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Steel and Composite Structures Volume 41, Number 3, November10 2021 , pages 385-402 DOI: https://doi.org/10.12989/scs.2021.41.3.385 |
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Multiple bi-directional FGMs topology optimization approach with a preconditioned conjugate gradient multigrid |
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Thanh T. Banh, Nam G. Luu, Qui X. Lieu, Jaehong Lee, Joowon Kang and Dongkyu Lee
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| Abstract | ||
| This article aims to introduce a multigrid preconditioned conjugate gradient (MPCG)-oriented topology optimization (TO) methodology using multiple bi-directional functionally graded (BFG) models for the first time. For that purpose, the MPCG paradigm is integrated into the TO procedure to more effectively and quickly resolve linear algebraic systems arising from the differential equations' discretization. In addition, a refined BFG material interpolation in Solid Isotropic Material with Penalization (SIMP), which is based on an alternating active-phase algorithm, is produced. In which continuously altered macroscopic material properties are represented by an explicit exponential function. This paper describes the well-founded mathematical formulations for multi-material topology optimization of BFG structures in great detail. Finally, several numerical examples are tested to demonstrate the proposed approach's capability and efficiency. | ||
| Key Words | ||
| bi-directional functionally graded materials (BFGMs); multigrid preconditioned conjugate gradient (MPCG); multiple materials; topology optimization | ||
| Address | ||
| Thanh T. Banh, Nam G, Jaehong Lee and Dongkyu Lee: Department of Architectural Engineering, Sejong University, Seoul 05006, Republic of Korea Qui X. Lieu: Faculty of Civil Engineering, Ho Chi Minh City University of Technology, (HCMUT) 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Viet Nam; Vietnam National University Ho Chi Minh City (VNU-HCM), Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Viet Nam Joowon Kang: Department of Architecture, Yeungnam University, Gyeongsan 38541, Korea | ||