Sofonea, Mircea - ed. ; Viano, Juan M. - ed.
Mathematical Modelling and Numerical Analysis in Solid Mechanics
The subject of topology optimization has undergone an enormous practical development since the appearance of the paper by Bends?e and Kikuchi (1988), where some ideas from homogenization theory were put into practice. Since then, several engineering applications as well as different approaches have been developed successfully. ; However, it is difficult to find in the literature some analytical examples that might be used as a test in order to assess the validity of the solutions obtained with different algorithms. As a matter of fact, one is often faced with numerical instabilities requiring a fine tuning of the algorithm for each specific case. ; In this work, we develop a family of analytical solutions for very simple topology optimization problems, in the framework of elasticity theory, including bending and extension of rods, torsion problems as well as plane stress and plane strain elasticity problems. All of these problems are formulated in a simplified theoretical framework. ; A key issue in this type of problems is to be able to evaluate the sensitivity of the homogenized elastic coefficients with respect to the microstructure parameter(s). Since we are looking for analytical solutions, we use laminates for which an explicit dependence of the homogenized coefficients on the microstructure is known.
Zielona Góra: Uniwersytet Zielonogórski
AMCS, volume 12, number 1 (2002) ; click here to follow the link
Biblioteka Uniwersytetu Zielonogórskiego
Sep 1, 2021
Sep 1, 2021
43
https://zbc.uz.zgora.pl/publication/65715
Edition name | Date |
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Analysis of optimality conditions for some topology optimization problems in elasticity | Sep 1, 2021 |
Myśliński, Andrzej Korbicz, Józef - red. Uciński, Dariusz - red.
Anita, Sebastian Arino, Ovide - ed.
Świerniak, Andrzej (1950- ) Ledzewicz, Urszula Schättler, Heinz Kimmel, Marek - red. Lachowicz, Mirosław - red. Świerniak, Andrzej - red.
Guria, M. Jana, R.N. Jurczak, Paweł - red.
Tomar, S.K. Goyal, N. Szekeres, A. Jurczak, Paweł - red.
Javidinejad, Amir Jurczak, Paweł - red.
Petureau, Louis Doumalin, P. Bremand, Fabrice Jurczak, Paweł - red.
Singh, R. Kumar, Varun Jurczak, Paweł - red.