Application of Topological Derivative to the Optimal Design of Three-Dimensional Structural Arrangements of Flat Plates
DOI:
https://doi.org/10.70567/mc.v41i16.85Palavras-chave:
Folded structures, Structural optimization, Topological optimizationResumo
This work addresses the problem of optimal topological design of three-dimensional structures composed of plate arrays based on the use of topological derivatives. These structural arrays consist of planar elements linked at their edges. Their modeling is performed by coupling a membrane model and a bending-plate model. The geometric and material representation is accomplished using level-set curves. To minimize a cost function, the topological derivative value is used to guide the evolution of the level-set curve. A theoretical framework and case studies of academic and industrial applications are presented.
Referências
Amstutz S. A penalty method for topology optimization subject to a pointwise state constraint. ESAIM: Control, Optimisation and Calculus of Variations, 16(3):523-544, 2010. https://doi.org/10.1051/cocv/2009013
Amstutz S. and Andrä H. A new algorithm for topology optimization using a level-set method. Journal of Computational Physics, 216(2):573-588, 2006. https://doi.org/10.1016/j.jcp.2005.12.015
Batoz J.L. An explicit formulation for an efficient triangular plate-bending element. International Journal for Numerical Methods in Engineering, 18:1077-1089, 1982. https://doi.org/10.1002/nme.1620180711
Campeão D., Giusti S., and Novotny A. Topology design of plates considering different volume control methods. Engineering Computations, 31(5):826-842, 2014. https://doi.org/10.1108/EC-10-2012-0244
Carvalho F., Ruscheinsky D., Anflor C., Giusti S., and Novotny A. Topological derivative-based topology optimization of plate structures under bending effects. Structural and Multidisciplinary Optimization, 63:617-630, 2021. https://doi.org/10.1007/s00158-020-02710-4
Felippa C. A study of optimal membrane triangles with drilling freedoms. Computer Methods in Applied Mechanics and Engineering, 192(16-18):2125-2168, 2003. https://doi.org/10.1016/S0045-7825(03)00253-6
Felippa C. and Militello C. Membrane triangles with corner drilling freedoms-ii. the andes element. Finite Elements In Analysis and Design, 12(3-4):189-201, 1992. https://doi.org/10.1016/0168-874X(92)90034-A
Novotny A. and Sokolowski J. Topological derivatives in shape optimization. Interaction of Mechanics and Mathematics. Springer-Verlag, Berlin, Heidelberg, 2013. https://doi.org/10.1007/978-3-642-35245-4
Romero A. Optimum design of two-material bending plate compliant devices. Engineering Computations, 39(1):395-420, 2022. https://doi.org/10.1108/EC-07-2021-0400
Romero A.A. and Giusti S.M. A robust topological derivative-based multi-material optimization approach: Optimality condition and computational algorithm. Computer Methods in Applied Mechanics and Engineering, 366:113044, 2020. https://doi.org/10.1016/j.cma.2020.113044
Sales V., Novotny A., and Rivera J.M. Energy change to insertion of inclusions associated with the Reissner-Mindlin plate bending model. International Journal of Solids and Structures, 59:132-139, 2015. https://doi.org/10.1016/j.ijsolstr.2015.01.019
Sokolowski J. and Zolésio J.P. Introduction to shape optimization - shape sensitivity analysis. Springer-Verlag, Berlin, Germany, 1992.
Zochowski A. Optimal perforation design in 2-dimensional elasticity. Mechanics of Structures and Machines, 16(1):17-33, 1988. https://doi.org/10.1080/08905458808960251
Downloads
Publicado
Edição
Seção
Licença
Copyright (c) 2024 Argentine Association for Computational Mechanics
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
Esta publicação é de acesso aberto diamante, sem custos para autores ou leitores.
Somente os artigos que foram aceitos para publicação e apresentados no congresso da AMCA serão publicados.
