Application of topology optimisation in the strut-and-tie method: a review

• Autorzy: Dudziak Sławomir

Identyfikatory

DOI

10.24425/ace.2025.154122

Warianty tytułu

PL

Zastosowanie optymalizacji topologicznej w metodzie strut-and-tie – przegląd literatury

• Języki publikacji: EN

Abstrakty

EN

The paper delivers an overview of the literature concerning the adaption of Topology Optimisation (TO) to the Strut-and-Tie Method (STM). In the beginning, the foundations and basics of STM are briefly summarised. STM is a practical implementation of the lower bound theory of plasticity for reinforced concrete (RC). It is generally used to design so-called D-regions (i.e. Discontinuity caused by irregular geometry or concentrated load) working under the complex stress state. These regions are modelled with the equivalent truss consisting of struts (representing the flow of compressive forces carried by concrete), ties (representing rebar) and nodes. The STM algorithm’s most demanding part is determining the layout of the truss, which correctly reflects force flow in a specific D-region. During this stage, TO methods can eliminate the designer’s arbitrary decisions. Analysed literature sources are divided into two groups differing in the adopted TO algorithms: the former uses layout optimisation procedures for trusses, whereas the latter uses TO methods for continuum domains. In the first approach, the equivalent truss is obtained explicitly as an outcome of the TO phase. In the second approach, the material continuum material layout is an inspiration for the ST model or is post-processed with image analysis methods and possibly shape optimisation methods to obtain bending-free bar structures. The advantages and limitations of both approaches are put forward in the conclusion section. Further development in this field is very likely, so future prospects are also anticipated.

PL

W artykule przedstawiono przegląd literaturowy dotyczący zastosowania optymalizacji topologicznej (TO) do metody Strut-and-Tie (STM). Na początku krótko przedstawiono podstawy teoretyczne i algorytm tej metody. STM jest inżynierską implementacją twierdzenia o dolnym oszacowaniu nośności plastycznej do projektowania konstrukcji żelbetowych. Warto podkreślić, że twierdzenie to zostało sformułowane dla materiałów sprężysto-idealnie plastycznych, a beton wykazuje ograniczoną zdolność do plastycznej redystrybucji naprężeń, więc właściwe oszacowanie nośności konstrukcji wymaga spełnienia dodatkowych warunków sformułowanych głównie w oparciu o wyniki badań eksperymentalnych. W ogólności STM jest stosowana do projektowania tzw. obszarów D (ang. Discontinuity – nieciągłość spowodowana zmianą geometrii lub obciążeniem skupionym) pracujących w złożonym stanie naprężenia. Obszary te modelowane są jako zastępcza kratownica składająca się z: zastrzałów (ang. Struts, odwzorowujących przepływ sił ściskających przenoszonych przez beton), cięgien (ang. Ties, reprezentujących zbrojenie) i węzłów. Największym wyzwaniem dla użytkownika STM jest dobór schematu kratownicy, który najlepiej odzwierciedla przepływ sił w konkretnym obszarze D. Podczas tego etapu metody TO mogą wyeliminować arbitralną decyzję projektanta. Analizowane źródła literaturowe zostały podzielone na dwie grupy różniące się stosowanym podejściem do optymalizacji topologicznej. W pierwszej stosowano procedury optymalizacji dyskretnego układu kratowego, a w drugim metody optymalizacji opracowane dla continuum. W pierwszym podejściu kratownica zastępcza otrzymywana jest bezpośrednio w procesie optymalizacji topologii kratownicy metodą siatki bazowej. Natomiast w drugim wynik optymalizacji dla obszaru ciągłego stanowi inspirację do doboru kształtu kratownicy lub jest poddawany post-processingowi metodami obróbki obrazu i ewentualnie optymalizacji kształtu w celu uzyskania prętowych układów wolnych od zginania, Zalety i ograniczenia obu podejść podsumowane są we wnioskach. Podjęto również próbę przewidzenia kierunków dalszego rozwoju tego podejścia do STM.

• Wydawca: Komitet Inżynierii Lądowej i Wodnej PAN ; Politechnika Warszawska, Wydział Inżynierii Lądowej
• Czasopismo: Archives of Civil Engineering
• Rocznik: 2025
• Tom: Vol. 71, nr 2
• Strony: 295--311
• Opis fizyczny: Bibliogr. 56 poz., il.

Twórcy

autor

Dudziak Sławomir

• Warsaw University of Technology, Faculty of Civil Engineering, Warsaw, Poland

• https://orcid.org/0000-0001-6287-2005

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