och täckskiktstjockleken hos en sandwichstruktur. Den nya sandwichoptimeringsmetoden används sedan för att minimera massan hos en sandwichbalk utsatt för statisk last.

Den samtidiga sandwichoptimeringen används slutligen för att minimera massan hos en sandwichbalk utsatt för samtidig statisk och dynamisk last, både för enskilda frekvenser och i frekvensband.

Resultaten visar att den nya metoden erbjuder signifikanta förbättringar jämfört med att bara optimera kärntopologin med fixerad täckskiktstjocklek, med minskning av massan med upp till 22%. Den slutliga strukturens massa visar sig också vara väldigt beroende av hur strängt det statiska bivillkoret är, speciellt vid jämförelse med det dynamiska bivillkoret vid enskilda frekvenser. Om den dynamiska excitationen sker över ett frekvensband, så är kostnaden för att sänka responsen beroende av frekvensbandet. Om frekvensbandet täcker den fundamentala resonansfrekvensen så är massan särskilt känslig för hur stringent bivillkoret är.

Den multifunktionella designmetodologin som presenteras i denna doktorsavhandling erbjuder designverktyg som kan användas till att designa fordonskomponenter med låg vikt tidigt i designprocessen utan att låsa fast designen i lösningar som kräver tung efterbehandling senare i designprocessen.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2024. , p. 189
Series
TRITA-SCI-FOU ; 2024:22
National Category
Vehicle Engineering
Identifiers
URN: urn:nbn:se:kth:diva-346041ISBN: 978-91-8040-915-5 (print)OAI: oai:DiVA.org:kth-346041DiVA, id: diva2:1855424
Public defence
2024-05-23, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2024-05-02 Created: 2024-04-30 Last updated: 2024-05-15Bibliographically approved
List of papers
1. Mass minimization with conflicting dynamic constraints by topology optimization using sequential integer programming
Open this publication in new window or tab >>Mass minimization with conflicting dynamic constraints by topology optimization using sequential integer programming
2022 (English)In: Finite elements in analysis and design (Print), ISSN 0168-874X, E-ISSN 1872-6925, Vol. 200, p. 103683-, article id 103683Article in journal (Refereed) Published
Abstract [en]

In this paper mass minimization of hysteretically damped structures subjected to static and time-harmonic loading is studied via the Topology Optimization of Binary Structures (TOBS) method. Elements are removed or added to the finite element model of a structure in every iteration based on the solution to an integer linear program (ILP). The ILP is constructed from the sensitivity information of the objective function and the constraints which are in the form of the static and dynamic compliance. The proposed methodology is demonstrated on a 2D clamped-clamped beam and compared with published results for a 2D cantilever beam. The optimization starts from the full design domain and solutions with low mass that fulfill the constraints for a range of different bounds are found. The results also indicate that the mass is much more sensitive to changes in the static compliance constraint than in the dynamic compliance constraint. The effect of mass and upper bound of the constraints on the dynamic compliance at the fundamental resonance frequency is also studied, though no clear conclusions can be drawn. Finally the sensitivity information at the converged topology is studied and it is shown that the algorithm converges because the structural regions that are non-critical for the different constraints do not overlap.

Place, publisher, year, edition, pages
Elsevier BV, 2022
Keywords
Topology optimization, Dynamics, TOBS, Multifunctional structures, Integer programming
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-308558 (URN)10.1016/j.finel.2021.103683 (DOI)000744028600004 ()2-s2.0-85120504134 (Scopus ID)
Funder
Vinnova
Note

QC 20220315

Available from: 2022-02-16 Created: 2022-02-16 Last updated: 2024-04-30Bibliographically approved
2. A sequential mixed-integer programming method for concurrent optimization of core topology and face sheet thickness of a sandwich beam
Open this publication in new window or tab >>A sequential mixed-integer programming method for concurrent optimization of core topology and face sheet thickness of a sandwich beam
2023 (English)In: Journal of Sandwich Structures and Materials, ISSN 1099-6362, E-ISSN 1530-7972, Vol. 25, no 6, p. 666-686Article in journal (Refereed) Published
Abstract [en]

A method is proposed that allows for the concurrent optimization of core topology and face sheet thickness of a sandwich beam under compliance constraints. The problem is solved using a novel mixed-linear extension of the Topology Optimization of Binary Structure (TOBS) topology optimization method aiming to minimize the total mass of the beam. The method has been demonstrated on a clamped beam example and the results have been compared to results from topology optimization of the core with a range of a priori fixed face sheet thicknesses. It is shown that the new method, starting from a fully populated core, finds a minimum mass that is lower than but in the neighbourhood of the best results from the topology optimization with fixed face sheet thicknesses. By varying the compliance constraint it is shown that the core topology approaches an ideal corrugated geometry as the compliance constraint is relaxed. The trends observed in the results are compared to analytical models for an idealized core.

Place, publisher, year, edition, pages
SAGE Publications, 2023
Keywords
concurrent optimization, mass minimization, mixed-integer linear programming, sandwich structures, Topology optimization
National Category
Computational Mathematics Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-338569 (URN)10.1177/10996362231174901 (DOI)000986386300001 ()2-s2.0-85161710719 (Scopus ID)
Note

QC 20231107

Available from: 2023-11-07 Created: 2023-11-07 Last updated: 2024-04-30Bibliographically approved
3. A topology and sizing optimisation method for lightweight sandwich structures subject to dynamic and static constraints
Open this publication in new window or tab >>A topology and sizing optimisation method for lightweight sandwich structures subject to dynamic and static constraints
(English)Manuscript (preprint) (Other academic)
Abstract [en]

A static-dynamic topology-sizing optimisation method is presented. Thesolution is based on a sequential Mixed-Integer Linear Programming solutionand aims to minimise the mass of a structure subjected to concurrentconstraints on static and dynamic response. It is shown that the classicalproblem of the dynamics of lightweight sandwich structures may be mitigatedthrough core topology and face sheet thickness combinations, retaining thestatic load carrying capacity while presenting stringent dynamic propertiesat a low mass penalty.A numerical example, in the form of a load carrying sandwich beam whichis excited at different frequencies, is used to demonstrate the method.

National Category
Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-346038 (URN)
Note

QC 20240514

Available from: 2024-04-30 Created: 2024-04-30 Last updated: 2024-05-14Bibliographically approved
4. Concurrent sizing and topology optimization of lightweight sandwich structures with load bearing and wide-band frequency response constraints
Open this publication in new window or tab >>Concurrent sizing and topology optimization of lightweight sandwich structures with load bearing and wide-band frequency response constraints
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The design of lightweight sandwich structures with constraints the response to static and dynamic loads is investigated. A concurrent optimization of the face sheet thickness and core topology is used to minimize the structural mass of a sandwich beam with constraints on both the static load bearing properties and the average response to a time-harmonic load over a frequency band. The results show that the mass of the resulting structure is very dependent on how tight the dynamic constrain is if the frequency band covers the fundamental resonance frequency of the structure. If the frequency band of excitation covers the second resonance frequency or is between two resonance frequencies, lowering the dynamic response is much cheaper in terms of mass.

National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-346039 (URN)
Note

QC 20240514

Available from: 2024-04-30 Created: 2024-04-30 Last updated: 2024-05-14Bibliographically approved

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