Topological classes of statically determinate beams with arbitrary number of supports

• Autorzy: Kozikowska A.

Warianty tytułu

PL

Klasy topologiczne statycznie wyznaczalnych belek o dowolnej liczbie podpór

• Języki publikacji: EN

Abstrakty

EN

The paper presents all topologies of statically determinate beams with arbitrary number of pin supports. The geometry of each beam with a fixed topology is optimized by a genetic algorithm, with absolute maximum moment as the objective function. An equality relation between minimum values of this function is defined on the set of all topologies as an equivalence relation. This relation partitions the set of topologies into equivalence classes, called topological classes, for uniform, linear and parabolic gravity loads. An in-depth description of these classes is provided. Exact formulas for optimal locations of supports and hinges are found for the uniform load.

PL

W pracy omówiono wszystkie topologie statycznie wyznaczalnych belek o dowolnej liczbie przegubowych podpór. Geometrię każdej belki o ustalonej topologii zoptymalizowano za pomocą algorytmu genetycznego z bezwzględnie maksymalnym momentem jako funkcją celu. Relację równości minimalnych wartości tej funkcji zdefiniowano na zbiorze wszystkich topologii jako relację równoważności. Na podstawie tej relacji dokonano podziału zbioru topologii na klasy równoważności, zwane klasami topologicznymi, pod równomiernym, linowym i kwadratowym grawitacyjnym obciążeniem. Przedstawiono szczegółową charakterystykę tych klas. Znaleziono ścisłe wzory na optymalne położenie podpór i przegubów belek obciążonych równomiernie.

Słowa kluczowe

EN

statically determinate beams; topology optimization; geometry optimization; equivalence classes

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2011
• Tom: Vol. 49 nr 4
• Strony: 1079--1100
• Opis fizyczny: Bibliogr. 25 poz., rys., tab.

Twórcy

autor

Kozikowska A.

• Faculty of Architecture, Bialystok University of Technology, Białystok, Poland,

Bibliografia

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