Topology optimisation as a tool for obtaining a multimaterial structure

• Autorzy: Kutyłowski R. , Rasiak B. , Szwechłowicz M.

Warianty tytułu

PL

Optymalizacja topologii narzędziem do uzyskania konstrukcji multimateriałowej

• Języki publikacji: EN

Abstrakty

EN

Topology optimisation problem solutions are generally presented in such a way that ultimately a material/ void (1/0) distribution is obtained in the design domain. For this purpose, filtering techniques are usually used or post-processing is applied in the optimisation process. As a rule, the result is quasi-optimal since no minimum value of the objective functional is then obtained. In this study an optimal body topology is determined. Its characteristic feature is that besides normal material and voids there is a material with poorer and varied parameters in the design domain. The latter material is often distributed in the form of a layer around the axis of each member of the construction and gets weaker with the distance from the axis. This means that the construction is multimaterial and individual layers can be distinguished in its members. In this sense, the construction is a layered one. The compliance functional is minimized under constraints imposed on the body mass, which means that the initially available mass is kept constant throughout the optimisation process. Looking for the functional stationary point one gets the following dependence: material density in a particular material point for the considered iteration is proportional to the strain energy accumulated in this point. A discretely updated Young modulus is used in the successive steps in the construction of stiffness matrices. The update for the individual material points in the successive iterations is based on the strain energy distribution in the previous step. The problem was solved numerically using FEM and identifying body material points with finite elements.

PL

Rozwiązania problemu optymalizacji topologii są najczęściej przedstawiane w ten sposób, że ostatecznie w obszarze projektowym mamy do czynienie z rozkładem typu materiał - pustka. W pracy wykazano, że rzeczywista optymalna konstrukcja to konstrukcja warstwowa składająca się z różnych materiałów, w której twardy rdzeń pręta otoczony jest coraz słabszymi warstwami. Zastosowano podejście energetyczne minimalizując funkcjonał podatności przy więzach nałożonych na masę ciała. Implementację numeryczną wykonano przy wykorzystaniu metody elementów skończonych.

Słowa kluczowe

EN

topology optimisation; layered multimaterial construction

PL

konstrukcje warstwowe; metoda elementów skończonych; konstrukcja multimateriałowa

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2011
• Tom: Vol. 11, no 2
• Strony: 391--409
• Opis fizyczny: Bibliogr. 9 poz., rys., wykr.

Twórcy

autor

Kutyłowski R.

autor

Rasiak B.

autor

Szwechłowicz M.

• Wrocław University of Technology, Wybrzeże Wyspiańskiego 25, 50-370 Wrocław, Poland

Bibliografia

• [1] Bendsoe M.P., Sigmund O.: Material interpolation schemes in topology optimisation, Archive of Applied Mechanics, Vol. 69, 1999, pp. 635-654.
• [2] Bendsoe M.P.: Optimal shape design as a material distribution problem, Struct. Optim., Vol. 1, 1989, pp. 193-202.
• [3] Glaucio H.P., Silva E.C.N., Chau H. Le.: Optimal design of periodic functionally gradem composites with prescribed properties, Struct. Multidisc. Optim., Vol. 38, 2009, pp. 469-489.
• [4] Kieback B., Neubrand A., Riedel J.: Processing techniques for functionally graded materials, Mater. Sci. Eng., A362, 2003, pp. 81-105.
• [5] Kutyłowski R., Rasiak B.: Influence of various design parameters on the quality of optima shape design in topology optimisation analysis, Proceedings in Applied Mathematics and Mechanics, Vol. 8, 2008, pp. 10797-10798.
• [6] Kutyłowski R., Szwechłowicz M.: Analyse des Penalty-Faktors in SIMP-Methode in Bezug auf die Konvergenz der Lösung (The power law factor analysis in SIMP method from the convergence point of view), Proceedings in Applied Mathematics and Mechanics, Vol. 8, 2008, pp.10803-10804.
• [7] Miyamoto Y., Kaysser W.A., Rabin B.H., Kawasaki A., Ford R.G.: Functionally gradem materials: design, processing and applications, Kluwer Academic, Dordrecht, 1999.
• [8] Ramm E., Bletzinger K.-U., Reitinger R., Maute K.: The challenge of structural optimisation, in: Topping B.H.V., Papadrakakis M. (ed) Advanced in Structural Optimisation, Int. Conf. on Computational Structures Technology held in Athen, 1994, pp. 27-52.
• [9] Suresh S., Mortensen A.: Fundamentals of functionally graded materials, Institute of Materiale (IOM) Communications, Serie 698, London 1988.